Simple+Linear+Regression+in+Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Regression\n",
    "\n",
    "In this notebook, we'll build a linear regression model to predict `Sales` using an appropriate predictor variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 1: Reading and Understanding the Data\n",
    "\n",
    "Let's start with the following steps:\n",
    "\n",
    "1. Importing data using the pandas library\n",
    "2. Understanding the structure of the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Supress Warnings\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the numpy and pandas package\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe thead th {\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>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>12.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>16.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>17.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  Radio  Newspaper  Sales\n",
       "0  230.1   37.8       69.2   22.1\n",
       "1   44.5   39.3       45.1   10.4\n",
       "2   17.2   45.9       69.3   12.0\n",
       "3  151.5   41.3       58.5   16.5\n",
       "4  180.8   10.8       58.4   17.9"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read the given CSV file, and view some sample records\n",
    "\n",
    "advertising = pd.read_csv(\"advertising.csv\")\n",
    "advertising.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Let's inspect the various aspects of our dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 4)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "advertising.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 200 entries, 0 to 199\n",
      "Data columns (total 4 columns):\n",
      " #   Column     Non-Null Count  Dtype  \n",
      "---  ------     --------------  -----  \n",
      " 0   TV         200 non-null    float64\n",
      " 1   Radio      200 non-null    float64\n",
      " 2   Newspaper  200 non-null    float64\n",
      " 3   Sales      200 non-null    float64\n",
      "dtypes: float64(4)\n",
      "memory usage: 6.4 KB\n"
     ]
    }
   ],
   "source": [
    "advertising.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        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>TV</th>\n",
       "      <th>Radio</th>\n",
       "      <th>Newspaper</th>\n",
       "      <th>Sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "      <td>200.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>147.042500</td>\n",
       "      <td>23.264000</td>\n",
       "      <td>30.554000</td>\n",
       "      <td>15.130500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>85.854236</td>\n",
       "      <td>14.846809</td>\n",
       "      <td>21.778621</td>\n",
       "      <td>5.283892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.300000</td>\n",
       "      <td>1.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>74.375000</td>\n",
       "      <td>9.975000</td>\n",
       "      <td>12.750000</td>\n",
       "      <td>11.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>149.750000</td>\n",
       "      <td>22.900000</td>\n",
       "      <td>25.750000</td>\n",
       "      <td>16.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>218.825000</td>\n",
       "      <td>36.525000</td>\n",
       "      <td>45.100000</td>\n",
       "      <td>19.050000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>296.400000</td>\n",
       "      <td>49.600000</td>\n",
       "      <td>114.000000</td>\n",
       "      <td>27.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               TV       Radio   Newspaper       Sales\n",
       "count  200.000000  200.000000  200.000000  200.000000\n",
       "mean   147.042500   23.264000   30.554000   15.130500\n",
       "std     85.854236   14.846809   21.778621    5.283892\n",
       "min      0.700000    0.000000    0.300000    1.600000\n",
       "25%     74.375000    9.975000   12.750000   11.000000\n",
       "50%    149.750000   22.900000   25.750000   16.000000\n",
       "75%    218.825000   36.525000   45.100000   19.050000\n",
       "max    296.400000   49.600000  114.000000   27.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "advertising.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 2: Visualising the Data\n",
    "\n",
    "Let's now visualise our data using seaborn. We'll first make a pairplot of all the variables present to visualise which variables are most correlated to `Sales`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(advertising, x_vars=