Chapter_3/Exerciese - Applied Questions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter - 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from scipy import stats\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. This question involves the use of simple linear regression on the Auto  data set.\n",
    "### (a) Use the lm() function to perform a simple linear regression with  mpg as the response and horsepower as the predictor. Use the  summary() function to print the results.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(397, 9)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>chevrolet chevelle malibu</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>buick skylark 320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>plymouth satellite</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>amc rebel sst</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>ford torino</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement horsepower  weight  acceleration  year  \\\n",
       "0  18.0          8         307.0        130    3504          12.0    70   \n",
       "1  15.0          8         350.0        165    3693          11.5    70   \n",
       "2  18.0          8         318.0        150    3436          11.0    70   \n",
       "3  16.0          8         304.0        150    3433          12.0    70   \n",
       "4  17.0          8         302.0        140    3449          10.5    70   \n",
       "\n",
       "   origin                       name  \n",
       "0       1  chevrolet chevelle malibu  \n",
       "1       1          buick skylark 320  \n",
       "2       1         plymouth satellite  \n",
       "3       1              amc rebel sst  \n",
       "4       1                ford torino  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto = pd.read_csv(r'E:\\programming\\dataset\\Into_to_statstical_learning\\Auto.csv')\n",
    "print(auto.shape)\n",
    "auto.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpg             float64\n",
       "cylinders         int64\n",
       "displacement    float64\n",
       "horsepower       object\n",
       "weight            int64\n",
       "acceleration    float64\n",
       "year              int64\n",
       "origin            int64\n",
       "name             object\n",
       "dtype: object"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#horsepower is of type object, it needs to be int or float to be able to fit for regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "auto['horsepower'] = auto['horsepower'].replace('?',np.nan)\n",
    "auto.dropna(inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "auto['horsepower'] = auto['horsepower'].astype('float')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpg             float64\n",
       "cylinders         int64\n",
       "displacement    float64\n",
       "horsepower      float64\n",
       "weight            int64\n",
       "acceleration    float64\n",
       "year              int64\n",
       "origin            int64\n",
       "name             object\n",
       "dtype: object"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    mpg   R-squared:                       0.606\n",
      "Model:                            OLS   Adj. R-squared:                  0.605\n",
      "Method:                 Least Squares   F-statistic:                     599.7\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           7.03e-81\n",
      "Time:                        10:40:40   Log-Likelihood:                -1178.7\n",
      "No. Observations:                 392   AIC:                             2361.\n",
      "Df Residuals:                     390   BIC:                             2369.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     39.9359      0.717     55.660      0.000      38.525      41.347\n",
      "horsepower    -0.1578      0.006    -24.489      0.000      -0.171      -0.145\n",
      "==============================================================================\n",
      "Omnibus:                       16.432   Durbin-Watson:                   0.920\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               17.305\n",
      "Skew:                           0.492   Prob(JB):                     0.000175\n",
      "Kurtosis:                       3.299   Cond. No.                         322.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('mpg ~ horsepower',data = auto).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### i. Is there a relationship between the predictor and the response?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Since there is a non negative ceofficient, there is a realtionship between predictor and response"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ii. How strong is the relationship between the predictor and the response?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can meauser the overall fit by R2 value, since R2 value is 0.60, we say that 60% of invariability is \n",
    "# explained by the predictor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### iii. Is the relationship between the predictor and the response positive or negative?\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the value of the coefficient is -0.1578, hence the relationship is negative."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### iv. What is the predicted mpg associated with a horsepower of 98? What are the associated 95 % confidence and prediction intervals ?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24.46707715])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# i am not sure about how to find prediction with a given confidence. For this question i am using a model, to train\n",
    "# and then predict an answer\n",
    "model = LinearRegression()\n",
    "model.fit(auto['horsepower'].to_frame(),auto['mpg'])\n",
    "model.predict(pd.Series([98]).to_frame())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we are getting the answer as 24.46 ,but we can't be sure about the confidence in the prediction and the resulting range \n",
    "# of the confidence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Plot the response and the predictor. Use the abline() function to display the least squares regression line.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2ea7da7f0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8))\n",
    "sns.regplot(auto['horsepower'],auto['mpg'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) Use the plot() function to produce diagnostic plots of the least squares regression fit. Comment on any problems you see with the fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Diagnostic plots cnotains four types of plot, residual vs fitted,normal q-q, scale-location,residuals vs leverage\n",
    "# Here i am plotting the first two graphs\n",
    "# one can refer to the link below to get more information - "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://data.library.virginia.edu/diagnostic-plots/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Residual Plot')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#dist of residuals\n",
    "plt.figure(figsize = (12,8))\n",
    "plt.ylim(-20,20)\n",
    "sns.regplot(result.fittedvalues,result.resid, lowess=True)\n",
    "plt.axhline(y = 0,linewidth = 0.5,linestyle = 'dashed',color = 'black')\n",
    "plt.xlabel('Fitted Vales')\n",
    "plt.ylabel('Residuals')\n",
    "plt.title('Residual Plot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the distribution has some kind of pattern"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Q-Q plot\n",
    "ax = stats.probplot(result.resid, dist='norm', plot=plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the q-q polt is close to ideal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. This question involves the use of multiple linear regression on the Auto data set.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>chevrolet chevelle malibu</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165.0</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>buick skylark 320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>plymouth satellite</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>amc rebel sst</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>ford torino</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement  horsepower  weight  acceleration  year  \\\n",
       "0  18.0          8         307.0       130.0    3504          12.0    70   \n",
       "1  15.0          8         350.0       165.0    3693          11.5    70   \n",
       "2  18.0          8         318.0       150.0    3436          11.0    70   \n",
       "3  16.0          8         304.0       150.0    3433          12.0    70   \n",
       "4  17.0          8         302.0       140.0    3449          10.5    70   \n",
       "\n",
       "   origin                       name  \n",
       "0       1  chevrolet chevelle malibu  \n",
       "1       1          buick skylark 320  \n",
       "2       1         plymouth satellite  \n",
       "3       1              amc rebel sst  \n",
       "4       1                ford torino  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Produce a scatterplot matrix which includes all of the variables in the data set.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ErCQbZjWlufG8Y3h+e99QLOHgWY1B06tbpqX42Inzx+jotEwLZ0ot9JPc1ePECquyfQupDgvlTAvJZMt6l4FsfkQsYSDwU0Vnb3mt/M7A576knzR3VhMHtjQED+j7jt+JFRZl+1ZSHRY7v/FuYrddeFywNGWrepfhOjolN8yVd20KmscfF/ebG34nVsSlGXaJqJUzrW5iFvUu+XyeD7/lEC6+9dV0zstPWxhURyc9jvutLrD7LWrc8DumRJ2XbqFhb+FLtsLyJhY1OWXI6EPhBnbxrY+wdsWxwcZIJoSVpy8cUyuQDB3YH8zR0TMwJMvc3lxPXV24c+KG3zHDoiLRyq1Q8iUPv7lUIxY3SrApRMuO54YJuOPvH8xxxU9HupOu+Okmvn7WEcHGGBzM8URHz5gA8mHtzcGMf3U9nzhVjVVeetQa9nHqw2DRrtCqEC0xTsvCkNIQdckEbdNH3hTbpqeDZlp19AyUDSCHvE7c8DtmxCUwZtmHIZ9XOrsH2NLVR2f3QHApYwusbvjpZIKVpy8ckT208vSFpAMa5bamNB87cT6X3vEYZ65ez6V3PMbHTpxPW8AnJItm6+7qccywykuPGm8lODmsbvgzG9O8Mr2eS9/zxqHYS9v0emYG7FW7c1e27G78tguPoy2QG6bUbH3MdVINzdZrBW+2PnHam+u5ftnRvLCjf+jCPGhmQ9C8dAus/OIWqZYWY1jd8BMJGePWSYgEvR4tnvbam+u5btnRbB52ncwJfJ244d8LvNn65FBVdg2ODIpes3RRUJ0TC6wCyHGpSbCQIIDCTexD335wzA0m5E3M6mkvMyp5YNU5i4K+vxv+vcBitxQnxvP1rlm+hNkzGis8u8lhkZduYWTqUuPkpYds+mFQiAY2NzGLVN6OngFW3DTyOllxU9jrxA3/XuDN1ieHRdAqTsxqSvO989/MQFZJCOQV6lMS1MikxslLD+lPhugL0cBuNx51Kq/FdVJdUbUphjdbnxypcdLtQhuZuJDPKy/3Zzn3ugc54Su/4NzrHuTl/mzQzJ7+zKt56WuWL+GSkw/nip9uoj9TfZsXC00gi1Rei+skMsMvItNE5EER+a2I/K+IfKl4/BAReUBEnhKRNSJSfeWORbzZ+uRob67n6lGiY1dH4OuNCxZpkOlUks6ia+HM1etZcdNGOnsGqnLzYlGTYBUTifo6idLVMwCcoKo9IlIH/FJEfgL8HXClqn5fRK4B/ga4OsJ5REYiIRza2sSa5UtGlFZ7YLc8dXVJDmtvHvN5hSxFjxMWaZBWGUpxwSTuYnCdRGb4tZCq0VP8tq74T4ETgA8Uj98AfJEqNfzZbJ5NHT2RShDEjbq6ZNUFciuFlSBYfSoxIve9vkr/dvN55bntvWMCr/NmNQXbjLVMS3H10kWR6vFD9NdJpGdYRJIi8hugA7gLeBrYqarZ4ks2A7OjnEOUxKU1njN5LCpqS4JgoytRQwqCbe/NcNlPHidTfIrI5PJc9pPHq1J+oqt/gK2v7Bqhx7/1lV109Ye7Hjt7M3zz7idHxES+efeTwfX4oybSrB5VzQFHiEgLcBvwJ+VeVu53RWQ5sBxg7ty5kc1xb4iLBIEzOazqNywEwSykjK3oz+TLNlv//vIl0BRmjMFcnjsf6+DOxzpGHP+/766uz8vkmU5VdwLrgCVAi4iUbjhzgBfH+Z3VqrpYVRe3tbVZTHPSWDRFdqYeViJtdclE2cBryL+v8aSMA/dBNyE3ThpkyKexuFzzUWb1tBV3+ohIA/AO4HHgHuD04ss+DNwe1RyixqI1nhVWYmAW42SzeV7c2c/z23t5cWd/cBVIq/oNi78v1fLGstqqqeHVmMhwQsdErK75qK+TCbl6ROR9ZQ6/DPxOVTvK/AzgAOAGEUlSuMGsVdU7ROQx4Psi8k/Ar4Fv7cG8pwRWFYlRY+W6sBjHQvN/PO2Z0EHXREJoTCdHBF4b08mqbIRuoWnVNo40RFvINEiDa97iOpGJ3NlF5L+AYyns1gHeBqwH5gP/qKo3BZnNOCxevFg3bNgQ5RA1TWf3AKdedV+kGidW47y4s58zVt0/Zoy1K44NVjna8counu7sGVPt+vq2Ztr3mRZkDLD5vOKiAFqi1PClmjdiIc+7iGxU1TGlxRMN7uaBP1HVrcU3249CCuabgXuBSA2/Ey1WrguLcSwC7hZBV7D5vCwE5yw1rSykIaLG4rxP1PDPKxn9Ih3AfFXdISKDwWbjVASrx32T4hcDCeDhQdeoxgC78xK14JxrWk0Oi/M+UcP/PyJyB/CD4venA/eKSBOwM9hsqhCTXqIxaFBeGidqZUMLCWCrvgJxqaoVKd9YRAK2RCxhEUuIegyL62SiPn4B3gf8OSDAL4Fb1Sj0P1V9/BaBRIsxwO6CsfD1Ru3nzWbzbNrazYph52TV0kUsiKBiOw6Nfra+3M/vO3vH1Aoc2tbEfvuGc8tYVO5WW4LCeD7+CRn+4hvsT8GnnwceUtU/TmoGe8FUNfwWgUSLMaywCiJHTZzOiQWd3QP8w22PcNqig4ZiIrdufIEvn7ow6Hnf0TvApj92jwm6L9h/OjObwoxTbQkK4xn+Cd0+ROQjwIPAqRTcPOtF5LxJzSCGWAQS41QdHBdfb5zOCUSfMz6rKc2n/nLBiAbln/rLBcFdVv2ZXNnK3ZAS03FJUJioj/8i4EhV3Q4gIrOAXwHfDjaTKsQqkBiHBuVgF6yMmjidEwv3CEBzfZLrlx0zoqFMaHLjFKOFrEKOS4LCRA3/ZqB72PfdwAvBZhEBFr5RiyBfXBqUQ3yClVY9ZC3Y2Z8ZEjYb7h5paawL5h7Z2Z8Z2n0PH6OpPhVsDIBpdeWN8rS6cAZzRkNd2XM/o6Eu2BjtzfWsOmfRUPvFUs/dkH9fEw3u3gi8iVflFU6h4Pp5EkBVvxpsRmWYrI/fMogYdZAvn1c2/bGb828atpZzFrNg/+ps6B6HYKXVLtmCLV19nLl6/RhjGbK/65auPr70n/87xsf/hb/+06DSwxbXvUW8IpPJ8vzOfjYP2+zNmdnAwS0NpNOT09Xc2wKup4v/SneJ24v/nz6pWRhhVTDS0TMwZPRL46z4zsagQb7tvZkho18a4/ybqrehu0WT8qjZ3pvhQ99+sOqD1GDjHkkkKKsAGvomaVGMlsnmaGlI87rWJpIJYWZTmpaGdFAff2dvhmXXPVT+ZjxJwz8eE32XHwN/D8wb9juqqguDzCIwVkFEiyBMXAKicSKTzdHWXD+icveadU9X5TmxcI+oSlkF0LUrjg02hhVN9UmWHnswy65/aOgmdtUHj6KpPpyP36LZ+kQN/3eAzwCPUkjnnNJYBREtgjBxCYjGiYZ0ks+etGCMz7ohXX3npLWpvmzcpTWg791KAdTC1dOXyXPhzQ+PuIldePPDrF1xLC2BvFalZutj7EoFmq13qup/quqzqvp86V+wWQTGqgm6hUSrN3SfemTzWjZtMOSOzAqLBuWlzctwoti8WPRJsHjKb2tKl2223hbwmp/ojv8LIvLvwN0UmqgDoKo/DDaTgFg1QU+lEiwo0xQ5ZPVmIiG8oa15jAxsVKqGUUpPAAwMZNnWlxn6vFob09TXR9oILjiD2fIX/2Bg3X+wCYZHHXexyuaycIuaPOWnU8wfZb9aG9OTDuzujom+0zLgMAoN00t/3QpMScNv1QQ9n1d+v603cknbpzp7qqZEfHcMDGR5clvvmEbV81ubqsr416XG0eOPQK7BSs44SiyCrmDjFrVI5c3nlWd29E0JPf7fqeqbgoy4B0w2ndOqpN6ifLvaSsR3h0XqoAUW0gBgJ3UQF6x6C0SdyjuV9PjXi8jhqvrYpEatEFYl9RaPlnEpEQebbAUL+jPl9fj/9QNHBmvqDfFqhG7lsrLoLXDZTx7ntEUH0UiSTC7PZT95PGwe/xTS4/9z4MMi8iwFH78whdM5rUrqLR4t41IiDjbZChakU8myevyhg5XZvJZNg1yzfEnQcaI2ypYuq6jjFRY3Y4trfqJX9knAG4B3An8NnFz8Oi4icpCI3CMij4vI/4rIJ4rHvygiW0TkN8V/79qbBZSjvbmeVaOi4qsiKKm3yLixGMOqgXRrY/lshdbGsEG+qJutz2pKc+05o87JOeGDlblxnpByAZ+QSkb51Kvu47jL7+HUq+5j09buoEJtFtk2VuSUsjfjkAVvFtf8hHb8e5i6mQU+raoPi8h0YKOI3FX82ZWq+i978J4Tpr4uMaJJdX3AgpQR46RGjRNBJkzUY1g1ja+rS7LfPmm+v3wJubySTAjplFBXF7D4xSBQnc8rdSkZcU7qUkI+r0F3sCmDJzGLKvc4FSFa1SREfs0HfbdhqOpLwEvF/3eLyOPA7KjGG05HzwDnlil5Dh2stCjdt5IHsOhVur03w/uuGhtEDrmWjp6BIaMPhYvyo4FlNDp6Brjip0+M8PNe8dMn+OIpbwz6GVpkkFgY5TgVIVqsxeKaN8mhE5F5wJHAA8BxwN+KyIeADRSeCrrK/M5yYDnA3LlzJzWeB3enJvEJVGtZP68QdteXSAiN6eSInV9jOhlJcVWUhsxSldWiLWLUa5lKwd09RkSagVuBT6rqKyJyNXAphTqAS4GvAGOauqjqamA1FNI5JzOmB3enJnEJVOs4ft7QQVeLnZ+FIbPK47cIIg8vqBxe7FhtN+MJt17cozcXqQPuAH5WTrq5+CRwh6q+cXfvM9k8fss+tRZ5w5Z9aqOs3M3nlS07+xjI6oiGHLNbGquqGG1zVx9/fvk9Y47fd/Hbg9YjbOnq4ziDceIglQ02NS/Vds3vbR7/pCk2aP8W8Phwoy8iBxT9/1Bo5fhoFONPGxXcDak2WMJqJxN1oMfyRvlyf3bMOAfsEzYoGvW5TxtV7lo97eXzymAuTzavSC4fPEhdGiPqm4uFi8RK8r1qg7sUfPnnAL8Tkd8Uj/09cLaIHEHB1fMcsCL0wFbBXYg+b9jicd8iIGo1jsW5TyWElacvHFO5G7oewcINY5UFZfHUmk4leefh7WMqnUPeKK1uLlUb3FXVX1Io9BrNj6Mas0ScmmHHJyAan+b0VpW7Fk+UFjdjq13yjIY6Pn7i/EjbIlo8hVlc89XXHXoClAJ8w4kiuGuBhaSt1edlMY7FGMMrd89cvZ4VN22ks2cgkoB76Yly9oxG2qaHV2WNUzOhrv7Bsjexrv7BYGOUeu6OLnaM4uYynNDXfPVIIk4Cy2bYFulj3zv/zWMColFU7kb9eVmM095cz3fPfzOZYZ9XOiWR9Eio9qbxEK9mQhY3mK7+Qb5x95Mjnva+cfeTQbV6LP6+Is3qCcVks3rg1SyVKCtRLXyXVj7YqLNtSkR9XjKZLJs6x0o/L2hrCqpnHpdMmJ19A/xhR/9QV6k5MwqtBOfObKClMYwhs0oesMjqqbZMq/GyemJr+C2Ii2SyxTqsiIv0sxVbuvr4+n8/xflvfR3JhJDLK9fe+wyfeMcbgn1eVvLSFhuxartWzNM5a4G4BF7jVB1sJf0clx1/OpXkV89sZ+3GzUPH5sxo4KLUYcHGyGRz3PlYB3c+1jHi+Bf+Ouzfl0UwfFZTmhvPO2aMHn+1ufmqL9o5hYhL4NWqJ6oFJenn4YSWfrZQtLTCQgnS8u8r6mA4wEA2zyW3P8qZq9dzye2PMhBBy82occO/F8RFMjlODd0tGlXHSWbYotm6RSaMFXE597F19Vh1/Im6EXoqlWB+28jGy21N6cgaukelP2KFRaNqS9dYHJqtW2TCWGF17qM+77E0/FaVglaN0J/s7I08qyfqdVhh0ah6vBTIusB1D3Fptm7l47fAIjXVRGwuyLtMMawexyzGGa+ysqNnINgYcXl8Bbu1rDx94QjXxcrTw3ch3d6b4UcPv8B15x7Nzz99PNedezQ/eviF4GvJ55XO7gG2dPXR2T0QPFYRpxiShVvU4m84ljt+q8cxz+qZelispX+wvGTD1886ItgYAILy7j+bzbLrHxqRYx9S999id1ny8UcppWCFReaQSzbsIVY7DM/qmXpYnZNykg2hJS4GsvmhwiooXPwX3vxw0CwSi93lcB//muVLuOTkw/nG3U8GlVKwJOrMIZds2EMsZA5K40RdWm0hcxCX3PhVklwAABYPSURBVGSIzzmB8WsSQjZbt+oiFxcfvwUWf8OxNPxWuu9WevxR68vn80pfJscltz864vOKQpfdgtg0pzfQ0RGRsmMU2mmEIU5d5CywsCuxlGywkDmwwmItcfq8qq2kfndYaNxsfbmf33f2jukffGhbE/vtG+bc5/PKc9t7xzxRzpvVVJUbi2qipiQb4qTHHxcNeyviFKhOJIR9G1Jcv+yYES7LkMYyp3Dvpq1cd+7RQ1o9t2z4A4e0vi7YGPBqtetw14VTOWJp+K2arVtgsZY4fV5xcits781w9rUPRPr0kkpQNnMopNfKqhGLFXHQaYqy5+5BwI3A/kAeWK2qXxeRmcAaYB6F1otnqGpXyLEt9fijJi4a9iXi0L8AbJrT26QLa9nMoTXLlwQbI05PYXEpqotyx58FPq2qD4vIdGCjiNwFnAvcraqXicjngM8BF4cc2Cr4ZoHF475qIRg+WsP+gOnhFS2jvmgsAvtW+vIWTy85g8whiwCyFXF5eonMEqrqS6r6cPH/3cDjwGzgPcANxZfdALw3ivFTqQQHtjQwd1YTB7Y0VKXRh1cf99/x1V9wwld+wTu++gvOvvaB4NXBF4yqDr4gcHUwxKfS2WIMsKkSTSXHUTNNhjPKSYHLTxtZ6Xz5aQsJOIQZcXl6MfHxi8g84EjgAWA/VX0JCjcHEWkf53eWA8sB5s6dazHNKYnFH5qVhn1cKp2tguEWaX1JEb559pF87Hu/Hnp6+ebZR5IMuBvPKdzwq2dHVDrf8Ktn+eIpbww2hhVxiSFFvg0WkWbgVuCTqvrKRH9PVVer6mJVXdzW1hbdBKc4JlV8Bhr2EJ9KZ6vm9BB9lWh9nTCzOc31y47h558+nuuXHcPM5jT1dWF3/Be+/VDSxc8nnUxw4dsPrcodf1wkzCPN4xeROuAO4Geq+tXisU3A24q7/QOAdaq6YHfvM1VbLwIMDuYKPWSLEsDtzfXU1YVV6os6B3pwMMemjp4xPusF7c1Vt5ZsNs9zO3p5YUf/0BgHzWxg3symYO6+bDbPi6/0jwmGH7hPeJdi1MHwjld28XRnDxfd8moe/8rTF/L6tmba95kWZIwdvQM83dHDp9b+dmiMK8/4M17f3szMprB+cYuMm2rK6jHP45dC5OZbwOMlo1/kP4APA5cVv94e1RyiZnAwxxMdPWOCoocFNphR50CLSNnq4CiCbxb53AODI8dYtXRR8DFeKRNAPnCfsGNYBMMzufyQ0YeCy+qiWx7h+wGzerJ5HTL6pTE+tfa3/PDCtwQbA+wybqLuX2BBlK6e44BzgBNE5DfFf++iYPD/UkSeAv6y+H1VYhEUtQqInnvdQyy7/iHOXL2eZdc/xLnXPVS1wd0Vo87JiioN7lp8XhZZPYPZ8jGRwcAtC+MkLx41ke34VfWXwHi32ROjGtcSi6BoXAKiEJ+1WH5ebc31I4Ki16x7OujnlU6VL95LB05Lfefh7Zy26KChddy68YXgAdG4ZNxYEMvKXStKQdExFa8BHystsgisKnfjsharz6shneSzJy0Y439vSIf7vNIpYeXpC8eMkU6F7bn78RPnR67HH5eMGwuqM7l9itDeXF+2sXe1NUK3aOgO8VlLYzrBVR88asQYV33wKBrTYS+nbF7L+t9DPlHuyuTZ8OwOvnv+EtZd9Da+e/4SNjy7g12ZcE8vXf2DZV1jofX445JxY0Es1Tkh+mybErt2ZdnenxkaZ1ZDmmnTwj5IWcgDWKwDbNYyMJBlW19mRLP1+vpwa9nS1cfX//spzn/r64aEza699xk+8Y43MHtGY9Bxjrv8njHH77v47cHG2dk3wB929A/JNpRuYnNnNtDSGOZmabGOEtWUcWNBbalzGmXbDA7meGp7b6TjWDRCHxjIll3H/NamoAbTYi2Dgzme3BbtOalLJfjVM9tZu3Hz0LE5Mxr4TGq3WcmTxsJ10Zcp3+Vr7YpjaQlkky0lG+KQcWNBLF09VhIEccnq2daXKbuObX3V2Zw+6nOSSgj/9oEjue7co1mzfAnXnXs0//aBI4MXvM1qSnPtOaNcF+eEdV1kc3namutZdc4i1ixfwqpzFtHWXB80UB0nyQaIvjm9BbHc8VtJEMQlqydOkg0WaxnM5tk1qlbgK+//s+Dpifm8UpeSEfUVdSkJ2hmtPpUoG0AO2bVMElJWsuGfTn1TsDGsiIs6Zyx3/FYSBBbjuGTD5LBYSzavfPoHIwuSPv2D3wa/UVrUV+TGCSCHzONPJYRlxx3CpXc8xpmr13PpHY+x7LhDgv99WRCXWoFYGn6rLJW4ZPW0NqbLrqO1MZrm9FFn9UR9TiyKnsCmXiCrWt7VE3Ap/Zkctz28hevOPZqff/p4rjv3aG57eAv9merLr49LrUAsXT3JZILGuuSIR+TGuiTJwHnWyWSC1uY6vnf+EvKqJERIJQk+TtTNw+vrU8xvbWLN8iWRZcKAkdpkMkFLmf4FIc9JyqruYZxx6gKO01RfvlagqT7cGNPSCU49amSXr5WnL2Ra4PRXC+JSKxDLdE6rhtsW48SpebgFFp+XlUjb9t5dPPnHsQJq8/dvZlZTGAG1ju5dvO+qX435vH544Vtonx5mjJd29vP+VfePGeMHK47lgJYwDd2tqDYff02lc1o9jlmME5dHSyusPi8LkbZdmTxX/HTTiKDoFT/dxL9+4EhoCjOGhY7OeC6rwcASFxZYPLVaEEvDb/U4ZjFOXB4trbD4vMYTaVu74lgODLiDTaeSdPYMsOKmjUPHovj7ilpHJzmOtEmyyoxliTjUCsTS1WP1OGbVQ9ZiLRYVtWDUv2BbL8/vGKb5P7ORea3hNP+f397L8SvXjTl+70VvY+6sQFtxCmvZsrNvTOP42S2NVdU/eOvL/fy+s5eLb33VZXX5aQs5tK2J/fatLldPtVFTrh6IPiBqNY7Fo6VV83CLiupcLk/fYG5Ejv01SxeRy+VJJAJV7hoFdy0ax4+noxMyJpJIJMrm8X/51IVB3t+ZPLHc8ccpuGvBizv7OaNM8C2062JLVx9nrl4/Zpw1y5cE02yxGMNC3wZszouFjk61BUTjRE3t+OMU3LXASl/eoqrWYozegRy/eKKD756/BFVFRLj94c28b9GcYPo2YHNeLGIiiYTwhrZm1q44doQr0Y1+5ai+RNoJYFEhajlO1Fg1D7eoqrUYoyGdZPEhM/nAtes5fuU6PnDtehYfMjOoTj682iRlOHNmNFAX0P1mUVRXEuc7Y9X9HL9yHWesup+nOnuqUuMmLkTm6hGRbwMnAx2q+sbisS8C5wOdxZf9var++LXea0+Cu9t6d5HJKrm8kkwI6ZTQ2jSt6oK7EH3g1aJBOdj4+AcHczzX1cfmYWuZM7OBeTMag41hkfsOhaDoM9t6x+Txv641bFA0ainjuLhEq5FKuHquB/4VuHHU8StV9V8iHJfBwRxbX8mMMTD7puuCVqPGJfCqqmNEx65ZuojQmwKLSmdVHdNsPfRarHrI7sqWz+P/2llHBB0n6vTEuLhE40SUPXfvFZF5Ub3/7hhPZnjN8iXMjkCGIMqLxiJnfLwxQgZEoSBw9f5rxgZeg1Y692bGX0s6zLm3qq1IJaRsHn+1iZt5LcrUoxLB3b8VkQ8BG4BPq2pXuReJyHJgOcDcuXMnNYCVzLAFJkJdLss8KWY1pbnxvGN4fvuwWoFZjcFb/NWnCi0eR2cPRZWaHBWlOMJol6i3RKwc1ob/auBSQItfvwKcV+6FqroaWA0FH/9kBrFogm6FRc641edlsfOzWstAdqQ76doPjXGj7jWK8F+/Lahallo83rLhD3zkrYcGHytK4iJzECdMtw6qulVVc6qaB64FjoliHCuZYQssJKYtpIzBJoOkran8uW8LOIaVJvuspjTvPeogll3/ECd85Rcsu/4h3nvUQVW5Uy65RGfPaKRtuqdyVppIC7iKPv47hmX1HKCqLxX//yngzap61mu9z540W7dqHp7JZOnsfXWctqY06UC+5BJRNw8H/7wmgzcPd6oF86weEfke8DagVUQ2A18A3iYiR1Bw9TwHrIhibKvm4ZlMlk2dY8dZ0NYUzJhZNA+3aBpfGqfc5xW6Of0zO/oiTbG1DFbGQRDMmXpE5upR1bNV9QBVrVPVOar6LVU9R1XfpKoLVfWU0u4/NFbNwzt7y4/TWWXNw705/eSwcFk5TpTEUrIhTs3W4zKG1TgWmUMerHSqnerKC5sgcWq2HpcxrMaxktHwYKVTzcRSnXNgIFvWLx6Fj/+lngEGh+ml16WEA5rrw/r4O3tYcdOra1l1ziLmt4X18W/rGyCbg5wqyWJFbWtjWK18C8mGfF55bnvvmBz7ebPC6fGDTZDacfaWmlLntGsenqC7jF767H3C6qikR2n+p1OJoAJXuZyyrWdwjEGeUZ+mri7YMGbN6aPOsbcI6jtOlMRyx2+FlV56HDTsIT7N6a0+L8fZW8bb8cfSx29FXOQU4iTZEBdZCMeJEjf8e4GFjn2cgrsWgVeLMaw+L8eJCnf17AUWkskWgepdu7JsfqV/jB7/nH0aglbvxqU5vfv4nWphPFePG/69IJ9XtuzsY2BYVk99Spjd0hjUkG3t7iebY0RAdL/pDUEN2ZOdvWNuYPMjMGQWEgQWY3hWj1MN1FRWjxXbezOcfe0DkQYS46JhX8JCgsBijHQ6FfyzcRwr3Me/F3iw0nGcasQN/17gwUrHcaqR2Pr4rXzJcQlWPr+zf0yD8oNbGtxv7ThVTE35+C2MJdiJddWPqtwN3XovkUiQGdWgfNXSRSQS/kDoOHEkljt+i+pNKyzWYlGB7DiOPTVVuWsRELXCYi0WFciO40wdYmn4raR5LbBYi0UFsuM4U4fIrmwR+baIdIjIo8OOzRSRu0TkqeLXGVGMHacOSRZrsWjo7jjO1CEyH7+IvBXoAW4c1mz9CmCHql4mIp8DZqjqxa/1XnuS1TM4mKOjZ2CosrK9Oay2vCUWGUrZbL7weeXypJIJ2pvrg8lOOI5TGcyzelT1XhGZN+rweyg0YAe4AVgHvKbhnyzZbJ5NHT2RauhYYlGJmkolPJDrODWCtRXcr9Rgvfi1PYpBOnoGykoQhG4e7jiOU41M2e2viCwXkQ0isqGzs3NSv+tZKo7jOONjbfi3isgBAMWvHeO9UFVXq+piVV3c1tY2qUE8S8VxHGd8rCt3/wP4MHBZ8evtUQzS3lzP9cuOHqMv71kqjuM4ERp+EfkehUBuq4hsBr5AweCvFZG/Af4AvD+KsRMJYTCrIxtun7M4eCaM4zhONRJlVs/Z4/zoxKjGLLG9N8P5N20YEdw9/6YNVSnZ4DiOE5pYOr3jJNngOI4Tmlga/jhJNjiO44QmloY/TpINjuM4oYmlHr+VTr7jOE41EkvDDzYyB47jONVILF09juM4zvi44Xccx6kx3PA7juPUGG74Hcdxagw3/I7jODVGZB24QiIincDze/jrrcC2gNOpJL6WqUdc1gG+lqnI3q7jYFUdI29cFYZ/bxCRDeVaj1UjvpapR1zWAb6WqUhU63BXj+M4To3hht9xHKfGqAXDv7rSEwiIr2XqEZd1gK9lKhLJOmLv43ccx3FGUgs7fsdxHGcYbvgdx3FqjFgZfhFZICK/GfbvFRH5pIjMFJG7ROSp4tcZlZ7r7tjNOlaKyBMi8oiI3CYiLZWe62sx3lqG/fwzIqIi0lrJeU6E3a1FRD4mIptE5H9F5IpKz3V37Obv6wgRWV88tkFEjqn0XCeCiHyq+Lk/KiLfE5FpInKIiDxQvObXiEhVNOMYZy03F/+2HhWRb4tI3V4PpKqx/AckgT8CBwNXAJ8rHv8ccHml57eH63gnkCoev7ya1jF6LcXvDwJ+RqE4r7XS89uL8/J24L+B+uLP2is9vz1cx53AXxWPvwtYV+n5TWD+s4FngYbi92uBc4tfzyoeuwa4oNJz3Yu1vAuQ4r/vhVhLrHb8ozgReFpVnwfeA9xQPH4D8N6KzWryDK1DVe9U1Wzx+HpgTgXntScMPycAVwKfBaoxw2D4Wi4ALlPVAQBV7ajozCbH8HUosE/x+L7AixWb1eRIAQ0ikgIagZeAE4Bbij+vpmt+9FpeVNUfaxHgQQJc93E2/GdRuDsC7KeqLwEUv7ZXbFaTZ/g6hnMe8BPjuewtQ2sRkVOALar628pOaY8Zfl7mA39RdC38QkSOruC8JsvwdXwSWCkiLwD/Any+YrOaIKq6hcJc/0DB4L8MbAR2Dtskbaawm57SlFuLqt5Z+nnRxXMO8NO9HSuWhr/ozzsF+EGl57I3jLcOEfkHIAvcXIl57QnD1yIijcA/AP+vsrPaM8qclxQwA1gCXASsFZEp3+ezzDouAD6lqgcBnwK+Vam5TZRivO49wCHAgUAT8FdlXjrlnyrLrUVElg57yVXAvar6P3s7ViwNP4UT/7Cqbi1+v1VEDgAofq2WR/HR60BEPgycDHyw+OhXLQxfy+sp/HH/VkSeo/Do+rCI7F/B+U2G0edlM/DD4tP4g0CegrjWVGf0Oj4M/LD4/x8A1RDcfQfwrKp2quoghfm/BWgpukug8PdVDW6r8daCiHwBaAP+LsRAcTX8ZzPSPfIfFP6oKX693XxGe8aIdYjIScDFwCmq2lexWe0ZQ2tR1d+paruqzlPVeRQM51Gq+sdKTnASjP77+hEFnzIiMh9IUx3KkKPX8SJwfPH/JwBPmc9o8vwBWCIijcWnrBOBx4B7gNOLr6mWa77cWh4XkY8A/wc4W1XzIQaKXeVu0Y3wAvA6VX25eGwWhQj5XAof7vtVdUflZvnajLOO3wP1wPbiy9ar6kcrNMUJU24to37+HLBYVae8sRznvKSBbwNHABngM6r688rN8rUZZx1/DnydgutqF3Chqm6s3Cwnhoh8CTiTgvvz18BHKPj0vw/MLB5bWgq+T2XGWUsvhcy37uLLfqiq/7hX48TN8DuO4zi7J66uHsdxHGcc3PA7juPUGG74Hcdxagw3/I7jODWGG37HcZwaww2/4zhOjeGG33GMEJFkpefgOOCG33HKIiKXisgnhn3/ZRH5uIhcJCIPFXsifGnYz38kIhuLWurLhx3vEZF/FJEHgGONl+E4ZXHD7zjl+RZFmQ8RSVBQsdwKvIGChs0RwCIReWvx9eep6iJgMfDxYrU4FETDHlXVN6vqLy0X4DjjkXrtlzhO7aGqz4nIdhE5EtiPQvn80RSa4fy6+LJmCjeCeykY+1OLxw8qHt8O5IBbLefuOK+FG37HGZ9/p9ABaX8KWjwnAv+sqquGv0hE3kZBWfFYVe0TkXXAtOKPd6lqzmrCjjMR3NXjOONzG3AShZ3+z4r/zhORZgARmS0i7RS6VXUVjf5hFHT5HWfK4jt+xxkHVc2IyD0UujnlgDtF5E+A+4t9VnqApRQ6In1URB4BNlFoi+k4UxZX53SccSgGdR+mIONdDdr0jjMh3NXjOGUQkcOB3wN3u9F34obv+B3HcWoM3/E7juPUGG74Hcdxagw3/I7jODWGG37HcZwaww2/4zhOjfH/Ae/BclXgCRcFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for col in auto.iloc[:,1:8].columns:\n",
    "    sns.scatterplot(auto[col],auto['mpg'])\n",
    "    plt.title(col)\n",
    "    plt.xlabel(col)\n",
    "    plt.ylabel('mpg')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Compute the matrix of correlations between the variables using the function cor(). You will need to exclude the name variable, cor() which is qualitative.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>year</th>\n",
       "      <th>origin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>mpg</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.777618</td>\n",
       "      <td>-0.805127</td>\n",
       "      <td>-0.778427</td>\n",
       "      <td>-0.832244</td>\n",
       "      <td>0.423329</td>\n",
       "      <td>0.580541</td>\n",
       "      <td>0.565209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cylinders</th>\n",
       "      <td>-0.777618</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.950823</td>\n",
       "      <td>0.842983</td>\n",
       "      <td>0.897527</td>\n",
       "      <td>-0.504683</td>\n",
       "      <td>-0.345647</td>\n",
       "      <td>-0.568932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>displacement</th>\n",
       "      <td>-0.805127</td>\n",
       "      <td>0.950823</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.897257</td>\n",
       "      <td>0.932994</td>\n",
       "      <td>-0.543800</td>\n",
       "      <td>-0.369855</td>\n",
       "      <td>-0.614535</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>horsepower</th>\n",
       "      <td>-0.778427</td>\n",
       "      <td>0.842983</td>\n",
       "      <td>0.897257</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.864538</td>\n",
       "      <td>-0.689196</td>\n",
       "      <td>-0.416361</td>\n",
       "      <td>-0.455171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>weight</th>\n",
       "      <td>-0.832244</td>\n",
       "      <td>0.897527</td>\n",
       "      <td>0.932994</td>\n",
       "      <td>0.864538</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.416839</td>\n",
       "      <td>-0.309120</td>\n",
       "      <td>-0.585005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>acceleration</th>\n",
       "      <td>0.423329</td>\n",
       "      <td>-0.504683</td>\n",
       "      <td>-0.543800</td>\n",
       "      <td>-0.689196</td>\n",
       "      <td>-0.416839</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.290316</td>\n",
       "      <td>0.212746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>year</th>\n",
       "      <td>0.580541</td>\n",
       "      <td>-0.345647</td>\n",
       "      <td>-0.369855</td>\n",
       "      <td>-0.416361</td>\n",
       "      <td>-0.309120</td>\n",
       "      <td>0.290316</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.181528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>origin</th>\n",
       "      <td>0.565209</td>\n",
       "      <td>-0.568932</td>\n",
       "      <td>-0.614535</td>\n",
       "      <td>-0.455171</td>\n",
       "      <td>-0.585005</td>\n",
       "      <td>0.212746</td>\n",
       "      <td>0.181528</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   mpg  cylinders  displacement  horsepower    weight  \\\n",
       "mpg           1.000000  -0.777618     -0.805127   -0.778427 -0.832244   \n",
       "cylinders    -0.777618   1.000000      0.950823    0.842983  0.897527   \n",
       "displacement -0.805127   0.950823      1.000000    0.897257  0.932994   \n",
       "horsepower   -0.778427   0.842983      0.897257    1.000000  0.864538   \n",
       "weight       -0.832244   0.897527      0.932994    0.864538  1.000000   \n",
       "acceleration  0.423329  -0.504683     -0.543800   -0.689196 -0.416839   \n",
       "year          0.580541  -0.345647     -0.369855   -0.416361 -0.309120   \n",
       "origin        0.565209  -0.568932     -0.614535   -0.455171 -0.585005   \n",
       "\n",
       "              acceleration      year    origin  \n",
       "mpg               0.423329  0.580541  0.565209  \n",
       "cylinders        -0.504683 -0.345647 -0.568932  \n",
       "displacement     -0.543800 -0.369855 -0.614535  \n",
       "horsepower       -0.689196 -0.416361 -0.455171  \n",
       "weight           -0.416839 -0.309120 -0.585005  \n",
       "acceleration      1.000000  0.290316  0.212746  \n",
       "year              0.290316  1.000000  0.181528  \n",
       "origin            0.212746  0.181528  1.000000  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto.iloc[:,:-1].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2eb694b38>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(auto.iloc[:,:-1].corr())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) Use the lm() function to perform a multiple linear regression with mpg as the response and all other variables except name as the predictors. Use the summary() function to print the results. Comment on the output.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    mpg   R-squared:                       0.821\n",
      "Model:                            OLS   Adj. R-squared:                  0.818\n",
      "Method:                 Least Squares   F-statistic:                     252.4\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):          2.04e-139\n",
      "Time:                        10:40:55   Log-Likelihood:                -1023.5\n",
      "No. Observations:                 392   AIC:                             2063.\n",
      "Df Residuals:                     384   BIC:                             2095.\n",
      "Df Model:                           7                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "================================================================================\n",
      "                   coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------\n",
      "Intercept      -17.2184      4.644     -3.707      0.000     -26.350      -8.087\n",
      "acceleration     0.0806      0.099      0.815      0.415      -0.114       0.275\n",
      "cylinders       -0.4934      0.323     -1.526      0.128      -1.129       0.142\n",
      "displacement     0.0199      0.008      2.647      0.008       0.005       0.035\n",
      "horsepower      -0.0170      0.014     -1.230      0.220      -0.044       0.010\n",
      "origin           1.4261      0.278      5.127      0.000       0.879       1.973\n",
      "weight          -0.0065      0.001     -9.929      0.000      -0.008      -0.005\n",
      "year             0.7508      0.051     14.729      0.000       0.651       0.851\n",
      "==============================================================================\n",
      "Omnibus:                       31.906   Durbin-Watson:                   1.309\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               53.100\n",
      "Skew:                           0.529   Prob(JB):                     2.95e-12\n",
      "Kurtosis:                       4.460   Cond. No.                     8.59e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 8.59e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "predictors = ' + '.join(auto.columns.difference(['name','mpg']))\n",
    "result = smf.ols('mpg ~ {}'.format(predictors),data = auto).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### i. Is there a relationship between the predictors and the response?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# since we are having non zero ceoffiencts, there is a relationship between the predictors and response.\n",
    "# also the value of f statistic is quite high, which supports the claim."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ii. Which predictors appear to have a statistically significant relationship to the response?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Origin,weight, year have very significan p value of 0, displacement also has a very low p value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### iii. What does the coefficient for the year variable suggest?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Coefficient of year is 0.7508. It means that if we increase the value of year by i unit, kepping all other predictors fixec,\n",
    "# we would expect 0.7508 increase in the response."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### d) Use the plot() function to produce diagnostic plots of the linear regression fit. Comment on any problems you see with the fit. Do the residual plots suggest any unusually large outliers?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Residual Plot')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#diagnotis plot\n",
    "#dist of residuals\n",
    "plt.figure(figsize = (12,8))\n",
    "plt.ylim(-15,15)\n",
    "sns.regplot(result.fittedvalues,result.resid, lowess=True)\n",
    "plt.axhline(y = 0,linewidth = 0.5,linestyle = 'dashed',color = 'black')\n",
    "plt.xlabel('Fitted Vales')\n",
    "plt.ylabel('Residuals')\n",
    "plt.title('Residual Plot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Q-Q plot\n",
    "ax = stats.probplot(result.resid, dist='norm', plot=plt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# in both of the graphs we can see some points in the uppwe right corner behaving as outliers\n",
    "# Q-Q plot is very colse to  the ideal, and the residuals distribution plot is also accetable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (e) Use the * and : symbols to fit linear regression models with interaction effects. Do any interactions appear to be statistically significant?\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    mpg   R-squared:                       0.870\n",
      "Model:                            OLS   Adj. R-squared:                  0.867\n",
      "Method:                 Least Squares   F-statistic:                     283.1\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):          5.43e-163\n",
      "Time:                        10:40:59   Log-Likelihood:                -961.89\n",
      "No. Observations:                 392   AIC:                             1944.\n",
      "Df Residuals:                     382   BIC:                             1983.\n",
      "Df Model:                           9                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "========================================================================================\n",
      "                           coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------\n",
      "Intercept              -40.8773     12.176     -3.357      0.001     -64.817     -16.937\n",
      "acceleration            -0.1742      0.088     -1.985      0.048      -0.347      -0.002\n",
      "cylinders               -3.0837      0.516     -5.971      0.000      -4.099      -2.068\n",
      "displacement            -0.0048      0.007     -0.713      0.476      -0.018       0.008\n",
      "horsepower               0.2260      0.119      1.897      0.059      -0.008       0.460\n",
      "origin                   0.8834      0.243      3.634      0.000       0.405       1.361\n",
      "weight                  -0.0038      0.001     -6.294      0.000      -0.005      -0.003\n",
      "year                     1.3597      0.139      9.771      0.000       1.086       1.633\n",
      "horsepower:cylinders     0.0308      0.004      7.336      0.000       0.023       0.039\n",
      "horsepower:year         -0.0065      0.001     -4.696      0.000      -0.009      -0.004\n",
      "==============================================================================\n",
      "Omnibus:                       39.241   Durbin-Watson:                   1.647\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               72.217\n",
      "Skew:                           0.596   Prob(JB):                     2.08e-16\n",
      "Kurtosis:                       4.732   Cond. No.                     7.54e+05\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 7.54e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "predictors = ' + '.join(auto.columns.difference(['name','mpg']))\n",
    "result = smf.ols('mpg ~ {} + horsepower*cylinders + horsepower*year'.format(predictors),data = auto).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we have added two tersms, horsepower*cyllinder and horsepower*year, for both of these the p values are significant\n",
    "# Adding the interaction terms has resulted in the increase of R2 value from 82.1 to 87.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) Try a few different transformations of the variables, such as log(X), √X, X2. Comment on your findings.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    mpg   R-squared:                       0.863\n",
      "Model:                            OLS   Adj. R-squared:                  0.860\n",
      "Method:                 Least Squares   F-statistic:                     267.4\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):          6.47e-159\n",
      "Time:                        10:40:59   Log-Likelihood:                -971.55\n",
      "No. Observations:                 392   AIC:                             1963.\n",
      "Df Residuals:                     382   BIC:                             2003.\n",
      "Df Model:                           9                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===========================================================================================\n",
      "                              coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------------\n",
      "Intercept                  10.7462      4.937      2.177      0.030       1.040      20.453\n",
      "acceleration               -0.2361      0.099     -2.392      0.017      -0.430      -0.042\n",
      "cylinders                  -3.2075      0.818     -3.920      0.000      -4.816      -1.599\n",
      "displacement               -0.0048      0.007     -0.663      0.508      -0.019       0.009\n",
      "horsepower                 -0.3386      0.034    -10.048      0.000      -0.405      -0.272\n",
      "origin                      0.8978      0.249      3.603      0.000       0.408       1.388\n",
      "weight                     -0.0035      0.001     -5.310      0.000      -0.005      -0.002\n",
      "year                        0.7373      0.045     16.459      0.000       0.649       0.825\n",
      "horsepower:cylinders        0.0312      0.007      4.664      0.000       0.018       0.044\n",
      "np.power(horsepower, 2)     0.0003      0.000      1.619      0.106   -6.39e-05       0.001\n",
      "==============================================================================\n",
      "Omnibus:                       39.733   Durbin-Watson:                   1.608\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               72.555\n",
      "Skew:                           0.605   Prob(JB):                     1.76e-16\n",
      "Kurtosis:                       4.725   Cond. No.                     5.38e+05\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.38e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "predictors = ' + '.join(auto.columns.difference(['name','mpg']))\n",
    "result = smf.ols('mpg ~ {} + horsepower*cylinders + np.power(horsepower,2)'.format(predictors),data = auto).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we saw in the chapter how the scatterplot between horsepower and mpg hinted a non linear realtionship\n",
    "# by adding a new term which is horsepower**2, we saw an increase in R2 value increase from 82.1 to 86.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10. This question should be answered using the Carseats data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(400, 11)\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "    }\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sales</th>\n",
       "      <th>CompPrice</th>\n",
       "      <th>Income</th>\n",
       "      <th>Advertising</th>\n",
       "      <th>Population</th>\n",
       "      <th>Price</th>\n",
       "      <th>ShelveLoc</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Urban</th>\n",
       "      <th>US</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9.50</td>\n",
       "      <td>138</td>\n",
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       "      <td>276</td>\n",
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       "      <td>42</td>\n",
       "      <td>17</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>11.22</td>\n",
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       "      <td>Yes</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10.06</td>\n",
       "      <td>113</td>\n",
       "      <td>35</td>\n",
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       "      <td>269</td>\n",
       "      <td>80</td>\n",
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       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.40</td>\n",
       "      <td>117</td>\n",
       "      <td>100</td>\n",
       "      <td>4</td>\n",
       "      <td>466</td>\n",
       "      <td>97</td>\n",
       "      <td>Medium</td>\n",
       "      <td>55</td>\n",
       "      <td>14</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.15</td>\n",
       "      <td>141</td>\n",
       "      <td>64</td>\n",
       "      <td>3</td>\n",
       "      <td>340</td>\n",
       "      <td>128</td>\n",
       "      <td>Bad</td>\n",
       "      <td>38</td>\n",
       "      <td>13</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Sales  CompPrice  Income  Advertising  Population  Price ShelveLoc  Age  \\\n",
       "0   9.50        138      73           11         276    120       Bad   42   \n",
       "1  11.22        111      48           16         260     83      Good   65   \n",
       "2  10.06        113      35           10         269     80    Medium   59   \n",
       "3   7.40        117     100            4         466     97    Medium   55   \n",
       "4   4.15        141      64            3         340    128       Bad   38   \n",
       "\n",
       "   Education Urban   US  \n",
       "0         17   Yes  Yes  \n",
       "1         10   Yes  Yes  \n",
       "2         12   Yes  Yes  \n",
       "3         14   Yes  Yes  \n",
       "4         13   Yes   No  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('E:\\programming\\dataset\\Into_to_statstical_learning\\Carseats.csv')\n",
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "shelveloc_mapping = {'Bad':0,'Good':1,'Medium':2}\n",
    "yes_no_mapping = {'Yes':1,'No':0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['ShelveLoc'] = data['ShelveLoc'].map(shelveloc_mapping)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['Urban'] = data['Urban'].map(yes_no_mapping)\n",
    "data['US'] = data['US'].map(yes_no_mapping)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sales</th>\n",
       "      <th>CompPrice</th>\n",
       "      <th>Income</th>\n",
       "      <th>Advertising</th>\n",
       "      <th>Population</th>\n",
       "      <th>Price</th>\n",
       "      <th>ShelveLoc</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Urban</th>\n",
       "      <th>US</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9.50</td>\n",
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       "      <td>1</td>\n",
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       "      <th>1</th>\n",
       "      <td>11.22</td>\n",
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       "      <th>2</th>\n",
       "      <td>10.06</td>\n",
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       "      <td>10</td>\n",
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       "      <td>80</td>\n",
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       "      <td>4</td>\n",
       "      <td>466</td>\n",
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       "      <td>2</td>\n",
       "      <td>55</td>\n",
       "      <td>14</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "      <th>4</th>\n",
       "      <td>4.15</td>\n",
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      ],
      "text/plain": [
       "   Sales  CompPrice  Income  Advertising  Population  Price  ShelveLoc  Age  \\\n",
       "0   9.50        138      73           11         276    120          0   42   \n",
       "1  11.22        111      48           16         260     83          1   65   \n",
       "2  10.06        113      35           10         269     80          2   59   \n",
       "3   7.40        117     100            4         466     97          2   55   \n",
       "4   4.15        141      64            3         340    128          0   38   \n",
       "\n",
       "   Education  Urban  US  \n",
       "0         17      1   1  \n",
       "1         10      1   1  \n",
       "2         12      1   1  \n",
       "3         14      1   1  \n",
       "4         13      1   0  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Sales          float64\n",
       "CompPrice        int64\n",
       "Income           int64\n",
       "Advertising      int64\n",
       "Population       int64\n",
       "Price            int64\n",
       "ShelveLoc        int64\n",
       "Age              int64\n",
       "Education        int64\n",
       "Urban            int64\n",
       "US               int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we now a complete quantative data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Fit a multiple regression model to predict Sales using Price, Urban, and US."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Sales   R-squared:                       0.239\n",
      "Model:                            OLS   Adj. R-squared:                  0.234\n",
      "Method:                 Least Squares   F-statistic:                     41.52\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           2.39e-23\n",
      "Time:                        10:41:01   Log-Likelihood:                -927.66\n",
      "No. Observations:                 400   AIC:                             1863.\n",
      "Df Residuals:                     396   BIC:                             1879.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     13.0435      0.651     20.036      0.000      11.764      14.323\n",
      "Price         -0.0545      0.005    -10.389      0.000      -0.065      -0.044\n",
      "Urban         -0.0219      0.272     -0.081      0.936      -0.556       0.512\n",
      "US             1.2006      0.259      4.635      0.000       0.691       1.710\n",
      "==============================================================================\n",
      "Omnibus:                        0.676   Durbin-Watson:                   1.912\n",
      "Prob(Omnibus):                  0.713   Jarque-Bera (JB):                0.758\n",
      "Skew:                           0.093   Prob(JB):                        0.684\n",
      "Kurtosis:                       2.897   Cond. No.                         628.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('Sales ~ Price + Urban + US',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Provide an interpretation of each coefficient in the model. Be careful—some of the variables in the model are qualitative!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from the coeffiecents we can see that  the Price and Urban are negatively related to Sales, and US is positively related\n",
    "# Looking at the p values, Price and Us have significant p-values, but Urban has a very high p values ,and its \n",
    "# better that we exclude it from the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) Write out the model in equation form, being careful to handle the qualitative variables properly.\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Sales = 13.0435 - 0.545*Price - 0.0219*Urban + 1.2006*US\n",
    "# in the above equation, Urban takes values (0,1) and so does US"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d) For which of the predictors can you reject the null hypothesis H0 : βj = 0?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# although all the predictors are having coefficients non zero, but since Urban has a high value, we will not use it as a \n",
    "# predictor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (e) On the basis of your response to the previous question, fit a smaller model that only uses the predictors for which there is evidence of association with the outcome.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Sales   R-squared:                       0.239\n",
      "Model:                            OLS   Adj. R-squared:                  0.235\n",
      "Method:                 Least Squares   F-statistic:                     62.43\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           2.66e-24\n",
      "Time:                        10:41:02   Log-Likelihood:                -927.66\n",
      "No. Observations:                 400   AIC:                             1861.\n",
      "Df Residuals:                     397   BIC:                             1873.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     13.0308      0.631     20.652      0.000      11.790      14.271\n",
      "Price         -0.0545      0.005    -10.416      0.000      -0.065      -0.044\n",
      "US             1.1996      0.258      4.641      0.000       0.692       1.708\n",
      "==============================================================================\n",
      "Omnibus:                        0.666   Durbin-Watson:                   1.912\n",
      "Prob(Omnibus):                  0.717   Jarque-Bera (JB):                0.749\n",
      "Skew:                           0.092   Prob(JB):                        0.688\n",
      "Kurtosis:                       2.895   Cond. No.                         607.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('Sales ~ Price + US',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) How well do the models in (a) and (e) fit the data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Removing the Urban from the first model, there is no change in the R2 value in the second model. Through this we can also \n",
    "# conclude that Urban has no say in the prediction of the response, hence its better to use the model with two predictors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (g) Using the model from (e), obtain 95 % confidence intervals for the coefficient(s).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for 95% of confidence value we calculate the range of x +/- 2*stddev(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With 95% confidence the range for Price coefficient is  [-0.0645, -0.0445]\n",
      "With 95% confidence the range for US coefficent is  [0.6836, 1.7156]\n"
     ]
    }
   ],
   "source": [
    "coeff_price = -0.0545\n",
    "std_price = 0.005\n",
    "range_price = [coeff_price - 2*std_price,coeff_price + 2*std_price]\n",
    "\n",
    "coeff_US = 1.1996\n",
    "std_US = 0.258\n",
    "range_US = [coeff_US - 2*std_US,coeff_US + 2*std_US]\n",
    "\n",
    "print('With 95% confidence the range for Price coefficient is ',range_price)\n",
    "print('With 95% confidence the range for US coefficent is ',range_US)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### (h) Is there evidence of outliers or high leverage observations in the model from (e)?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Residual Plot')"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#dist of residuals\n",
    "plt.figure(figsize = (12,8))\n",
    "plt.ylim(-15,15)\n",
    "sns.regplot(result.fittedvalues,result.resid, lowess=True)\n",
    "plt.axhline(y = 0,linewidth = 0.5,linestyle = 'dashed',color = 'black')\n",
    "plt.xlabel('Fitted Vales')\n",
    "plt.ylabel('Residuals')\n",
    "plt.title('Residual Plot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "#from the graph, we can see its a good fit, and there is no pattern"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11. In this problem we will investigate the t-statistic for the null hypothesis H0 : β = 0 in simple linear regression without an intercept. To begin, we generate a predictor x and a response y as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "\n",
    "X = np.random.normal(size = 100)\n",
    "Y = 2*X + np.random.normal(size = 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'X':X,'y':Y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.624345</td>\n",
       "      <td>2.801562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.611756</td>\n",
       "      <td>0.000995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.528172</td>\n",
       "      <td>-0.652852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.072969</td>\n",
       "      <td>-1.552359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.865408</td>\n",
       "      <td>0.635903</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X         y\n",
       "0  1.624345  2.801562\n",
       "1 -0.611756  0.000995\n",
       "2 -0.528172 -0.652852\n",
       "3 -1.072969 -1.552359\n",
       "4  0.865408  0.635903"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Perform a simple linear regression of y onto x, without an intercept. Report the coefficient estimate βˆ, the standard error of this coefficient estimate, and the t-statistic and p-value associated with the null hypothesis H0 : β = 0.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                 OLS Regression Results                                \n",
      "=======================================================================================\n",
      "Dep. Variable:                      y   R-squared (uncentered):                   0.798\n",
      "Model:                            OLS   Adj. R-squared (uncentered):              0.796\n",
      "Method:                 Least Squares   F-statistic:                              391.7\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):                    3.46e-36\n",
      "Time:                        10:41:07   Log-Likelihood:                         -135.67\n",
      "No. Observations:                 100   AIC:                                      273.3\n",
      "Df Residuals:                      99   BIC:                                      275.9\n",
      "Df Model:                           1                                                  \n",
      "Covariance Type:            nonrobust                                                  \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "X              2.1067      0.106     19.792      0.000       1.896       2.318\n",
      "==============================================================================\n",
      "Omnibus:                        0.880   Durbin-Watson:                   2.106\n",
      "Prob(Omnibus):                  0.644   Jarque-Bera (JB):                0.554\n",
      "Skew:                          -0.172   Prob(JB):                        0.758\n",
      "Kurtosis:                       3.119   Cond. No.                         1.00\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y~X + 0',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "# coefficient estimate is 2.1067, std_error is 0.106,value of t-statistic is 19.792. P value is significant.\n",
    "# Hence, we reject null hypothesis, and there is a realationship between predictor and response."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Now perform a simple linear regression of x onto y without an intercept, and report the coefficient estimate, its standard error, and the corresponding t-statistic and p-values associated with the null hypothesis H0 : β = 0.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                 OLS Regression Results                                \n",
      "=======================================================================================\n",
      "Dep. Variable:                      X   R-squared (uncentered):                   0.798\n",
      "Model:                            OLS   Adj. R-squared (uncentered):              0.796\n",
      "Method:                 Least Squares   F-statistic:                              391.7\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):                    3.46e-36\n",
      "Time:                        10:41:07   Log-Likelihood:                         -49.891\n",
      "No. Observations:                 100   AIC:                                      101.8\n",
      "Df Residuals:                      99   BIC:                                      104.4\n",
      "Df Model:                           1                                                  \n",
      "Covariance Type:            nonrobust                                                  \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "y              0.3789      0.019     19.792      0.000       0.341       0.417\n",
      "==============================================================================\n",
      "Omnibus:                        0.476   Durbin-Watson:                   2.166\n",
      "Prob(Omnibus):                  0.788   Jarque-Bera (JB):                0.631\n",
      "Skew:                           0.115   Prob(JB):                        0.729\n",
      "Kurtosis:                       2.685   Cond. No.                         1.00\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('X~y + 0',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Coef estimate is 0.3789, std_error is 0.019, value of t statistic is 19.792, and p value is significant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) What is the relationship between the results obtained in (a) and (b)?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Alhtought the coeff estimates and their std_errors were different, the value of t - statistic was sama in both the cases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d)  Show algebraically, and confirm numerically in R, that the t-statistic can be written as\n",
    "(\n",
    "√n − 1)\n",
    "n\n",
    "i=1 xiyi\n",
    "\u0016(\n",
    "\n",
    "n\n",
    "i=1 x2\n",
    "i )(\n",
    "n\n",
    "i=1 y2\n",
    "i ) − (\n",
    "\n",
    "n\n",
    "i=1 xiyi )2"
   ]
  },
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![37bd9870-c7df-4434-89cf-550bd53befe3.jpg](attachment:37bd9870-c7df-4434-89cf-550bd53befe3.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  (e) Using the results from (d), argue that the t-statistic for the regression of y onto x is the same as the t-statistic for the regression of x onto y.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The formula of t - statistic is symmetric for x and y, therefore if we interchange the values of x and y \n",
    "# we will get the same value of t - statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) In R, show that when regression is performed with an intercept, the t-statistic for H0 : β1 = 0 is the same for the regression of y onto x as it is for the regression of x onto y.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.800\n",
      "Model:                            OLS   Adj. R-squared:                  0.798\n",
      "Method:                 Least Squares   F-statistic:                     391.4\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           5.39e-36\n",
      "Time:                        10:41:08   Log-Likelihood:                -134.44\n",
      "No. Observations:                 100   AIC:                             272.9\n",
      "Df Residuals:                      98   BIC:                             278.1\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.1470      0.094      1.564      0.121      -0.039       0.334\n",
      "X              2.0954      0.106     19.783      0.000       1.885       2.306\n",
      "==============================================================================\n",
      "Omnibus:                        0.898   Durbin-Watson:                   2.157\n",
      "Prob(Omnibus):                  0.638   Jarque-Bera (JB):                0.561\n",
      "Skew:                          -0.172   Prob(JB):                        0.755\n",
      "Kurtosis:                       3.127   Cond. No.                         1.15\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y~X',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      X   R-squared:                       0.800\n",
      "Model:                            OLS   Adj. R-squared:                  0.798\n",
      "Method:                 Least Squares   F-statistic:                     391.4\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           5.39e-36\n",
      "Time:                        10:41:09   Log-Likelihood:                -49.289\n",
      "No. Observations:                 100   AIC:                             102.6\n",
      "Df Residuals:                      98   BIC:                             107.8\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0440      0.040     -1.090      0.279      -0.124       0.036\n",
      "y              0.3817      0.019     19.783      0.000       0.343       0.420\n",
      "==============================================================================\n",
      "Omnibus:                        0.456   Durbin-Watson:                   2.192\n",
      "Prob(Omnibus):                  0.796   Jarque-Bera (JB):                0.611\n",
      "Skew:                           0.118   Prob(JB):                        0.737\n",
      "Kurtosis:                       2.698   Cond. No.                         2.12\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('X~y',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "# t value is same  =19.783"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. This problem involves simple linear regression without an intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Recall that the coefficient estimate βˆ for the linear regression of Y onto X without an intercept is given by (3.38). Under what circumstance is the coefficient estimate for the regression of X onto Y the same as the coefficient estimate for the regression of Y onto X?\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<-- insert picture here -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Generate an example in R with n = 100 observations in which the coefficient estimate for the regression of X onto Y is different from the coefficient estimate for the regression of Y onto X.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.random.normal(size = 100)\n",
    "Y = 2*X + np.random.normal(size = 100)\n",
    "data = pd.DataFrame({'X':X,'y':Y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coef_1 is [2.11910764], coef_2 is [0.38298135]\n"
     ]
    }
   ],
   "source": [
    "lin_x_on_y = LinearRegression(fit_intercept=False)\n",
    "lin_x_on_y.fit(data['X'].to_frame(),data['y'])\n",
    "coef_1 = lin_x_on_y.coef_\n",
    "\n",
    "lin_y_on_x = LinearRegression(fit_intercept= False)\n",
    "lin_y_on_x.fit(data['y'].to_frame(),data['X'])\n",
    "coef_2 = lin_y_on_x.coef_\n",
    "\n",
    "print('coef_1 is {}, coef_2 is {}'.format(coef_1,coef_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) Generate an example in R with n = 100 observations in which the coefficient estimate for the regression of X onto Y is the same as the coefficient estimate for the regression of Y onto X\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we need to choose x and y in such a way that their variabce is same. \n",
    "X = np.random.normal(size = 100)\n",
    "y = np.random.permutation(X)\n",
    "data = pd.DataFrame({'X':X,'y':y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coef_1 is [-0.15473722], coef_2 is [-0.15473722]\n"
     ]
    }
   ],
   "source": [
    "lin_x_on_y = LinearRegression(fit_intercept=False)\n",
    "lin_x_on_y.fit(data['X'].to_frame(),data['y'])\n",
    "coef_1 = lin_x_on_y.coef_\n",
    "\n",
    "lin_y_on_x = LinearRegression(fit_intercept= False)\n",
    "lin_y_on_x.fit(data['y'].to_frame(),data['X'])\n",
    "coef_2 = lin_y_on_x.coef_\n",
    "\n",
    "print('coef_1 is {}, coef_2 is {}'.format(coef_1,coef_2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "#both the coefficients are same"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 13. In this exercise you will create some simulated data and will fit simple linear regression models to it. Make sure to use set.seed(1) prior to starting part (a) to ensure consistent results.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Using the rnorm() function, create a vector, x, containing 100 observations drawn from a N(0, 1) distribution. This represents a feature, X.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "X = np.random.normal(loc = 0,scale = 1,size = 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Using the rnorm() function, create a vector, eps, containing 100 observations drawn from a N(0, 0.25) distribution\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps = np.random.normal(loc = 0,scale = 0.25,size = 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) Using x and eps, generate a vector y according to the model\n",
    "### Y = −1+0.5X + eps\n",
    "### What is the length of the vector y? What are the values of β0 and β1 in this linear model?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "length of y is  100\n"
     ]
    }
   ],
   "source": [
    "Y = -1 + 0.5*X + eps\n",
    "print('length of y is ',Y.size)\n",
    "# beta0 = -1 , beta1 = 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d) Create a scatterplot displaying the relationship between x and y. Comment on what you observe.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Relationship b/w X and Y')"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (14,6))\n",
    "sns.scatterplot(Y,X)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.title('Relationship b/w X and Y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (e) Fit a least squares linear model to predict y using x. Comment on the model obtained. How do βˆ0 and βˆ1 compare to β0 and β1?\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "estimated beta0 is  -0.9632466175754496\n",
      "estimated beta1 is  0.5238567834127928\n"
     ]
    }
   ],
   "source": [
    "data = pd.DataFrame({'X':X,'y':Y})\n",
    "lin_model = LinearRegression(fit_intercept=True)\n",
    "lin_model.fit(data['X'].to_frame(),data['y'])\n",
    "\n",
    "print('estimated beta0 is ',lin_model.intercept_)\n",
    "print('estimated beta1 is ',lin_model.coef_[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the estimated values are pretty similar to the true values\n",
    "# estimated ~ [-0.96,0.52]\n",
    "# true ~ [-1,0.5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) Display the least squares line on the scatterplot obtained in (d). Draw the population regression line on the plot, in a different color. Use the legend() command to create an appropriate legend\n",
    ".\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tmp_x = np.linspace(data['X'].min(),data['X'].max(),100)\n",
    "tmp_y = -1 + 0.5*tmp_x\n",
    "\n",
    "plt.figure(figsize = (14,6))\n",
    "sns.scatterplot(X,Y)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Y')\n",
    "plt.plot(data['X'],lin_model.predict(data['X'].to_frame()),color = 'orange',label = 'Predicted Line')\n",
    "plt.title('Relationship b/w X and Y')\n",
    "plt.plot(tmp_x,tmp_y,color = 'green',label = 'True Line')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (g) Now fit a polynomial regression model that predicts y using x and x2. Is there evidence that the quadratic term improves the model fit? Explain your answer.\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.800\n",
      "Model:                            OLS   Adj. R-squared:                  0.798\n",
      "Method:                 Least Squares   F-statistic:                     391.4\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           5.39e-36\n",
      "Time:                        10:54:23   Log-Likelihood:                 4.1908\n",
      "No. Observations:                 100   AIC:                            -4.382\n",
      "Df Residuals:                      98   BIC:                            0.8288\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.9632      0.023    -40.999      0.000      -1.010      -0.917\n",
      "X              0.5239      0.026     19.783      0.000       0.471       0.576\n",
      "==============================================================================\n",
      "Omnibus:                        0.898   Durbin-Watson:                   2.157\n",
      "Prob(Omnibus):                  0.638   Jarque-Bera (JB):                0.561\n",
      "Skew:                          -0.172   Prob(JB):                        0.755\n",
      "Kurtosis:                       3.127   Cond. No.                         1.15\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# withoud x**2 term\n",
    "result = smf.ols('y~X',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.800\n",
      "Model:                            OLS   Adj. R-squared:                  0.796\n",
      "Method:                 Least Squares   F-statistic:                     193.8\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.32e-34\n",
      "Time:                        10:54:48   Log-Likelihood:                 4.2077\n",
      "No. Observations:                 100   AIC:                            -2.415\n",
      "Df Residuals:                      97   BIC:                             5.400\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept         -0.9663      0.029    -33.486      0.000      -1.024      -0.909\n",
      "X                  0.5234      0.027     19.582      0.000       0.470       0.576\n",
      "np.power(X, 2)     0.0039      0.021      0.181      0.856      -0.038       0.046\n",
      "==============================================================================\n",
      "Omnibus:                        0.893   Durbin-Watson:                   2.152\n",
      "Prob(Omnibus):                  0.640   Jarque-Bera (JB):                0.552\n",
      "Skew:                          -0.170   Prob(JB):                        0.759\n",
      "Kurtosis:                       3.132   Cond. No.                         2.10\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# adding x**2 term\n",
    "result = smf.ols('y~X + np.power(X,2)',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "# There is no change in R2 value, showing that adding the X**2 term has not benefited in predicting y.\n",
    "# also the p value is very high(0.856), hence, we cannot reject null hypothesis, and we conclude that y is not dependent on X**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (h) Repeat (a)–(f) after modifying the data generation process in such a way that there is less noise in the data. The model (3.39) should remain the same. You can do this by decreasing the variance of the normal distribution used to generate the error term  in (b). Describe your results.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "X = np.random.normal(loc = 0,scale = 1,size = 100)\n",
    "\n",
    "eps = np.random.normal(loc = 0,scale = 0.01,size = 100)\n",
    "\n",
    "Y = -1 + 0.5*X + eps\n",
    "\n",
    "# beta0 = -1 , beta1 = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For less noisy data - \n",
      "estimated beta0 is  -0.998529864703018\n",
      "estimated beta1 is  0.5009542713365117\n"
     ]
    }
   ],
   "source": [
    "data = pd.DataFrame({'X':X,'y':Y})\n",
    "lin_model = LinearRegression(fit_intercept=True)\n",
    "lin_model.fit(data['X'].to_frame(),data['y'])\n",
    "\n",
    "beta_0_low =lin_model.intercept_\n",
    "beta_1_low = lin_model.coef_[0]\n",
    "\n",
    "print('For less noisy data - ')\n",
    "print('estimated beta0 is ',beta_0_low)\n",
    "print('estimated beta1 is ',beta_1_low)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Data with low noise')"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# data with low noise\n",
    "sns.regplot(data['X'],data['y'])\n",
    "plt.title('Data with low noise')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       1.000\n",
      "Model:                            OLS   Adj. R-squared:                  1.000\n",
      "Method:                 Least Squares   F-statistic:                 2.237e+05\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):          2.16e-166\n",
      "Time:                        11:04:43   Log-Likelihood:                 326.08\n",
      "No. Observations:                 100   AIC:                            -648.2\n",
      "Df Residuals:                      98   BIC:                            -642.9\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.9985      0.001  -1062.519      0.000      -1.000      -0.997\n",
      "X              0.5010      0.001    472.943      0.000       0.499       0.503\n",
      "==============================================================================\n",
      "Omnibus:                        0.898   Durbin-Watson:                   2.157\n",
      "Prob(Omnibus):                  0.638   Jarque-Bera (JB):                0.561\n",
      "Skew:                          -0.172   Prob(JB):                        0.755\n",
      "Kurtosis:                       3.127   Cond. No.                         1.15\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y~X',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "range for beta 0 for low noise data  [-1.0005298647030179, -0.996529864703018]\n",
      "range for beta 1 for low noise data  [0.4989542713365117, 0.5029542713365117]\n"
     ]
    }
   ],
   "source": [
    "beta_0_std_low = 0.001\n",
    "beta_0_range_low = [beta_0_low - 2*beta_0_std_low,beta_0_low + 2*beta_0_std_low]\n",
    "\n",
    "beta_1_std_low = 0.001\n",
    "beta_1_range_low = [beta_1_low - 2*beta_1_std_low,beta_1_low + 2*beta_1_std_low]\n",
    "\n",
    "print('range for beta 0 for low noise data ',beta_0_range_low)\n",
    "print('range for beta 1 for low noise data ',beta_1_range_low)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The estimated values of beta0 and beta1 are more closed to the actual value of beta0 and beta1\n",
    "# (-1,0.5) ~ (-0.998,0.500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (i) Repeat (a)–(f) after modifying the data generation process in such a way that there is more noise in the data. The model (3.39) should remain the same. You can do this by increasing the variance of the normal distribution used to generate the error term  in (b). Describe your results.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "X = np.random.normal(loc = 0,scale = 1,size = 100)\n",
    "\n",
    "eps = np.random.normal(loc = 0,scale = 1,size = 100)\n",
    "\n",
    "Y = -1 + 0.5*X + eps\n",
    "\n",
    "# beta0 = -1 , beta1 = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For more noisy data - \n",
      "estimated beta0 is  -0.8529864703017983\n",
      "estimated beta1 is  0.5954271336511716\n"
     ]
    }
   ],
   "source": [
    "data = pd.DataFrame({'X':X,'y':Y})\n",
    "lin_model = LinearRegression(fit_intercept=True)\n",
    "lin_model.fit(data['X'].to_frame(),data['y'])\n",
    "\n",
    "beta_0_high =lin_model.intercept_\n",
    "beta_1_high = lin_model.coef_[0]\n",
    "\n",
    "print('For more noisy data - ')\n",
    "print('estimated beta0 is ',lin_model.intercept_)\n",
    "print('estimated beta1 is ',lin_model.coef_[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(data['X'],data['y'])\n",
    "plt.plot('Data with high noise')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.244\n",
      "Model:                            OLS   Adj. R-squared:                  0.236\n",
      "Method:                 Least Squares   F-statistic:                     31.60\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.79e-07\n",
      "Time:                        11:18:51   Log-Likelihood:                -134.44\n",
      "No. Observations:                 100   AIC:                             272.9\n",
      "Df Residuals:                      98   BIC:                             278.1\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.8530      0.094     -9.076      0.000      -1.039      -0.666\n",
      "X              0.5954      0.106      5.621      0.000       0.385       0.806\n",
      "==============================================================================\n",
      "Omnibus:                        0.898   Durbin-Watson:                   2.157\n",
      "Prob(Omnibus):                  0.638   Jarque-Bera (JB):                0.561\n",
      "Skew:                          -0.172   Prob(JB):                        0.755\n",
      "Kurtosis:                       3.127   Cond. No.                         1.15\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y~X',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "range for beta 0 for high noise data  [-1.0409864703017984, -0.6649864703017982]\n",
      "range for beta 1 for high noise data  [0.38342713365117165, 0.8074271336511716]\n"
     ]
    }
   ],
   "source": [
    "beta_0_std_high = 0.094\n",
    "beta_0_range_high = [beta_0_high - 2*beta_0_std_high,beta_0_high + 2*beta_0_std_high]\n",
    "\n",
    "beta_1_std_high = 0.106\n",
    "beta_1_range_high = [beta_1_high - 2*beta_1_std_high,beta_1_high + 2*beta_1_std_high]\n",
    "\n",
    "print('range for beta 0 for high noise data ',beta_0_range_high)\n",
    "print('range for beta 1 for high noise data ',beta_1_range_high)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We can see as we increase the noise the estimated values of beta0 and beta1 shift far away from the real values\n",
    "# estimated = (-0.852,0.594)\n",
    "# real = (-1,0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (j) What are the confidence intervals for β0 and β1 based on the original data set, the noisier data set, and the less noisy data set? Comment on your results.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "range for beta 0 for low noise data  [-1.0005298647030179, -0.996529864703018]\n",
      "range for beta 1 for low noise data  [0.4989542713365117, 0.5029542713365117]\n",
      "\n",
      "\n",
      "range for beta 0 for high noise data  [-1.0409864703017984, -0.6649864703017982]\n",
      "range for beta 1 for high noise data  [0.38342713365117165, 0.8074271336511716]\n"
     ]
    }
   ],
   "source": [
    "print('range for beta 0 for low noise data ',beta_0_range_low)\n",
    "print('range for beta 1 for low noise data ',beta_1_range_low)\n",
    "print('')\n",
    "print('')\n",
    "print('range for beta 0 for high noise data ',beta_0_range_high)\n",
    "print('range for beta 1 for high noise data ',beta_1_range_high)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For high noise data, the range is way more wide as compared to the low noise data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 14. This problem focuses on the collinearity problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) Perform the following commands in R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(5)\n",
    "x1 = np.random.uniform(size = 100)\n",
    "x2 = 0.5*x1 + np.random.normal(size = 100) / 10\n",
    "y = 2 + 2*x1 + 0.3*x2 + np.random.normal(size = 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) What is the correlation between x1 and x2? Create a scatterplot displaying the relationship between the variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          X1        X2         y\n",
      "X1  1.000000  0.819369  0.662657\n",
      "X2  0.819369  1.000000  0.583263\n",
      "y   0.662657  0.583263  1.000000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2efd61320>"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JpuCcwrJaTXsUkt4L/BvwDUnrJb2h5u6vpt0ws2YafQIv6yBzkr2ApOZ5eL0nq9cq9fS/gJMi4rXAB4HbJP1R9b5y/BVa1+m2i1iSvYCkUnBOYVm9VqmnKRHxLEBE/EjS6cA3Jc3DO81ZTrpt0bokB+KTSsG5iszqtepR/E7SK8duVIPGW6lsV/qalNtlJZTFEtzddhFLeiA+iRRcNy1VYslo1aO4jLoUU0Rsl7QE+EyqrbLCqx/snD19Kk+MvJB6aWY3lsLOOXSA2y8+hX6J6QP9HD69/V5AGoPOjZYlL1MVmSWv6RIekp4EbgS+HBF7qz87EvgycHxEvKHhL+aszEt4lEWjSp0bP3ASf/3Qz/j2huf2H5fGEtzdNFdgsueS5mvhqqfe0+kSHicBxwHrJL1N0v8AfgT8ADgloYYtkbRR0iZJlze4/5OSNkh6TNJDko5N4nltchqNE1zytbWcfdIxBxyXRkqoNg+/6rLTuefS00oZJGDyg8ZpDjqXtYosbWXc4TAJTVNPEbEV+Eg1QHyHyn7Wp0bEcBJPLKkfuA5YTGX/7NWSVkbEhprD1gFDEbFD0keBq4H3JfH81rlm4wT1qYm0UkL1eytMVFE+LU92vKXbxmuKrpt6sxPVah7F4ZJupFIauwT4OvAtSW9L6LlPBjZFxJMRsRu4g8pA+X4R8XBE7KjefBSYl9Bz2yQ0G+x8+cyBws+OLlJ57WQHjT3onK1eLhtulXr6V+AJKp/ovx0RHwfOB/5S0j8k8NxHA5trbg9Xf9bMh4BvNbpD0jJJayStGRkZSaBp1kqjSp2rzl7EDY/8nM++6wS+/pE3ctclbyzEJ636VMG2ncX5Y59sxVPZly4pm17uwbWqenpzfZopIn4MvEnSxQk8d6MrSMOPdZI+AAwBb2l0f0SsAFZAZTA7gbaVVhZplfp6/X2jwV/+8wa+veE5vv/kFm66YIhXHHZIIYJEo0H3wUOnHfAHn/Qfe7vvwWTnPZR56ZIy6saKu3a1GqNoOhYRETcl8NzDQO3o5zwq4yAHkHQG8GfAWyJiVwLP27WyzKHWjhOMjgZfPGsRf/HfinWxajbo/oWlJ/LBr67ef1ySf+wTfQ8mO94y2d+39vVy2XCey4yvBhZKOg54GjgXeH/tAZJeR6VEd0lEPHfwQ1itvGYtF/Vi1SxVcNzcmfs/GSb9x95tM8ft93q5B5dboIiIvZKWAw8A/cDNEbFe0hXAmohYCVwDHArcLQngVxFxZl5tLrpey6GOl+JpliqYMa0/tT/2XnsPek1RPxSlLdeNiyLiPuC+up99rub7MzJvVIlNJodalJLRdrWT4mmWKpg7M715Ab2cx7bu1XRmdlllOTO7aBfXTscoylgfPrJ9F2ddv+qgC3J9iifr96iMr6UZtJ6Z7a1QO1TEC0KnOdQy5tXbTfFknSro5Ty2dS9vhdqhok6+6WTphTLm1Ys82czLX1i3caDoUBkvrs0U+aLbjCebmWXHqacONRu0nD7Qz8j2XaVKO5SxPtwpHrPseDC7Q43GKG7945PZtXe0UOMW7SrawLyZZavVYLYDxSTUX1yD4I+u//64lThmZkXjqqeU1FfUPL11R2HGLdxDaJ9fK7PWHCgSVJTJVuOV7vrC+HsNFw48/ySOP2IWU6a41sMMXPWUqKJU4rQq3S3SfgxF0HDhwNvW8szzO1N/TXp1tzQrH/coElSUSpxWpbtlnFw3URPpMTV7rZ7bvovpA1NSe02KOGHTrBkHioR1MhM46VRQqxRYlvM/Jntenfz+RC/AzV6rLS/u5qiXHdL+yU7wXILo+oBt3cOppxzUphx+++KuxFNBrVJgWU2um2yKq9Pfn+iM+TkzB7jx/JMO2q3vG2s3J75HRe257NjVPRM2rfu5R5Gx+k+8/+eiN/DZex9P9JNlqxTYnJkD3PrHJ/PLLTuYMdDPjt37OHbOjMTHUSab4ur09yfaY+rrE8cfMYvbP3wKz23fxZYXd3PL93/BJxYfn+oeFb/4zYuFKHwwa4cDRcbqLxozBvpT+WTZKgW2a+/o/uA01ttI2mRTXJ3+fieVZ1Om9DFv9gymD0zhqJcdwuvnL0p9j4q/eegJbvzASVzytbWlmQ1vvSvX1JOkJZI2Stok6fIG979Z0r9K2ivpnDzamLT6i8a2nXsyXWcpq8UMJ5vi6vT3O608S2Mhv7EU41g7ao28sIujDj+Eey49jVWXnc49l57mgWwrrNwChaR+4DrgHcAJwHmSTqg77FfARcDt2bYuPfUXwBse+TnXnLPooAvb7OlTUymdzGowe7KlwpO54I+l3fK8ANeOSyy/fV3D9/jw6QNeZdZKIc/U08nApoh4EkDSHcBSYMPYARHxVPW+0TwamIb6BfhGXtjFkYcdwj9e+ib27B1lYEo/s6dP5YmRF1IpncxqUuBkS4Un8/tF2K6ytuc2vHUnV9+/kS8sPZFXHnEo06f29iRHK588A8XRwOaa28PAKZ08kKRlwDKA+fPnT75lKWrnAjiyfRfXPriRz77rBA6fPpVtO/dw7YMb+eJZiyZ9AcxypdjJXrCLcMHvVH3Pbd3mbXzwq6tZddnppT0n6115BopGH6c6yq9ExApgBVQWBZxMo7Iw3gVwdHSUC990HJd947H9F/Orzl7E6OjkO1Z5TQrstWVDirKci1kS8hzMHgaOqbk9D3gmp7YUyr5gf5CAyhjCZd94jH0JhcCsd2DrxWVDirKci1kS8uxRrAYWSjoOeBo4F3h/ju0pjIhoOOBc1iXhm1Va3XXJG4mIruxhFGU5F7Mk5NajiIi9wHLgAeCnwF0RsV7SFZLOBJD0BknDwHuAGyWtz6u9WSrj1qStNKu0embbzq7uYXjvbOsWuc6jiIj7IuJVEfHKiPhi9Wefi4iV1e9XR8S8iJgZEXMi4jV5tjcr3Za2aBb4xuZupDWXw8yS4ZnZBVT2tEX9wPXs6VMPqrS66uxFfOmBjft/x+scmRWXA8U48qrWKWtpaLPVWxcOHro/8Eni8ysfZ93mbft/r8ypNbNu59VjW+jFap3JajZwvXXnnv35+lccdgifWHx816TWzLqdexQt9MImP0lrZ4mQsqfWzHqNA0UDY+mmHbv3es+ACWp3ollZU2tmvcippzq16aZ/+3/bu6pMNQvdVrFlZu5RHKQ23XTDIz/nqrMXHbCUhi96rTmtZNZ9HCjq1ObY123expceqCzO9+pXzGL6wBRf9NrgtJJZd3HqqU795LB1m7fxhW9uYPrAlK6ZXVu7Z3eSe12YWXdyoKjT7Tl2l/ya2USprAvNNTM0NBRr1qyZ1GOUaUnsibZ1ZPsuzrp+1UFVSd1Q8lum982saCStjYihRvd5jKKBIuTY27noNZsF3WonvKy2Qs1aJ6+FmbXHqacCajc91GxCYKvF9bptZdoxnbwWZtYeB4oCavei10nvoFvHYLq1p2RWBE49FVC7F71Ottvs1nkO3nrULD259igkLZG0UdImSZc3uH+apDur9/9Q0oLsW5m9dtNDnfYOunFDnW7tKZkVQW5VT5L6gZ8Bi6nsn70aOC8iNtQccymwKCI+Iulc4KyIeF+rx02i6ilvExmYdaXP7/m1MOtcUaueTgY2RcSTAJLuAJYCG2qOWQp8vvr914G/laTotpreOhNJDxWhQqso/FqYpSPPQHE0sLnm9jBwSrNjImKvpOeBOcBvMmlhjnzRM7OiyDNQNMoJ1PcU2jkGScuAZQDz58+ffMt6lFM3ZtZInoFiGDim5vY84JkmxwxLmgK8DPht/QNFxApgBVTGKFJpbZfzhDUzaybPqqfVwEJJx0kaAM4FVtYdsxK4sPr9OcC/dPv4RF48Yc3MmsmtR1Edc1gOPAD0AzdHxHpJVwBrImIl8PfAbZI2UelJnJtXe7udJ6yZWTO5TriLiPuA++p+9rma718C3pN1u7JQtPEAT1gzs2a8hEcOirjUtyesmVkzXmY8B0Vd6rtovRwzy05RJ9z1rKKOB3juhpk14tRTDrp1qW8z604OFDnweICZlYlTTzno1qW+zaw7OVDkxOMBZlYWTj2ZmVlLDhRmZtaSU08T4HkGZtaLHCja5NVVzaxXOfXUJq+uama9yoGiTUWdTW1mljYHijZ5NrWZ9SoHijZ5NrWZ9SoPZrfJs6nNrFfl0qOQ9HJJD0p6ovrv7CbH3S9pm6RvZt3Gei6NbWx0NBjZvount+5gZPuuXPfUMLN05JV6uhx4KCIWAg9VbzdyDXB+Zq1qoogbDRWBXxez3pBXoFgK3FL9/hbg3Y0OioiHgO1ZNaoZl8Y25tfFrDfkFSiOjIhnAar/HjGZB5O0TNIaSWtGRkYSaWAtl8Y25tfFrDekFigkfUfS4w2+lib9XBGxIiKGImJocHAw6Yd3aWwTfl3MekNqgSIizoiIExt83Qv8WtJRANV/n0urHZ2oH6CdPX2qS2MbcMmwWW/Iqzx2JXAhcGX133tzasdBmq3ptHDwUJfG1nHJsFlvyGuM4kpgsaQngMXV20gakvSVsYMkfQ+4G3i7pGFJf5h2w5oN0G7duYfBWdM4evYMBmdN88WwamwDJr8uZt0rlx5FRGwB3t7g52uAD9fc/i9Ztgs8QGtmVs9LeNTxAK2Z2YEcKOp4gNbM7EBe66mOB2jNzA7kQNHA2ACtmZk59WRmZuNwoDAzs5acepqg0dFg287d7Ny9j30RHDK1n7kzPX/AzLqXA8UEjI4GT215kV//7iU+/fXHDpi5ffyRsxwszKwrOfU0AVte3M0vt+zYHyTAS2ubWfdzoJiA3Xv3MWOg3zO3zaynOFBMwMCUfnbs3ueZ22bWUxwoJmDOzAGOnTODa85Z5JnbZtYzPJg9AX19YsGcmRw+Yyp3LjuVfQGHTO1z1ZOZdTUHignq6xMvnzkNZubdEjOzbDj1ZGZmLeUSKCS9XNKDkp6o/ju7wTGvlfQDSeslPSbpfXm01cys1+XVo7gceCgiFgIPVW/X2wFcEBGvAZYA/1vS4Rm20czMyC9QLAVuqX5/C/Du+gMi4mcR8UT1+2eA54DBzFpoZmZAfoHiyIh4FqD67xGtDpZ0MjAA/LzJ/cskrZG0ZmRkJPHGmpn1stSqniR9B3hFg7v+bIKPcxRwG3BhRIw2OiYiVgArAIaGhmKCTTUzsxZSCxQRcUaz+yT9WtJREfFsNRA81+S4w4B/Bv48Ih5NqalmZtZCXqmnlcCF1e8vBO6tP0DSAHAPcGtE3J1h28zMrEZegeJKYLGkJ4DF1dtIGpL0leox7wXeDFwk6cfVr9fm01wzs96liO5K6UsaAX6ZwEPNBX6TwOOUSa+dc6+dL/ice0Gn53tsRDSsLO26QJEUSWsiYijvdmSp1865184XfM69II3z9RIeZmbWkgOFmZm15EDR3Iq8G5CDXjvnXjtf8Dn3gsTP12MUZmbWknsUZmbWkgOFmZm11POBQtISSRslbZJ00HLnkqZJurN6/w8lLci+lclp43w/KWlDdQ+QhyQdm0c7kzTeOdccd46kkFT6Usp2zlnSe6vv9XpJt2fdxqS18X97vqSHJa2r/v9+Zx7tTIqkmyU9J+nxJvdL0t9UX4/HJL2+4yeLiJ79AvqprEj776msTvsT4IS6Yy4Fbqh+fy5wZ97tTvl8TwdmVL//aJnPt91zrh43C/gu8CgwlHe7M3ifFwLrgNnV20fk3e4MznkF8NHq9ycAT+Xd7kme85uB1wOPN7n/ncC3AAGnAj/s9Ll6vUdxMrApIp6MiN3AHVT2yqhVu3fG14G3S1KGbUzSuOcbEQ9HxI7qzUeBeRm3MWntvMcAXwCuBl7KsnEpaeecLwaui4itABHRcGHOEmnnnAM4rPr9y4BnMmxf4iLiu8BvWxyylMpaeRGVRVUPry7COmG9HiiOBjbX3B6u/qzhMRGxF3gemJNJ65LXzvnW+hCVTyRlNu45S3odcExEfDPLhqWonff5VcCrJK2S9KikJZm1Lh3tnPPngQ9IGgbuA/57Nk3LzUT/3ptKbZnxkmjUM6ivF27nmLJo+1wkfQAYAt6SaovS1/KcJfUB1wIXZdWgDLTzPk+hkn56K5Ve4/cknRgR21JuW1raOefzgK9GxJclvRG4rXrODfe56SRqadYAAAJ5SURBVAKJXbt6vUcxDBxTc3seB3dH9x8jaQqVLmur7l6RtXO+SDqDygZTZ0bErozalpbxznkWcCLwiKSnqORyV5Z8QLvd/9f3RsSeiPgFsJFK4Cirds75Q8BdABHxA+AQKgvodau2/t7b0euBYjWwUNJx1f0vzqWyV0at2r0zzgH+JaojRSU07vlW0zA3UgkSZc9bwzjnHBHPR8TciFgQEQuojMucGRFr8mluItr5f/1PVAoXkDSXSirqyUxbmax2zvlXwNsBJL2aSqDo5r2TVwIXVKufTgWej+oW1BPV06mniNgraTnwAJWqiZsjYr2kK4A1EbES+HsqXdRNVHoS5+bX4slp83yvAQ4F7q6O2f8qIs7MrdGT1OY5d5U2z/kB4A8kbQD2AZ+OiC35tXpy2jznTwE3SfoElRTMRSX+0Iekf6CSOpxbHXf5C2AqQETcQGUc5p3AJmAH8MGOn6vEr5OZmWWg11NPZmY2DgcKMzNryYHCzMxacqAwM7OWHCjMzKwlBwqzFEg6RtIvJL28ent29faxku6XtE1StywZYl3OgcIsBRGxGfg74Mrqj64EVkTEL6nMVTk/r7aZTZQDhVl6rgVOlfRx4D8DXwaIiIeA7Xk2zGwienpmtlmaImKPpE8D9wN/UF3+2qx03KMwS9c7gGepLDxoVkoOFGYpkfRaYDGVFWk/0emmMWZ5c6AwS0F1F8S/Az4eEb+iMoD9pXxbZdYZBwqzdFxMZeXdB6u3rwf+o6S3SPoecDeVbXWHJf1hbq00a4NXjzUzs5bcozAzs5YcKMzMrCUHCjMza8mBwszMWnKgMDOzlhwozMysJQcKMzNr6f8DjiV+3fOY5HgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = pd.DataFrame({'X1':x1,'X2':x2,'y':y})\n",
    "corr = data.corr()\n",
    "print(corr)\n",
    "sns.scatterplot(data['X1'],data['X2'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) Using this data, fit a least squares regression to predict y using x1 and x2. Describe the results obtained. What are βˆ0, βˆ1, and βˆ2? How do these relate to the true β0, β1, and β2? Can you reject the null hypothesis H0 : β1 = 0? How about the null hypothesis H0 : β2 = 0?\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.444\n",
      "Model:                            OLS   Adj. R-squared:                  0.433\n",
      "Method:                 Least Squares   F-statistic:                     38.74\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           4.31e-13\n",
      "Time:                        11:39:24   Log-Likelihood:                -123.67\n",
      "No. Observations:                 100   AIC:                             253.3\n",
      "Df Residuals:                      97   BIC:                             261.1\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      1.8158      0.162     11.231      0.000       1.495       2.137\n",
      "X1             2.0758      0.488      4.257      0.000       1.108       3.044\n",
      "X2             0.7584      0.817      0.929      0.355      -0.862       2.379\n",
      "==============================================================================\n",
      "Omnibus:                        0.718   Durbin-Watson:                   1.960\n",
      "Prob(Omnibus):                  0.698   Jarque-Bera (JB):                0.574\n",
      "Skew:                          -0.185   Prob(JB):                        0.750\n",
      "Kurtosis:                       2.981   Cond. No.                         12.5\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y~X1 + X2',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>beta0</th>\n",
       "      <th>beta1</th>\n",
       "      <th>beta2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>2.0000</td>\n",
       "      <td>2.0000</td>\n",
       "      <td>0.3000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Predicted</th>\n",
       "      <td>1.8158</td>\n",
       "      <td>2.0758</td>\n",
       "      <td>0.7584</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            beta0   beta1   beta2\n",
       "True       2.0000  2.0000  0.3000\n",
       "Predicted  1.8158  2.0758  0.7584"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tmp = pd.DataFrame({'beta0':[2,1.8158],'beta1':[2,2.0758],'beta2':[0.3,0.7584]}) \n",
    "tmp.index = ['True','Predicted']\n",
    "tmp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [],
   "source": [
    "# since the predicted values for beta1  and beta2 are != 0. We reject the null hypothese for both the cases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d) Now fit a least squares regression to predict y using only x1. Comment on your results. Can you reject the null hypothesis H0 : β1 = 0?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.439\n",
      "Model:                            OLS   Adj. R-squared:                  0.433\n",
      "Method:                 Least Squares   F-statistic:                     76.72\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           5.93e-14\n",
      "Time:                        11:39:57   Log-Likelihood:                -124.11\n",
      "No. Observations:                 100   AIC:                             252.2\n",
      "Df Residuals:                      98   BIC:                             257.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      1.8229      0.161     11.295      0.000       1.503       2.143\n",
      "X1             2.4468      0.279      8.759      0.000       1.892       3.001\n",
      "==============================================================================\n",
      "Omnibus:                        0.357   Durbin-Watson:                   1.986\n",
      "Prob(Omnibus):                  0.836   Jarque-Bera (JB):                0.272\n",
      "Skew:                          -0.127   Prob(JB):                        0.873\n",
      "Kurtosis:                       2.963   Cond. No.                         4.17\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y~X1',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [],
   "source": [
    "# since beta1 != 0, we reject the null hypotheses, also p value is 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### e) Now fit a least squares regression to predict y using only x2. Comment on your results. Can you reject the null hypothesis H0 : β1 = 0?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.340\n",
      "Model:                            OLS   Adj. R-squared:                  0.333\n",
      "Method:                 Least Squares   F-statistic:                     50.53\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.92e-10\n",
      "Time:                        11:41:51   Log-Likelihood:                -132.23\n",
      "No. Observations:                 100   AIC:                             268.5\n",
      "Df Residuals:                      98   BIC:                             273.7\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      2.1250      0.157     13.572      0.000       1.814       2.436\n",
      "X2             3.6070      0.507      7.108      0.000       2.600       4.614\n",
      "==============================================================================\n",
      "Omnibus:                        1.537   Durbin-Watson:                   1.828\n",
      "Prob(Omnibus):                  0.464   Jarque-Bera (JB):                1.597\n",
      "Skew:                          -0.272   Prob(JB):                        0.450\n",
      "Kurtosis:                       2.704   Cond. No.                         5.89\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y~X2',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we reject the null hypothses, as coef != 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (f) Do the results obtained in (c)–(e) contradict each other? Explain your answer.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "# No, we can't say that the reults are contradicting each other. In the combined model in (c), the two predictors were \n",
    "# highly correlated, (that's how they were created, x2 is depencdent on x), and due to this collinearity effect, the \n",
    "# one of the predictors is not able to expain the results. While when we use separate models, there is no concept of collunearity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (g) Now suppose we obtain one additional observation, which was unfortunately mismeasured.\n",
    "\n",
    "> x1=c(x1, 0.1)\n",
    "> x2=c(x2, 0.8)\n",
    "> y=c(y,6)\n",
    "### Re-fit the linear models from (c) to (e) using this new data. What effect does this new observation have on the each of the models? In each model, is this observation an outlier? A high-leverage point? Both? Explain your answers.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = np.append(x1,0.1)\n",
    "x2 = np.append(x2,0.8)\n",
    "y = np.append(y,6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame({'X1':x1,'X2':x2,'y':y})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can make a point here, that for x1, the value 0.1 is within the range of earlier value, however\n",
    "# for x2 and y, 0.8 and 6, respecively, are outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2efe59160>"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data['X1'],data['X2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can see the newly added data point is an outlier, is separately located from the others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.425\n",
      "Model:                            OLS   Adj. R-squared:                  0.414\n",
      "Method:                 Least Squares   F-statistic:                     36.26\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.64e-12\n",
      "Time:                        12:12:01   Log-Likelihood:                -129.50\n",
      "No. Observations:                 101   AIC:                             265.0\n",
      "Df Residuals:                      98   BIC:                             272.8\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      1.8697      0.168     11.111      0.000       1.536       2.204\n",
      "X1             1.2421      0.432      2.876      0.005       0.385       2.099\n",
      "X2             2.2711      0.698      3.254      0.002       0.886       3.656\n",
      "==============================================================================\n",
      "Omnibus:                        0.673   Durbin-Watson:                   1.803\n",
      "Prob(Omnibus):                  0.714   Jarque-Bera (JB):                0.465\n",
      "Skew:                          -0.165   Prob(JB):                        0.792\n",
      "Kurtosis:                       3.035   Cond. No.                         10.2\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y~X1 + X2',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.363\n",
      "Model:                            OLS   Adj. R-squared:                  0.357\n",
      "Method:                 Least Squares   F-statistic:                     56.46\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           2.60e-11\n",
      "Time:                        12:13:58   Log-Likelihood:                -134.68\n",
      "No. Observations:                 101   AIC:                             273.4\n",
      "Df Residuals:                      99   BIC:                             278.6\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      1.9419      0.175     11.116      0.000       1.595       2.288\n",
      "X1             2.2829      0.304      7.514      0.000       1.680       2.886\n",
      "==============================================================================\n",
      "Omnibus:                       12.832   Durbin-Watson:                   1.773\n",
      "Prob(Omnibus):                  0.002   Jarque-Bera (JB):               21.470\n",
      "Skew:                           0.522   Prob(JB):                     2.18e-05\n",
      "Kurtosis:                       5.003   Cond. No.                         4.14\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y~X1',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2f3167080>"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(data['X1'],data['y'])\n",
    "# in this case, the point is 'outlier, since it has a very high value of y'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.377\n",
      "Model:                            OLS   Adj. R-squared:                  0.370\n",
      "Method:                 Least Squares   F-statistic:                     59.84\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           8.79e-12\n",
      "Time:                        12:14:05   Log-Likelihood:                -133.59\n",
      "No. Observations:                 101   AIC:                             271.2\n",
      "Df Residuals:                      99   BIC:                             276.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      2.0962      0.154     13.604      0.000       1.790       2.402\n",
      "X2             3.7581      0.486      7.736      0.000       2.794       4.722\n",
      "==============================================================================\n",
      "Omnibus:                        1.784   Durbin-Watson:                   1.803\n",
      "Prob(Omnibus):                  0.410   Jarque-Bera (JB):                1.826\n",
      "Skew:                          -0.299   Prob(JB):                        0.401\n",
      "Kurtosis:                       2.726   Cond. No.                         5.68\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "result = smf.ols('y ~ X2',data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2f0c5ff98>"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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j9tlogu8mN9YYm5lv/HX1+kb2Dvbxscs7yrqxhsc137XRXeVBPZMEeAFUx4g4W6laAazUgzf288X9rzMZiuNQVsOrhKG5MBejvd5DOG7Y+oZa6OuTyrEXM7CfmYrw+MEg33vzDOFktY1Dwccu72DvYIBrepqLcp6VWG0r3mogAV4A5RkRl6OOvZTVLLs2d9HZ4GU2ksDQGo/TQWejF6dDoZQibpgV8YZqR+veI6PWxho/OXZuvvGX28HtW6yNNXpa6opynkKthaCeSQK8SCvliLiUVTvlrBCaiSa4vKthwcIXra2A+qef21LWFFOxW/capuZn759n31CQw6en08c7Gjzcvb2XO7b20OArfchxORzUe50lae5VaSTAi7IoZdVOrmoWO0f2y81tlCvFpLVmJppgci5elCZg4ZjBM2+d4fGDQUanIunjl3c1cO9ggF1XdJZ8srKaatXtJAFelEUpq3aWOtexsRnbR/aVNrcxE4kzGYoTN1Yf2M/NRHnq0Ajffn2U2YxFTx/pb2PvQIBtfaVv/JXajLqaatXtJAFelEUpq3aWOlcsYdJcZ++niEqp9pmLJhifixUlsL8/Nsu+4SAvHB0jkUzteFwOPnX1OvbsCLChvbSVVy6HwwrqaySvXggJ8KIsSjmyXepcqT4tmbI/RRRjcrac1T7hmMF4KJZuBPbK8XG++eopRqfDrC+g26OpNa9+MM6+oSAHT06mj7fUublzew+7r+uhxV+6xl9Oh0ouQHKt6RRMLrYHeKWUExgCRrTWd9h9PlEdSjmyXepcj7x4fNlPEdXWviFTJG4wEYoRjs03Anvl+DgPv3AMl0PR5HNxYS7Kwy8c4wtsWjLIR+MGzx0Z4/HhIB+Oz7/xXdLuZ8+OAJ+8el3JRs0uhwO/1ylBvQClGMF/ATgCNJXgXKKKlHJku9S5lvsUUW3tG2DxwJ7yzVdP4XLMf2pJ3fM3Xz11UYCfCMX41qHTPH3oNJPh+d4zAxta2DvYx/UbWy/Kr6/008Fy3E4H/mQPmHL3Vq9GtgZ4pVQA+CXgz4B/Y+e5hCjUrs1d7AlO8rWfnmAuZlDvcfIbH7s0HbyrqX1DOGYwGV48sKeMTodpyipT9LkdnJme3/Luwwtz7B8e4Qdvn0lvrOFyKG65qos9OwJc1tWw6HOv5NPBUlJljRLUV8/uEfx/AX4fqIx2cEJkOHB0jP0HR+hs9LIhOZrdf3CErYEWdm3uqor2DaFYgslQPK+e7Oub6rgwF10w7xCJm6xr9HHwpLWxxs9PjKe/1+hz8dmt67lzey8dDcs3/irk08FiHErhl7LGorMtwCul7gDGtNbDSqldyzzuAeABgA0bNth1OUJcJFcKJt+J4HKskl3JLkr3Xd/Hwy8cIxw38LkdhGMGM1EDw9R8cd8b6cf1tPi4Z0eA27Z0XzQJvZR8Ph0spi65EXWD11VRe6nWCjtH8B8Fdiulbgd8QJNS6h+01r+a+SCt9aPAo2Dt6GTj9QixQK4UzHITwamgfmxshplIgla/m44Gr+0TsaGYVe4YSxRe7rizv40vsIl/+PmHfHBhjmjcJJ5sUwBwbW8zewcC3HBZe8GNv5b6dNDddHFLArfTQWOyrHG5BVDVtAFNpbItwGut/x3w7wCSI/gvZgd3IcopnxTMYpOzmdU1oWgCU1sNxLwuJ011blsmYrPLHVdiZDLMyycu8N7YLJHkG4RDwU1XWBtrXLV+5XUQ2Z8OInGThKm57/q+5HkKS8FUcwVTJZE6eLFmrbQWPzO1Ezc1TodCm3B+NkpTnbuoE7Gr3fdUa83h01bjr5+9dz69sYbf4+T2a7u5e0eA7ibfqq8z9engm6+e4sx0mO5kFc2NV3bS6LPq1QtZWVqNFUyVqCQBXmt9ADhQinOJ6leqj+YrrcXPTO14nA4SpkYpiCVXiRZjIna5csd8GKbmJ8fOs2/4FEdGZ9LHuxq93L2jl9uvXU+Dt7j/++/sb2Nnf1u6Y2ODb+W91aupgqmSyQheVJRSfzRfSS1+Zmqns9HL6ckIJlY74FAssaoVuZG4wWQoTii2sg2tQ7GE1fhreIQz0/ONv65c18jewQA3buooWuOvBXXvzXV8/oaNfHpLd1GqYKqhgqkaSIAXFaUaPppnpnYavC7aG9yMz8WpczvoavSt6BNHNGEwMbfywD42HeGJ10b47hujzCVH/Qr4xcva2TMYYGtvc1GrVFJ1726nos3vYToc4y9++C4tfnfFbDkoJMCLClMNH82zUzsb2xv493etLI0US5hMhGL86MjYilaBvnt2hseGghx4Zyy9sYbX5eC2a7q5Z6B32RHvSleeOpRi33AQn9tBg9f6XbmSn16K9UZcKU3aqp0EeFFRquWj+WrbLMQSJpOhGLPRRMGrQE2tefn4BfYNBXk9OJU+3lbv4a7tPdyxtYfmrDfJbCtZeZpZs352JmL7G3Glb8lYDSTAi4pS6x/NMwN7Sr6rQCNxgx+8fZb9w0GCE/MLiPo76tkzEOATm7vybvyV7zm97vmgnlkbn/1GPBOJc2Yqggbuf/RlGW1XCAnwIi+VXtlSKbJfpxv623jp+Dgnx+fobqpj70DgohFyrlWg43Mxnjo0whMHRwhlVNVc0dXAb3z8UgYuubjxVy7LnTOf/uqZb8QJw2Rk0prQ7W3xSc16BZEAL3KqhsqWSpD9Op04P8vPT1ygo8FDc/J1WywNstQq0OY6D3/+/Xd4/ujZdOMvgCaf1S53JprANFnR5OlF51QQi5tsaKvPa8OOzDfigycncDkV6xp9NCXTNpU2Mb5WyfYnIqfMyhalrD/dTpXe01RYsiuApsNxHApmIgkUVjrE5VB889VTC37uvuv7SJiacNzA1Nak69mZKO+cneH7h62ujs5krry/3U93k49mn3vR58pX6pzRhIHToUgYJhrFb++6LO/n2LW5i2888BE6G71c3tmQDu5QeRPja5UEeJHTqYlQzp2PhPU6+VwO4oZJLPmfUizYJm+xBlw7+9v4nZuswPrBhTDnZud7zQRa6/i9WzfRXu9mXZN3QQ17Ps28FuN2Ovj0lm7+9HPX0NPiZzaaYF1THQ/tvmZFI+6+Vj/hrJW2lTgxvhZJikbkVC2VLeWUMEy6m3ycnY6k3wzdTivYZ67mzG7ANRWO8+3XT/PUodOMz8XSx68LNLN3MMBH+ttxKMWBo+fybua1GKUU9R4njb75XjC3Xt3NrVd3r+h+M+caGjxOppMNy2pxYryaSYAXOdV6Zctq/PDtM/z1j61AV+9xpatjfG4H9R4n4yGTBq8TjV7QgCs4EeLx4RG+f/gM0YzGXzdf2cXewQBXrFu4hUKuZl5LqUvuhtRQYC+Y5WTPNYTjBhqrbcNUOF51E+O1TAK8yKmUlS3V0iI2mjB45o1RvvLsO+la8kjcCtRuh2ImkiDQWs9ntzbz2qkpzkyHWdfo4xf623n6jdO89P6FdOOveq+TO65dz13be+laovHXUs28FqtZdzmsdryNvuXb8a7UYquNAVr8Hp75vRuLfj6xchLgRV5KUdnylz98l68eeB/D1HhdDhKGuaBapxKCfzRh9YqZiyb4+j9/eFEtOUBTnYevff669M/cb5j8+N3z7B8O8uhP5iemu5t8ycZf3QvSX0tJNfNaTCoF0+Bz5fVcq1ENq42FRQK8WFapguqBo2N89cD7mFrjcigShtVjvb3ek67WKWd/8EjcYCpsBfaU0ekwTgWnJqLpXHur352e+JyNJvjuG6M8+doIYzPR9M9dtb6RvQN9fHxTR8Eba2RbaiGSnWROpnpIgBdLKmX9+yMvHidhWkFSoVAKMK0Sw+BEqGxNyJbbzLre7eTD8RBoMIGEaRKeitLhd/HfDrzH9948s2BhUnOdm//t+j725sib51KMdryrIXMy1UMCvFhSKYPqqYkQXqcDQ0Nq3Y5SEE2YBFr9JU8L5LXnqVKYGrL3mTwfSrB/eMR6CFaOvb3eg6nhqddPc0l7fV5NvTK5nQ7qvS7qvU68roUlq6VOXVX7auO1RAK8WFIpg2pfqx/DNLkwG8fE2kDD0NYCnwdv7OeRF4+XJC0wF00wGc5vM+u5WAKnAxbbHtXtUHQ0eHEoqPcuvObsfi9LcShFvdeaLPUtsfl1uba2q9bVxmtNzs93Sqn/XSnVWoqLEZVluQUsB46Ocf+jL/Oxr7zA/Y++zIGjY6s614M39uN2OmlvcONMLg5yKMXv7LqMXZu7ePDGfuKGJhRLoLVe9cYamczkxtOnxkOcnY7kFdzDcQOXw7FEcIe2ejcmGr93YWDOZ3GSz+2ks9HLhjY/nY3eJYM7yCpjsbx8RvDdwKtKqYPA3wLPaq2zP5WKGrRUrvWG/raijxoXfOx3XPyx3460gGFqpsNxpiNxDDO/f9LnZ6M89doI335jlJnI/ISrUlYdu9LQ4nezvtn6ZJHv4qR8GnwtRipaxHJyBnit9R8ppf5v4FPArwP/VSn1GPA3Wuv37b5AUT5LBdWvfP8oY9MRDG1tU9fZ6E2PGlcTcHN97C9WWiBhmEyF48xEEph5jlXePzfLvqEgLxwdI5F8M3A7FZe213P8/CymttIyVu25M70AabnFSdaI20njKkobpaJFLCevf1Vaa62UOgOcARJAK7BfKfWc1vr37bxAUV7ZQfXA0THeHZvFqbCaVJma05MR1jd7K37UGDdMJkNxZqNWmicXrTWvfDDO/qEgwycn08db6tx8blsPu7f10Or3pHdGWmwB0mKLkz66qYMmn5sG3+pLG6WiRSxH5fqHrpT6XeDXgPPA14CntNZxpZQDOKa1zr/9XA6Dg4N6aGioWE8niiSzSmM6HCcSN1Co9NJ3U2sUsH1DK9944CPlvdhFxBImk+EYL7yd37Z4sYTJc2+fZf/BIB9emH/TuqTNz56BALde1YV3mbz4YpRS1HudNPncy+bUVyL1+5GKlrVJKTWstR5c7Hv5jOA7gLu11h9mHtRam0qpO4pxgaJyZVdpjE6F0clSRpdp/am1JqErb9SYuTgpny3qJkMxnn79NN86dJqJUDz9PDs2tLBnIMDOS9twFNh73e10FG20vhSpaBFLyScH/+VlvnekuJcjKk12LbzP5SRmmDgAl1MRM0ycDkV/W31FBBmtNXMxK7BnVsMst0Vdd7OP/QeD/ODts+k2vS6H4hObu9gzEODyroaCrmGxzo1ClIPUwYtlF8pkV2l0NnoZmQhjAJs66tM53y995qoyXb3FMDUzkTjT4QQJ8+Laxewt6rTWmFpz5Mw0n//6q+njjT4Xn926nju399LR4C3oGtxOq8lXg9eeJl9QPc3YRGWQAL/G5Vook12l0ehz09FoMBc1KqI1bCRuMB2OMxczlp04TW1R53M5mIkmV6lmFLH3tPjYsyPAp7d0X7S5SS5+j4umOvubfJVrUZOoXhLg17hc7QgWq9JwO5385X1byxpUZqOJi9Iwy9l9XQ//+fl3CUUTZGxvysZ2P7/+0Uv5xcvaC8qRp+rWm2xqybuYcvXjEdVLAvwal2uhTCX1HTFMzWwkwXQkvmAbvOWcngzzxMERvvfWaLpfO1iljr+ycwP3DAYKuga/x5WsW3euaLPr1ZBFTaJQEuDXuHwWypS7SiOaMJgOJ/KuXwc4fHqKfUNBfvreeVKLVP0eJ7df283d2wN0Ny++scZiSpFbz4csahKFsi3AK6V8wIuAN3me/VrrP7brfGJlKnmhTChmpWEWa9W7GMPU/PS98+wbOsXbozPp450NXu7e0csvbV1Pgze/f/JL1a2Xc5Kzkn9XojLlXOi04ie2Pr/Wa61nlVJu4KfAF7TWLy/1M7LQqTwqaaGMaWpmogmmw/mnYUKxBM+8dYYnDo4wOhVJH9/U1cC9gwFuuqIz75F3arTe6HNflJPPnOTMDLAP7b6mZK9XJf2uRGVY7UKnFUk2JJtN/tWd/K/qm5TVYplauVMwYK0enY7EmS2gP8y5mShPHAzynTdHmYtao3wF3HBZO3sHA2ztbc47T55PJUwlTHJWwu9KVA9bc/BKKScwDFwOfFVr/fNFHvMA8ADAhg0b7LycVZMyteJbbCu8XN49O8O+oSAH3j2X7gLpdTn49DXd3LOjl762/HLSToei0XXsRukAAB12SURBVOemMc+dkWSSU1QbWwO81toAtimlWoAnlVJbtNZvZT3mUeBRsFI0dl7PalXCCK4WpFabpvra5MPUmp8fH2ff8CkOnZpKH2/1u7lzey+7t/bQ7Hcv8wzzvG6rg2Oj11VQJYxMcopqU5IqGq31pFLqAHAb8FaOh1esYo/gajHds5yEYTITSTATWXy16WIiccNq/DUc5NTE/EYZl3bUs2cgwC2bu/Lqn+50KBq8Vm69kH7rmWSSU1QbO6toOoF4MrjXAbcCX7HrfKVQzBFcqdI9lfAmku9q00zjczG+dWiEbx06zXTGxhqDl7SydzDA4CWteY2+PS4HTXXugkfri6mkNQGZKuF3LCqTnSP49cDfJfPwDuAxrfV3bDyf7Yo5gitFuqeccwamqZmNWaP1fFebApw4P8f+4SA/PHKWuDG/scYtm9exZ6CX/s78Gn/5PS6a64rf7KvSJjllXkgsx84qmjeA7XY9fzkUcwRXigm7cswZROIGM5EEc9H8q2G01gx/OMH+4SCvfDCRPt7kc7F7Ww93buulrd6T83kcytpRqanOndekaS2QeSGxHFnJWqBijeBKMWFXqqqPVO36TCSebrebj1jC5EfvjLFvOMjxc3Pp44HWOu7ZEeDT16zLa3MMl8NBc51VDeOwqed6pTo2NkMomiBuzm+f2OB1SWWPACTAl00pJuzsfhNZyabVANPhON9+4zRPvXaaC3Ox9PGtgWb2DgS44bL2vDbW8LmdNNW5qS9DX5hKcODoWHpf2cztE9sb3GxsL6yHvahNEuDLpBQTdsV6E8mexPv1X9zIjo2tBS1KAhiZCLP/YJBn3zpDJDnSdyi4+UprY40ruxtzPodSVjVMU50Lr2ttb6bxyIvHafW7uTAXQyd31zLRjM/F+fd3SWWPkABfVnZP2BXjTSQ1iedyQKPXxchkiD/+9mG+8IlNi+5nmk1rzZsjU+wbDvLP711IL2Wu9zj5pa3ruXt7L11NuRt/OZSiqc5d0va8le7URIiOBi9el5Pzs1FihonH6aDO7ZD8uwAkwNe81b6J/PWP38ehwOV0YJgan8uJ1tZWd8sFeMPU/Pjdc+wbCvLO2fnGX+uavNy9I8DtW7qpz6PxV3Z+XUoC56VScE11bpqScy2hWIKuxvw7ZYraJgFeLCpVu37iwpy11V1GJsbndnBmOrzoz81GE3zvzVGeODjC2Ew0ffyq9Y3sHejj45s68tpYw+100OxfWL8uJYELycIrkYsEeJG22IbVqa3uMrexi8RNupvqFvzs2ekITxwc4btvjhKKzTf++timDvYOBNjS25zXNXjdTlrq3IuO7qUkcKFKXXglKocEeEEkbjAbTSw6aXrf9X08/MIxwnEDn9tBJG6SMDX3Xd8HwNEz0+wbCvLjd8+lN9bwuRzctqWbewYC9LbUZZ9uUX6Pixa/e9mySGn2dbFKW3glKosE+DVKa81sNMF0jpWmO/vb+AKb+OarpzgzHaa7qY57BwPEDJMvfPM13hyZTj+2vcHDXdt6+ex162n05W78pVILk/LsDyPNvoQojAT4NSZhmExHrEVJ+dau7+xvY2d/G+G4wbNvneGrB95nZHI+B39ZZz17B/u4+crOvFaQpipimusu3lRjOZJzFqIwEuDXiEjcYDoSZy6af8OvlAuzUZ46dJpvv76w8dfOS9u4dyDA9g0tyy40euX4ePoTQKDVz2/fdBmfuHpdwfcgOWchCmPbln0rIVv2FZdhWmmYQlsIpBw/N8u+4SDPHxkjYc43/vrk1evYMxBgY3t9zud45fg4f/nCMTwuB/UeJ5GEyVQ4TmeDl5loYs2XOgqxWmXZsk+UTzhmMBMprD1vitaaVz+YYN/QKYZPTqaPt9S5+dy2HnZv66HVn7vxF1iteh9/LYjP7aDea+XkE4bBZMjamu/yroY1X+oohJ0kwFeR5Rb5GKZmJhJnJpLIe7PqTLGEyQ+PnGXfcJAPL8xXpWxo87NnIMAnr+rCm0fjL1jYqnd0KrKg8uX8bBSHAkNrlFJrvtRRCDtJgK8SSy3y+cO4wbZLWgmtYLQOMBWK863XrY01JkLx9PHtG1rYOxBg56VteTX+Amjwumj2uxf0iMmufIkZJgrwZEzGVlupo6ymFdVCAnyVyFzko7XVGjZuJPirHx/nL375uoKf7+R4iMeHgzz79tl0ft7pUNx8ZSd7BwJsWpe78RdYpY71XictdZ5FSx2zK1+cDkXC0HQ2etOPqaZSR1lNK6qJBPgqcXJ8jiafm7hhYiYnPL2upVsGLEZrzevBKR4bOsXLx8fTxxu8Lu7Yup67tvcuCLzLSdWwt9S5l23+lV35srHNz4W5GE6HQmtdNaWOqVH7wZMTKKC72ScpJlHxJMBnqMSP3qlVpl2NPs7P5m4ZsJiEYXIg2fjr2Nhs+vj6Zh/37AjwmS3deW9tp5SiyWfl2PPt6pi92jL1OldLqWPmqN3UGgWcnozQ0wKNPnfVpZjE2iEBPin1P3HcMJgKxRmdCnPw5AS/s+syfvfWK0p6LdGEwVzUYC46P2H6y4PLtwxYzGwkwXfeOM0Tr41wfnZ+Y40tPU3sGQzw0cvya/wF833YW/35B/alFGN5fSnfjDPTYx6ng4ShQcG5mSiNPndVpZjE2iIBPumRF48TNwwuzMZRyupmaJiarx54n62BFttHmIapmY0kmIkuXrO+WMuA+67vW7Rl7+hUmMeHR/jeW6NE4vMba3x8Uyf3Dga4an1TQdfW4HPR6veUbJ/TXMG71HnwzB44HQ1eTk+FURqiCZNQLFEVKSaxNkmATzo1EWIqZAX3VNWIU0HC1LbmVwupWU+1DFjK4dNT7BsK8tP3zqcbf9W5ndx+bTd37+hlfXN+jb9SGrwuWvyLT57aJZ/gXequkpmVQKm+62dnIiit6Gr0VXyKSaxdEuCT+lr9jE6FF4xStbYmMoudX40lTGajiQUpmJUyTM1P3zvPvqEgb4/ON/7qbPBy145e7rh2PQ2+/H/NqVRMi99t64h9qVF6PsG71F0lsyuBXE4rsD+0+xoJ7KKiSYBPevDGfg6enMAwNU5lBXcTTaPPXZT8atwwCUUNZmPLd2/MVyiW4Jm3zvDEwRFGpyLp45u6Grh3MMBNV3QWlCvPtypmKYXkxJcbpecTvEvdVVJ64IhqJQE+adfmLn5n12V89cD7JEyN1+Wg0efG43KuOL+aMEzmihjUwZrYe/K1Eb79xmnmovMba9xwWTt7BwJsDTQv2/grW67Ank/gLjQnvtwoPZ/gXY6uktJ3XVQjCfAZfvfWK9gaaFnVSM0wNXMxa/OMSJGCOsCxszPsGw7yo3fOpdv8elwOPn3NOu7ZEWBDW2Gj13yqYhYL3F/c//pFjcIKzYkvN0r/089tyRm8VzKirsQSWCHsJgE+y0pGamYyqM9FDcLxxSdLUy1zR6fDrF+mAmbB82rNKyfGeWwoyKFT842/Wv1u7tzWy+7remj2595YI1u+VTHZgTth6EUbhc1F4xdN4C6XE19ulJ5v8C7k9ySrT8VaJQF+FcIxg5lo7h7rrxwf5+EXjuFyWIuELsxFefiFY3yBTYsG+Wjc4LkjZ9k/PMLJ8fkgeWlHPXsGAtyyuWtFlS2FVsVkj7SXahQWN6wVqfnmxHOlWIqdDpG9XMVaJQG+QCupgPnmq6dwOVR6FWoqqH3z1VMLAvxEKMa3XjvNt14/zVR4vvHXwCWt3DsYwDQ0/zQU5O9f+iDvTwGwsAlYIamKvlY/H1yYZTqcIGaYJAyN08GCZmJ1bicel4O4ofPOiZd60lL2chVrlQT4PKQmS5dahJTL6HSYpqxSRZ97vo/MBxfm2D8U5LkjZ4kb1icBl0Nxy1Vd7B0I0N/ZYG2c8aP38v4UAFCfLHdMBeRCUxU39LfxygfjOJS1UAogYUK7d+FIfVNXYzoXn2/ALuWkpezlWp1k3mT1bAvwSqk+4O+BbsAEHtVaP2zX+YpNa81czGA2kiAUS+T+gWWsb6rjwtzCPjLhmEG9x8WXnniTV07MN/5q8rn47HU93Lmth/aG+cZf+X4KAKjzOGn1e/Bl9W8vNFXx0vFxOhs8zESsEbzHqUiY2tqRqdG7YKReyVUmspdr9ZF5k+KwcwSfAP5PrfVBpVQjMKyUek5r/baN51y1aMJgJmKlYPLdlDqX+66f7yPjdSnG5+JMRxIkTM375+cACLTWcc+OAJ++Zt1FgRlyfwoA8LqdtPk9SzYOKzRVcWoiREeDl85GX/rYdDjGmekoU+G4ramVYo7epI69+si8SXHYFuC11qPAaPLrGaXUEaAXqLgAHzdM5qKJFe+GlMvO/jZ+M3Yp//0nJxiZDJP5vnFtbzP3Dga44bL2ZTfWWOxTQKqbpNvpoLXeQ4N3+V9noamKxR7vcjrYsaGVbzzwkVy3vWIHjo7xxf2vM5t8kz0/G+WL+1/nP+25blVBfqU/K6mC0pN5k+IoSZMRpdRGYDvw80W+94BSakgpNXTu3LlSXA5g5dWnwnFGJsOcGg8xPhezJbiPTIR5+Plj/Pmz7zA6HcHUVj775is7+W+/sp2H79vGRy/vyLlr0n3X95EwrWoVjfVnwtT85scvJdBalzO4g5WqSE2Gaq1zNsoq9PHF8h+eOcJkKI42wakU2oTJUJz/8MwRW8+7mFSqYGwmsiBVcODoWMmvZS3pa/UTzlpHIvMmhbN9klUp1QA8Dvye1no6+/ta60eBRwEGBweLkxNZQqpefTaaIBwr3iKkbFpr3hqZ5rHhU/zzexdI3VS9x8nt167n7h29rGvyLfsc2bK7SQZa/fz2rsv4xFXr8n6OQlMV5UptnLgQsiZ2kzO7SoE2NSculH70ZleqQD4VLE/mTYrD1gCvlHJjBff/pbV+ws5zLSW1a5BV2riyfUvzZZianxw7x2NDQY6emUkf72r0cs9AgNu3dFOfx0g7W+YiqUCLnz+781puuTr/wJ6p0FRFJU+eloIdqQKZQMxN5k2Kw84qGgX8DXBEa/0Xdp1nKeGYFdRDseJNli5lLprge2+d4YmDQc5OR9PHr+xu5N6BADde0Zn3xhrZUoukPC4HHfUeJsMx/p/vvI3ToWr2H3t/Rz3HxmZRWlujdw2mhk2d9SW/FjtKLGUCMT9rfXBRDHaO4D8K/AvgTaXUoeSx/0tr/T27ThiJW7sgzUUNEmbx8+nZzk5HeOLgCN97c5S52Hzjr1+8vJ17B/rY0ttUUOOvbEop9g0HqXM7qPdao0i/x1HzweAPbtvMv93/OjORBAnDxOVw0Op38we3bS75tdiRKpAJRFEqdlbR/BQr3tkqlrAqYGaL0Fs9X0fPTLNvKMiP3z2XrojxuRzctqWbe3YE6G0tbGONxaT6xZxNTu5lKmcwsCt3nP28/+Ijl/DS8fGyfzy3I1UgC69EqVTlStbVrixdCcPUvPT+BfYNB3lzZCp9vL3ew13be7lj6/r0bj8rtdhmG6sJBsUOxnbljhd73v0HRypmQ41ipwpkAlGUStUEeK01s1H7K2CyReIGzx4+w/7hEUYm5xcV9XfWc+9AgJs3d61656PlWveuNBjYEYztyh2vtZy0TCCKUqn4AB+Jz68sNW2sgMk2PhezNtZ4/TTTkflWBTsvbePegQDbN7SsKr+eUu+1UjFLdXhcaTCwI2jalTteizlpmUAUpVCRAT5hWB0b7VpZupz3z82yfzjIC0fH0o2/3E7FJ69ex56BABvbi1PJsVS/mMWsJBjYETTtyh1LTloIe1RUgDe15sxUZNXNvQqltWbowwkeGwoy/OFE+nhznZvPXdfD7m09tNV7inKuXP1iisWOoGlX7lhy0kLYo6ICfGpZfKnEEibPHznLvuEgH2SskuxrrWPvYIBPXrUObx4j7Hx4XA5a/Z4VLXTKls/kqR1B067cseSkhbCHsnNlZ6Gu3bZDf+u5F20/z4+OjPHff3qCsZnIgsZf2/pauHcwwM5L23L2hslXMQM7LJw8zQzci1WcpN4IFguaq6mwkWX2QlQOpdSw1npw0e9Ve4AvZK/Tk+Mh/urA+/w8o/86QJ3bwW98rJ+7dvSu+NqzFTuwp9z/6MsXpV5CsQRdjb68OzwW8iZRzJ8VQhTfcgG+JN0k7ZJaxn9hLrpgl6NXjs8HcK01r5+a5A+ffIvP/49X08HdoazNqy9t99PR4OUnx84X5Zq8bifdzT4Crf6iB3ewJk/rstJGhU6eZlbYpPZWdTsVj7x43NafFUKUVkXl4Au13C5HOy5p4cfvnmPfcJB3z86mf8apoK3eQ7PPne5W6HLqBRtnrITX7aTV714wsrZDMSZPV1NhsxZLGoWoVlU9gh+dDuNzL7wFt1Px/rkZfuVrr/Bn3zuaDu7X9DTxJ5+9mi09zfjcznRwh/mNM1YiNWLvbamzPbhDcXq0r6bXtvTpFqJ6VHWAX99URyRu1cnHDZOxmSgnzoeYiRqcm43iUHDjFR381/u38//dv50br+jk/p0bFt04477r+wo6d6kDe8quzV08tPsauhp9TIXjdDX6Cs5/r+ZNolybgAghClfVk6yvHB/nP/7gHUIxY8Go0uN0cMd167l7ey89LRePzFMTs2emw3TnmJjNVqpUjN1SlTDHzk4TMzQel4NNXY15VcQsV50jhCitmquiMUzNz947z77hIIdPz28S5XYqbt28jt/adRkNvuIG4FoJ7JmkIkaI6rdcgK+qaBWOGTzz1hkePxhkdCqSPl7nduJ2KS5tq+emKzqLGtzdTgdt9cUvd6wEa63JlxBrTVVErXMzUZ58bYTvvDHKbHR+petV3Y2cnYngdzup8zgZD8V4+IVjfIFNeadcluJyOGipd9PkW10L4EomFTFC1LaKDvDvjc3y2NApfvTOufS2ex6Xg09dvY49OwL8lx8eo97jWrRMcqUB3qEUzXVuWvzuonSLrGTS5EuI2lZxAd7UmldOjLNvOMhrJyfTx1v9bj63rYfd1/XQ4rcaf41Oh2nKSsf43I4V17Q3+tyL9mSvVbXY5EvaKAgxr6IC/FQ4zr/8+hAnx+dTBJe0+9k7EODWq9Zd1DN9fVMdF+aiC1Z2rqSm3e9x0Va/dE/2WlVrTb7s2nFKiGpVUQH+7HQERzK4D2xoYe9gH9dvbF0yVXLf9X08/MIxwnEDn9tBJG4WVNPucTlor/fa3rq3ki3Xa77aRsMyaSzEQhUV4BXw6WusjTUu62zI+fid/W18gU0F17S7HA5a69001vAE6mpV42hYJo2FWKiiAvylHfX8wW2bC/qZnf1teU+oOpSixe+mua72J1BXqxpHwzJpLMRCFZV0tmtyUylFU52bvjY/LX6PBPc8FKNrZalJGwUhFqqoAG8Hv8dFb0sdHQ1enA4J7PmqxqZixejTI0QtqagUTTGVau/TWlWtJZQr2aBciFpVcwHe7XTQWu+hoQZbC5RSrZVQCrEW1UwUdDoULXUemupckmMvEhkNC1Hdqj7AO5ITqC117gWbeAghxFpn2ySrUupvlVJjSqm3bHp+murcBFrraKv3SHAXQogsdlbRfB24zY4nbvC5CLRalTFrpW+MEEIUyrYUjdb6RaXUxmI+Z73XRat/7fWMEUKIlaiKHHydx0mr34PPLSWPojiqrc+OECtR9gCvlHoAeACgJ7CwSZjUsudPAlb+qrHPjhArUfZch9b6Ua31oNZ6sK29A7Bq2dc1+ehtqZPgnodUwBqbiSwIWAeOjpX70ipSZp8dpaw/3U7FIy8eL/elCVFUZQ/wmRTQ2eilr81fk3ug2kUCVmGqsc+OECthWxRVSn0D2AV0KKWCwB9rrf9muZ/xuBzSwncFKrVNbqWmjaTrpFgrbBvBa63v11qv11q7tdaBXMFdrFwlNgar5LSRdJ0Ua0VFpWjEylRiwKrktJF0nRRrhSS6a0AlNgZLpY1mInHOzUSJGSZuh2IqHC/bNWWSPjtiLZAAXyMqLWD1tfr54MIsF2bjKGU1g4ubmplIggNHxyrqWoWoVZKiEbZ48MZ+xufiaDQK0KZ1vNXvrog0jRBrgYzghS12be6iweskEjeJGSYep4OOBh+NPlfZq3uEWCskwAvbXLGu6aJyxFAsIeWIQpSIpGiEbSqxukeItUQCvLCNlCMKUV6SohG2qrTqHiHWEhnBCyFEjZIAL4QQNUoCvBBC1CgJ8EIIUaMkwAshRI1SWutyX0OaUuoc8GHyrx3A+TJeTrmt5fuXe1+b5N5X5hKtdedi36ioAJ9JKTWktR4s93WUy1q+f7l3ufe1xq57lxSNEELUKAnwQghRoyo5wD9a7gsos7V8/3Lva5Pce5FVbA5eCCHE6lTyCF4IIcQqSIAXQogaVTEBXinVppR6Til1LPln6yKP2aaUekkpdVgp9YZS6pfLca3FopS6TSn1jlLqPaXUlxb5vlcp9U/J7/9cKbWx9Fdpjzzu/d8opd5O/p6fV0pdUo7rtEuu+8943B6llFZK1Uz5YD73rpS6N/n7P6yU+sdSX6Nd8vh3v0Ep9SOl1GvJf/u3r+qEWuuK+A/4c+BLya+/BHxlkcdcAWxKft0DjAIt5b72Fd6vE3gf6Ac8wOvA1VmP+W3gr5Nf3wf8U7mvu4T3fjPgT379W7Vy7/nef/JxjcCLwMvAYLmvu4S/+03Aa0Br8u9d5b7uEt77o8BvJb++GvhgNeesmBE88Dng75Jf/x1wZ/YDtNbvaq2PJb8+DYwBi67gqgI7gfe01se11jHgm1ivQabM12Q/cItSSpXwGu2S89611j/SWqc2b30ZCJT4Gu2Uz+8e4E+xBj6RUl6czfK5998Evqq1ngDQWo+V+Brtks+9a6Ap+XUzcHo1J6ykAL9Oaz0KkPxz2V0ilFI7sd4F3y/BtdmhFziV8fdg8tiij9FaJ4ApoL0kV2evfO49078CnrH1ikor5/0rpbYDfVrr75Tywkogn9/9FcAVSqmfKaVeVkrdVrKrs1c+9/4nwK8qpYLA94B/vZoTlnRHJ6XUD4HuRb71hwU+z3rgfwK/prU2i3FtZbDYSDy7ZjWfx1SjvO9LKfWrwCBwk61XVFrL3r9SygH8Z+DzpbqgEsrnd+/CStPswvrk9hOl1Bat9aTN12a3fO79fuDrWuv/Vyl1A/A/k/e+ojhX0gCvtb51qe8ppc4qpdZrrUeTAXzRj2VKqSbgu8Afaa1ftulSSyEI9GX8PcDFH8dSjwkqpVxYH9nGS3N5tsrn3lFK3Yr15n+T1jpaomsrhVz33whsAQ4kM3LdwNNKqd1a66GSXaU98v13/7LWOg6cUEq9gxXwXy3NJdomn3v/V8BtAFrrl5RSPqxGZCtKU1VSiuZp4NeSX/8a8K3sByilPMCTwN9rrfeV8Nrs8CqwSSl1afK+7sN6DTJlviZ7gBd0cvalyuW892SK4hFgdw3lYFOWvX+t9ZTWukNrvVFrvRFrDqIWgjvk9+/+KaxJdpRSHVgpm+MlvUp75HPvJ4FbAJRSVwE+4NyKz1jumeWM2eN24HngWPLPtuTxQeBrya9/FYgDhzL+21bua1/FPd8OvIs1j/CHyWMPYf3PTPKXuw94D3gF6C/3NZfw3n8InM34PT9d7msu5f1nPfYANVJFk+fvXgF/AbwNvAncV+5rLuG9Xw38DKvC5hDwqdWcT1oVCCFEjaqkFI0QQogikgAvhBA1SgK8EELUKAnwQghRoyTACyFEjZIAL0QGpVSfUuqEUqot+ffW5N9vqqVOpmJtkDJJIbIopX4fuFxr/YBS6hHgA+BxQGutjymleoBh4Cpd/cvnRQ2TAC9EFqWUGyuA/y1WZ8Pt2ur+l/mY14E9OtndVIhKVNJeNEJUA611XCn1b4HvY60kzA7u1d7JVKwRkoMXYnGfwdpQZkvmwYxOpr+uq7eTqVgjJMALkUUptQ34JPAR4P9IBvVa6mQq1ggJ8EJkSO6Y9VfA72mtTwL/EfhPNdbJVKwRMskqRAal1APALVrrX07+3YnVyfNp4I+AwxkP/7zW+lDpr1KI/EiAF0KIGiUpGiGEqFES4IUQokZJgBdCiBolAV4IIWqUBHghhKhREuCFEKJGSYAXQoga9f8DVJwhuLsDGncAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(data['X2'],data['y'])\n",
    "# in this case, the righmost point tends to follow the general trend, but is far away from the distribtuion, \n",
    "# so, it is a high leverage point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 15. This problem involves the Boston data set, which we saw in the lab for this chapter. We will now try to predict per capita crime rate using the other variables in this data set. In other words, per capita crime rate is the response, and the other variables are the predictors\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(506, 13)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "\n",
    "boston_data = load_boston()\n",
    "data = pd.DataFrame(data = boston_data['data'],columns = boston_data['feature_names'])\n",
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (a) For each predictor, fit a simple linear regression model to predict the response. Describe your results. In which of the models is there a statistically significant association between the predictor\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ZN    -0.0739  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INDUS    0.5098  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CHAS    -1.8928  0.2094\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NOX    31.2485  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RM    -2.6841  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AGE    0.1078  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DIS    -1.5509  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RAD    0.6179  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TAX    0.0297  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PTRATIO    1.1520  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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FJBTiZgyls3zmvkdLLsQS15ANVdMev4iEwmjgZS/EMqrunFVT8ItIKFTqx68TuKqn4BeRUEiqH3/NaIuJSCjEDG68+JSSC7HcePEpxNTEXzUd3BWRUBjOBHzhR9tKunN+4Ufb+PIlyxpdWugo+EUkFBIxo3f/CFfeuaUwr7MtRUK7/FVTU4+IhMKsphi3rFxe0tRzy8rlzGpSjFVLe/wiEgqZrDOrybj9itMLY/VAQCarXj3VUvCLSCg4sGdglKs3/rZwAteNF5/CEc1NjS4tdPQbSURCIRt4IfQh14f/6o2/1Xj8B0DBLyKhkPUKF2JxBX+1FPwiEgpxs7IncGmsnuop+EUkFMzgK5ecWtKr5yuXnIpyv3o6uCsioZBqitGaSvD3F53M7GScwXSW1lSClLpzVk3BLyKhMJgOuOKbD5W083e2pfjumjNoa2lgYSGkr0oRCYVMhdE5M+rVUzXt8YtIKCRixp+dNJ/3LD+mMFbP3Vue05ANB0DBLyKhkErG+K/vPpl0xskGzsK2FKcuOlnBfwAU/CISCjGDXfvSfPBbWwpn7t68cjnHtDU3urTQUfCLSCgMjAR8dfMTJcMyf3XzE3z2L9/EnNmNri5cFPwiEgpmcPlZx3Ht3VsLe/zXvWep+vEfAPXqiYggcHr7R9i5Z5De/hFdp1RCx51C6EOuR8+1d29FIzZUT3v8ERAEztN9AzzTN1g48eXY9tksbm8hpgNjEhJBhbF6AiV/1bTHHwF7h9L0D4+WzOsfHmXvULpBFYlUT2P11I6CPwJGM8GELm+JmDGaCRpUkdRaFJryEjFj3YqlJWP1rFuxVN05D4CaeiLCxn04xk9LeAWBs31XP6s3dBcOet66qoslC1oPq6a84UzA9fdvL+nVc/3927npUl1svVoK/ggwg1cGR/nMfY8WgmHdiqXMa0k2ujSpgb6BdCH0IdfuvXpDN/euPZuO1sOnj3vFi63XoaknCJy+gTTpTJZkIk57S5JYzCrODxs19URAOutcs6m0N8Q1m7aS1rVKDwvpTLbsQc90JtugiuojVqGpp9bBGwTOthf38e6v/ZKzr3uAd3/tl2x7cR+ZTMD2Xf0l87fv6g9ls5r2+IuMjGR4aTBNJnASMWPe7CTNzeHfREGFwa3C+IaViZKJeNkxbJKJeKNLq6l0dmaaenr7R1hz55aSHaU1d25h45Vnlv1ldc/as5jfOqumNdRb+FOtRkZGMrw4MMJoxokZjGadFwdGeA2EPvzjsVxviPHD2cbze0rT+fmayQTs3j/CaDagKR5j/hHNJBL6wQgwPJyhb+jVHYb2VJJZsyZ/z4zf5kcm4yU7HR0tSZLJ6b3v2lJN3HDxm+kfCsgETmdbijNPeDOzE00HVNtUz63axzvYGsbee+6w7r2nsP5nf2Djlh4g9z6e1VSbL7jR0Sy794+QCZz/ufoM7nu4hy/93x1AfhTQbFB2B2pkNHy/rBqSaGb2DuAmIA583d2/WOt1FL+IiZgx/4hmmiZ5g/SnM7wyOMraux4utIN/7bLTaGmKH3Dwz1R74FTriRl8Z81bACMbOK2z4gylcyGxc88gs5tjDI8GZN0JRrPs6h9iQWvu53TfQJqRTJYjUzE831/a3RnOpHmlP5iwfYtraYrnvhiGRrOTflkUf6k0J2IYuQN5xXVO9gtssmCpdFs6naF3IDd/zuw4+4eDiuFWLoTHnufsJuepvpEJ48ec2N7CrFmJsutPJuMMpUdIZ3LrJJMl0+SkswHuubbsPUOjDPePlDzv4prH1xmPGXf+6o/8j58/Xajh+Hb4Y98IVxXVdsvK5RzX3szeoYD2VJKXh0cLX+bJuDGQznJUKs7ASMBRqRhPFy1/z1VvYc/g6ITHe13+uZYzPJxhR99AYftc+aeLef9Zx5EdGJnWl0AmE/D8viHS+R0ygA+ddwIAv3qqj/XvX868loM/jjE6muWZPYM89/IQs5NxFrWn+KvlnVx46kISMSMWA6P8DtTY+7yW6r2jZT7DJz+YWRx4Ang70AM8BFzq7r+vtExXV5d3d3dPex2jo1m27d4/4cP4hvlHVAz/nXsGed/6X5e9yMPCtuoHApmpnhbTWc8rg8M8uycXTu9b3sk5b1wwYdts+eNLfO6H2wrTi+Y28/ze3EHDG1a8mZZZyZIP7wXLOic8xpKOFv7QN1hSy7oVS7n+/u307h/hlpXLecOC1pI3cCYTsG1Xf0mYrFuxlOf6BnjjwjkT1vH6eS0l4T8+WIqDF6h429j8z17wRl4zZ/a0nttY+Bdv8++uOaPi+6Y9lSy7/uPbm0u+LP7spPl8+PzXl9yveLuNr7lSnV+77DS+9a/PsHFLT6GGcrV978ozuf2XT5VdfnBktPBab1xzBhcXLf+ra88tmR57vI1rzuC1FT4jxZ+ri5d3svLMY0t2roq/JMvp2z/Mzr3DE3bIjj5qFo/u3Efn3BTHHJmq6hdEOb39wzy5ez/XbNo64T0xVuex7c08tnN/4XjZ2Ot0/LwWFhyVmnol01TuM1HuszMdZrbF3bvGz2/Eb/XTgSfd/Sl3TwPfAS6q5Qp273/1QwW5n2Mf/NYWdu8fqbhMrS/yUKmnRd9AbU+ams569o8Ehe1x0WmdZbfNeScdXTK9fzgoPO4xc1tKllnRtajsY/SWqeWaTVu56pwT6NkzxFVlXoPd+1/doyxe5qwTO8qu46XB0u3XN5Que7++ofSkt43NP+m1R037uZXb5pO9byqtf+9QUDL/PcuPmXC/4u02vuZKda6962FWv/X4khrK1TaaDSouX/xaj45bfvx04fEm+YwU17D6rccXAnz861HJ8GgwYZm1dz1MOhNwxe0PccU3H5p0+ekayQSFQB//nhirs3/o1WMM311zBp+54CSuv387wzU+H6bcZ6LcZ+dgNKKpZyHwXNF0D/CW8XcyszXAGoBFixZVtYIDCfFEhXbwAz05ZKZ6WkxnPcXbo9Jp78W//MaHxvjtGY9Zxe1bbv6cVNOr98mWfkhGK7SbZqf5Gk71Wk9VZzXPbUzxNp/sfTNZbcXz56Sapt5u06xz7LjNWA3laovFbFqv4fhjQ1MdKyqnuIbpbNvxpvP61uIKXNlJ3hPF6ynbnbTGzbeVPhPjPzsHoxF7/OW20oRXzt3Xu3uXu3d1dHRUtYKxN1uxqV6g9lSSm1cuL+kqdvPK5bSnDqyvezIRL1tDrXtaTGc9xdsjVuG0dyvqC10cGuOXh9yHpNL2LTd/79Doq/cZ1x7aFI+VPw1/mq/hZK/1ZLcdyHMbU7zNj0rFKr5vprN+gL1Do1Nvt2nWOTb/5pXLmZOKle3+2BSzab2GyXjp8s2J8o/XPEnzw5xUvLB9prNtx6u0DceGaahV8DZN8p4oXk8tM6JiLRU+E+M/OwejEW38ZwKfc/c/z09/CsDd/6HSMjPRxg8H3/ug2KHUxp9OZ9jeO1BVG39xe73a+Cu38ffsGeKxz53P3qFgwvtmstqK59eqjf/mlctZ0JpkNOsclYoxMBKwbyRLT/6A5WA6S+fcFEMjo/yvrS9M2cb/rQ/8CZmAkgOeAyPZwvRgOssxc1N0TtLGHgRO/8gI+4cDmuLGrv6JF1KZrI2/0mf5p4/v4rtbeqZcfrqGhzM82TfAVWXeE2PrfHHvIKcsOorRDDXJiEpmoo2/EcGfIHdw93xgJ7mDu//R3R+rtEy1wQ/V9+qph0OlVw9Q0iNkfG+Z8b1YyvXQOTIVY99QdcuM9XYYHs2SmEavnkw2IBmyXj1TvbaV1j9ZN8nink3T7dXTFDOSiRgD6SyJmNHSHOOVoSxzW+Ilr9uRqRgvD2QLy788PEomG5Ao06snEzjzWuITvtQOputqKhmb8N6bavnxn+VUMkb/cLbmwVv8mox/TxyZirNvaObO1i3+TEz22ZnKIRP8+WLeCXyZXHfOb7j7f5vs/gcS/CIiUVcp+BvSj9/dfwT8qBHrFhGJOp16KSISMQp+EZGIUfCLiESMgl9EJGIa0qunWmbWCzzT6Dpm2DzgpUYX0UBRf/6gbRD15w8Hvw2OdfcJZ8CGIvijyMy6y3XDioqoP3/QNoj684f6bQM19YiIRIyCX0QkYhT8h671jS6gwaL+/EHbIOrPH+q0DdTGLyISMdrjFxGJGAW/iEjEKPgbzMy+YWa7zezRMrd93MzczOY1oraZUmkbmNmHzWy7mT1mZtc3qr6ZUG4bmNkyM/u1mT1iZt1mdnoja6wnMzvGzB4ws8fzr/dH8/PnmtmPzWxH/m9bo2uth0me/zoz22ZmW83sXjObU4v1Kfgb73bgHeNnmtkx5C5I/+xMF9QAtzNuG5jZueSuxbzU3d8E3NCAumbS7Ux8H1wPfN7dlwH/JT99uMoAf+vubwTOAD5kZicBnwQ2u/uJwOb89OGo0vP/MXCyuy8ldx2TT9ViZQr+BnP3/we8XOamG4FPUOaylIebCtvgg8AX3X0kf5/dM17YDKqwDRw4Mv//o4DnZ7SoGeTuL7j7w/n/9wOPk7s+90XAHfm73QG8qzEV1lel5+/u/8fdM/m7/RrorMX6FPyHIDO7ENjp7r9tdC0N9HrgT83sQTP7mZn9SaMLaoCPAevM7Dlyv3hqsrd3qDOzxcCpwIPAAnd/AXLhCMxvXGUzY9zzL/bXwP+uxToU/IcYM5sN/B25n/ZRlgDayP3svQbYaMVXhI+GDwJXu/sxwNXAbQ2up+7M7AjgbuBj7r6v0fXMtErP38z+jlxz0F21WI+C/9BzAnAc8Fsze5rcT7uHzew1Da1q5vUA93jOb4CA3IBVUXI5cE/+/98DDtuDuwBm1kQu9O5y97HnvcvMjs7ffjRw2Db5VXj+mNnlwAXAZV6jE68U/IcYd/+du89398XuvphcAJ7m7i82uLSZ9s/AeQBm9nogSfRGanweeFv+/+cBOxpYS13lf83dBjzu7v9YdNP3yX0Bkv9730zXNhMqPX8zewdwLXChuw/WbH06c7exzOzbwDnk9mZ3AZ9199uKbn8a6HL3wzb0ym0D4E7gG8AyIA183N1/0qga663CNtgO3ESu2WsYWOvuWxpVYz2Z2b8Dfg78jtyvO4BPk2vn3ggsItfD7b3uXq4zRKhN8vy/AjQDffl5v3b3qw56fQp+EZFoUVOPiEjEKPhFRCJGwS8iEjEKfhGRiFHwi4hEjIJfIsXMsvnRLh81s++Z2cL89CNm9qKZ7SyaTo67/w/Gj45oZleb2bCZHZWf/vOi5ffnRxd9xMw2mNk5ZvbDomXflR91cZuZ/c7MDstxaOTQo+CXqBly92XufjK58wPel59eBtwC3Dg27e7pcfd/GfjQuMe7FHgIeDeAu/9L0eN1kzvbcpm7rypeyMxOITf+zkXu/gbgQuAGM1tav6cukqPglyj7OfC6Ku7/r+RGjATAzE4AjgD+M7kvgGp8HPiCu/8RIP/3H8iNSyRSVwp+iSQzSwB/Qe5MyencPw6cT24IgTGXAt8m9wWyxMyqGTnyTcD4s3C78/NF6krBL1GTMrNHyIXss0w94uXY/fuAueQujDHmEuA77h6QG0ztvVXUYUy81kK5eSI1l2h0ASIzbCjf/l7V/fMHb39Iro3/K/m2+BOBH+dHi04CTwH/fZqP+xjQBWwtmnca8PsqahM5INrjF5kGd38F+Ajw8fzwuZcCnxsbRdXdXwssNLNjp/mQNwCfyl90Y+ziG58GvlTj0kUmUPCLTJO7/xvwW3JNPJcA9467y735+dN5rEfIDbf7AzPbBvwA+ER+vkhdaXROEZGI0R6/iEjEKPhFRCJGwS8iEjEKfhGRiFHwi4hEjIJfRCRiFPwiIhHz/wHx6xHIW7vb3QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B    -0.0363  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LSTAT    0.5488  0.0000\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "simple_coeff = []\n",
    "predictor = [col for col in data.columns if col != 'CRIM']\n",
    "for col in predictor:\n",
    "    result = smf.ols('CRIM ~ {}'.format(col),data = data).fit()\n",
    "    print('{}    {:.4f}  {:.4f}'.format(col,result.params[col],result.pvalues[col]))\n",
    "    simple_coeff.append(result.params[col])\n",
    "    sns.scatterplot(data[col],data['CRIM'])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from aboce point, we can conclude that every predictor except CHAS, has a significant relation with CRIM."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (b) Fit a multiple regression model to predict the response using all of the predictors. Describe your results. For which predictors can we reject the null hypothesis H0 : βj = 0?\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.442\n",
      "Model:                            OLS   Adj. R-squared:                  0.428\n",
      "Method:                 Least Squares   F-statistic:                     32.55\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           4.84e-55\n",
      "Time:                        13:17:22   Log-Likelihood:                -1658.8\n",
      "No. Observations:                 506   AIC:                             3344.\n",
      "Df Residuals:                     493   BIC:                             3398.\n",
      "Df Model:                          12                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      9.9967      6.979      1.432      0.153      -3.716      23.709\n",
      "ZN             0.0364      0.019      1.943      0.053      -0.000       0.073\n",
      "INDUS         -0.0694      0.084     -0.825      0.410      -0.235       0.096\n",
      "CHAS          -1.3117      1.179     -1.112      0.267      -3.629       1.005\n",
      "NOX           -6.9288      5.225     -1.326      0.185     -17.195       3.338\n",
      "RM            -0.3348      0.573     -0.585      0.559      -1.460       0.790\n",
      "AGE            0.0013      0.018      0.074      0.941      -0.034       0.037\n",
      "DIS           -0.7089      0.271     -2.612      0.009      -1.242      -0.176\n",
      "RAD            0.5389      0.088      6.151      0.000       0.367       0.711\n",
      "TAX           -0.0014      0.005     -0.263      0.793      -0.011       0.009\n",
      "PTRATIO       -0.0834      0.179     -0.465      0.642      -0.436       0.269\n",
      "B             -0.0096      0.004     -2.625      0.009      -0.017      -0.002\n",
      "LSTAT          0.2356      0.069      3.431      0.001       0.101       0.371\n",
      "==============================================================================\n",
      "Omnibus:                      685.174   Durbin-Watson:                   1.511\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            97204.794\n",
      "Skew:                           6.921   Prob(JB):                         0.00\n",
      "Kurtosis:                      69.475   Cond. No.                     1.51e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.51e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "sum_predictor = ' + '.join(predictor)\n",
    "result = smf.ols('CRIM ~ {}'.format(sum_predictor),data = data).fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [],
   "source": [
    "# although the coeff are all non zero, but inspecting the p values, we can only reject null hypothesis of RAD,DIS and LSTAT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (c) How do your results from (a) compare to your results from (b)? Create a plot displaying the univariate regression coefficients from (a) on the x-axis, and the multiple regression coefficients from (b) on the y-axis.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "multi_coeff = [result.params[col] for col in predictor]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a2f83b3cf8>"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(simple_coeff,multi_coeff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [],
   "source": [
    "#removing the outlier point for NOX\n",
    "simple_coeff.remove(31.24853120112292)\n",
    "multi_coeff.remove(-6.928835572793048)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-2.8866952185799843, 1.3546267815366226)"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "sns.scatterplot(simple_coeff,multi_coeff)\n",
    "\n",
    "lims = [\n",
    "    np.min([ax.get_xlim(), ax.get_ylim()]),  # min of both axes\n",
    "    np.max([ax.get_xlim(), ax.get_ylim()]),  # max of both axes\n",
    "]\n",
    "ax.plot(lims, lims, 'k-', alpha=0.75, zorder=0,color = 'orange')\n",
    "ax.set_aspect('equal')\n",
    "ax.set_xlim(lims)\n",
    "ax.set_ylim(lims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (d) Is there evidence of non-linear association between any of the predictors and the response? To answer this question, for each predictor X, fit a model of the form\n",
    "Y = β0 + β1X + β2X2 + β3X3 + epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ZN\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.058\n",
      "Model:                            OLS   Adj. R-squared:                  0.053\n",
      "Method:                 Least Squares   F-statistic:                     10.35\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.28e-06\n",
      "Time:                        13:33:57   Log-Likelihood:                -1791.2\n",
      "No. Observations:                 506   AIC:                             3590.\n",
      "Df Residuals:                     502   BIC:                             3607.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===================================================================================\n",
      "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "Intercept           4.8461      0.433     11.192      0.000       3.995       5.697\n",
      "ZN                 -0.3322      0.110     -3.025      0.003      -0.548      -0.116\n",
      "np.power(ZN, 2)     0.0065      0.004      1.679      0.094      -0.001       0.014\n",
      "np.power(ZN, 3) -3.776e-05   3.14e-05     -1.203      0.230   -9.94e-05    2.39e-05\n",
      "==============================================================================\n",
      "Omnibus:                      569.133   Durbin-Watson:                   0.875\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            33700.991\n",
      "Skew:                           5.272   Prob(JB):                         0.00\n",
      "Kurtosis:                      41.565   Cond. No.                     1.89e+05\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.89e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "INDUS\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.260\n",
      "Model:                            OLS   Adj. R-squared:                  0.255\n",
      "Method:                 Least Squares   F-statistic:                     58.69\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.55e-32\n",
      "Time:                        13:33:57   Log-Likelihood:                -1730.3\n",
      "No. Observations:                 506   AIC:                             3469.\n",
      "Df Residuals:                     502   BIC:                             3486.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "======================================================================================\n",
      "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept              3.6626      1.574      2.327      0.020       0.570       6.755\n",
      "INDUS                 -1.9652      0.482     -4.077      0.000      -2.912      -1.018\n",
      "np.power(INDUS, 2)     0.2519      0.039      6.407      0.000       0.175       0.329\n",
      "np.power(INDUS, 3)    -0.0070      0.001     -7.292      0.000      -0.009      -0.005\n",
      "==============================================================================\n",
      "Omnibus:                      611.788   Durbin-Watson:                   1.116\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            51742.286\n",
      "Skew:                           5.820   Prob(JB):                         0.00\n",
      "Kurtosis:                      51.153   Cond. No.                     2.47e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 2.47e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "CHAS\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.003\n",
      "Model:                            OLS   Adj. R-squared:                  0.001\n",
      "Method:                 Least Squares   F-statistic:                     1.579\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):              0.209\n",
      "Time:                        13:33:57   Log-Likelihood:                -1805.6\n",
      "No. Observations:                 506   AIC:                             3615.\n",
      "Df Residuals:                     504   BIC:                             3624.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=====================================================================================\n",
      "                        coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------------\n",
      "Intercept             3.7444      0.396      9.453      0.000       2.966       4.523\n",
      "CHAS                 -0.6309      0.502     -1.257      0.209      -1.617       0.355\n",
      "np.power(CHAS, 2)    -0.6309      0.502     -1.257      0.209      -1.617       0.355\n",
      "np.power(CHAS, 3)    -0.6309      0.502     -1.257      0.209      -1.617       0.355\n",
      "==============================================================================\n",
      "Omnibus:                      561.663   Durbin-Watson:                   0.817\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            30645.429\n",
      "Skew:                           5.191   Prob(JB):                         0.00\n",
      "Kurtosis:                      39.685   Cond. No.                     3.42e+32\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The smallest eigenvalue is 4.39e-63. This might indicate that there are\n",
      "strong multicollinearity problems or that the design matrix is singular.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "NOX\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.297\n",
      "Model:                            OLS   Adj. R-squared:                  0.293\n",
      "Method:                 Least Squares   F-statistic:                     70.69\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           3.81e-38\n",
      "Time:                        13:33:58   Log-Likelihood:                -1717.2\n",
      "No. Observations:                 506   AIC:                             3442.\n",
      "Df Residuals:                     502   BIC:                             3459.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "====================================================================================\n",
      "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------------\n",
      "Intercept          233.0866     33.643      6.928      0.000     166.988     299.185\n",
      "NOX              -1279.3713    170.397     -7.508      0.000   -1614.151    -944.591\n",
      "np.power(NOX, 2)  2248.5441    279.899      8.033      0.000    1698.626    2798.462\n",
      "np.power(NOX, 3) -1245.7029    149.282     -8.345      0.000   -1538.997    -952.409\n",
      "==============================================================================\n",
      "Omnibus:                      614.412   Durbin-Watson:                   1.159\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            53523.997\n",
      "Skew:                           5.851   Prob(JB):                         0.00\n",
      "Kurtosis:                      52.008   Cond. No.                     1.36e+03\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.36e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "RM\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.068\n",
      "Model:                            OLS   Adj. R-squared:                  0.062\n",
      "Method:                 Least Squares   F-statistic:                     12.17\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.07e-07\n",
      "Time:                        13:33:58   Log-Likelihood:                -1788.6\n",
      "No. Observations:                 506   AIC:                             3585.\n",
      "Df Residuals:                     502   BIC:                             3602.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===================================================================================\n",
      "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "Intercept         112.6246     64.517      1.746      0.081     -14.132     239.382\n",
      "RM                -39.1501     31.311     -1.250      0.212    -100.668      22.368\n",
      "np.power(RM, 2)     4.5509      5.010      0.908      0.364      -5.292      14.394\n",
      "np.power(RM, 3)    -0.1745      0.264     -0.662      0.509      -0.693       0.344\n",
      "==============================================================================\n",
      "Omnibus:                      585.097   Durbin-Watson:                   0.913\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            40144.207\n",
      "Skew:                           5.465   Prob(JB):                         0.00\n",
      "Kurtosis:                      45.245   Cond. No.                     5.36e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.36e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "AGE\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.174\n",
      "Model:                            OLS   Adj. R-squared:                  0.169\n",
      "Method:                 Least Squares   F-statistic:                     35.31\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.02e-20\n",
      "Time:                        13:33:58   Log-Likelihood:                -1757.9\n",
      "No. Observations:                 506   AIC:                             3524.\n",
      "Df Residuals:                     502   BIC:                             3541.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "====================================================================================\n",
      "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------------\n",
      "Intercept           -2.5488      2.769     -0.920      0.358      -7.989       2.892\n",
      "AGE                  0.2737      0.186      1.468      0.143      -0.093       0.640\n",
      "np.power(AGE, 2)    -0.0072      0.004     -1.988      0.047      -0.014    -8.4e-05\n",
      "np.power(AGE, 3)  5.745e-05   2.11e-05      2.724      0.007     1.6e-05    9.89e-05\n",
      "==============================================================================\n",
      "Omnibus:                      577.477   Durbin-Watson:                   1.025\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            39586.670\n",
      "Skew:                           5.336   Prob(JB):                         0.00\n",
      "Kurtosis:                      44.997   Cond. No.                     4.74e+06\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 4.74e+06. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "DIS\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.278\n",
      "Model:                            OLS   Adj. R-squared:                  0.274\n",
      "Method:                 Least Squares   F-statistic:                     64.37\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           3.14e-35\n",
      "Time:                        13:33:58   Log-Likelihood:                -1724.0\n",
      "No. Observations:                 506   AIC:                             3456.\n",
      "Df Residuals:                     502   BIC:                             3473.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "====================================================================================\n",
      "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------------\n",
      "Intercept           30.0476      2.446     12.285      0.000      25.242      34.853\n",
      "DIS                -15.5544      1.736     -8.960      0.000     -18.965     -12.144\n",
      "np.power(DIS, 2)     2.4521      0.346      7.078      0.000       1.771       3.133\n",
      "np.power(DIS, 3)    -0.1186      0.020     -5.814      0.000      -0.159      -0.079\n",
      "==============================================================================\n",
      "Omnibus:                      577.742   Durbin-Watson:                   1.129\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            42444.706\n",
      "Skew:                           5.305   Prob(JB):                         0.00\n",
      "Kurtosis:                      46.596   Cond. No.                     2.10e+03\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 2.1e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "RAD\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.400\n",
      "Model:                            OLS   Adj. R-squared:                  0.396\n",
      "Method:                 Least Squares   F-statistic:                     111.6\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           2.31e-55\n",
      "Time:                        13:33:58   Log-Likelihood:                -1677.1\n",
      "No. Observations:                 506   AIC:                             3362.\n",
      "Df Residuals:                     502   BIC:                             3379.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "====================================================================================\n",
      "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------------\n",
      "Intercept           -0.6055      2.050     -0.295      0.768      -4.633       3.422\n",
      "RAD                  0.5127      1.044      0.491      0.623      -1.538       2.563\n",
      "np.power(RAD, 2)    -0.0752      0.149     -0.506      0.613      -0.367       0.217\n",
      "np.power(RAD, 3)     0.0032      0.005      0.703      0.482      -0.006       0.012\n",
      "==============================================================================\n",
      "Omnibus:                      659.751   Durbin-Watson:                   1.351\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            77838.247\n",
      "Skew:                           6.526   Prob(JB):                         0.00\n",
      "Kurtosis:                      62.343   Cond. No.                     5.43e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.43e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "TAX\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.369\n",
      "Model:                            OLS   Adj. R-squared:                  0.365\n",
      "Method:                 Least Squares   F-statistic:                     97.80\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           7.34e-50\n",
      "Time:                        13:33:58   Log-Likelihood:                -1689.9\n",
      "No. Observations:                 506   AIC:                             3388.\n",
      "Df Residuals:                     502   BIC:                             3405.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "====================================================================================\n",
      "                       coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------------\n",
      "Intercept           19.1836     11.796      1.626      0.105      -3.991      42.358\n",
      "TAX                 -0.1533      0.096     -1.602      0.110      -0.341       0.035\n",
      "np.power(TAX, 2)     0.0004      0.000      1.488      0.137      -0.000       0.001\n",
      "np.power(TAX, 3) -2.204e-07   1.89e-07     -1.167      0.244   -5.91e-07    1.51e-07\n",
      "==============================================================================\n",
      "Omnibus:                      644.161   Durbin-Watson:                   1.293\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            69773.212\n",
      "Skew:                           6.278   Prob(JB):                         0.00\n",
      "Kurtosis:                      59.141   Cond. No.                     6.16e+09\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 6.16e+09. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "PTRATIO\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.114\n",
      "Model:                            OLS   Adj. R-squared:                  0.108\n",
      "Method:                 Least Squares   F-statistic:                     21.48\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           4.17e-13\n",
      "Time:                        13:33:58   Log-Likelihood:                -1775.8\n",
      "No. Observations:                 506   AIC:                             3560.\n",
      "Df Residuals:                     502   BIC:                             3577.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "========================================================================================\n",
      "                           coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------------\n",
      "Intercept              477.1840    156.795      3.043      0.002     169.129     785.239\n",
      "PTRATIO                -82.3605     27.644     -2.979      0.003    -136.673     -28.048\n",
      "np.power(PTRATIO, 2)     4.6353      1.608      2.882      0.004       1.475       7.795\n",
      "np.power(PTRATIO, 3)    -0.0848      0.031     -2.743      0.006      -0.145      -0.024\n",
      "==============================================================================\n",
      "Omnibus:                      572.356   Durbin-Watson:                   0.945\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            36070.763\n",
      "Skew:                           5.294   Prob(JB):                         0.00\n",
      "Kurtosis:                      42.985   Cond. No.                     3.02e+06\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 3.02e+06. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "B\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.150\n",
      "Model:                            OLS   Adj. R-squared:                  0.145\n",
      "Method:                 Least Squares   F-statistic:                     29.49\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.41e-17\n",
      "Time:                        13:33:58   Log-Likelihood:                -1765.3\n",
      "No. Observations:                 506   AIC:                             3539.\n",
      "Df Residuals:                     502   BIC:                             3555.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept         18.2637      2.305      7.924      0.000      13.735      22.792\n",
      "B                 -0.0836      0.056     -1.483      0.139      -0.194       0.027\n",
      "np.power(B, 2)     0.0002      0.000      0.716      0.474      -0.000       0.001\n",
      "np.power(B, 3) -2.652e-07   4.36e-07     -0.608      0.544   -1.12e-06    5.92e-07\n",
      "==============================================================================\n",
      "Omnibus:                      591.816   Durbin-Watson:                   0.983\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            43468.746\n",
      "Skew:                           5.544   Prob(JB):                         0.00\n",
      "Kurtosis:                      47.032   Cond. No.                     3.59e+08\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 3.59e+08. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n",
      "LSTAT\n",
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                   CRIM   R-squared:                       0.218\n",
      "Model:                            OLS   Adj. R-squared:                  0.213\n",
      "Method:                 Least Squares   F-statistic:                     46.63\n",
      "Date:                Tue, 23 Jun 2020   Prob (F-statistic):           1.35e-26\n",
      "Time:                        13:33:58   Log-Likelihood:                -1744.2\n",
      "No. Observations:                 506   AIC:                             3496.\n",
      "Df Residuals:                     502   BIC:                             3513.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "======================================================================================\n",
      "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------\n",
      "Intercept              1.2010      2.029      0.592      0.554      -2.785       5.187\n",
      "LSTAT                 -0.4491      0.465     -0.966      0.335      -1.362       0.464\n",
      "np.power(LSTAT, 2)     0.0558      0.030      1.852      0.065      -0.003       0.115\n",
      "np.power(LSTAT, 3)    -0.0009      0.001     -1.517      0.130      -0.002       0.000\n",
      "==============================================================================\n",
      "Omnibus:                      607.734   Durbin-Watson:                   1.239\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):            53621.219\n",
      "Skew:                           5.726   Prob(JB):                         0.00\n",
      "Kurtosis:                      52.114   Cond. No.                     5.20e+04\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 5.2e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n",
      "\n",
      "--------------------------------------------------------------------------------------------\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for col in predictor:\n",
    "    print(col)\n",
    "    result = smf.ols('CRIM ~ {0} + np.power({0},2) + np.power({0},3)'.format(col),data = data).fit()\n",
    "    print(result.summary())\n",
    "    print()\n",
    "    print('--------------------------------------------------------------------------------------------')\n",
    "    print()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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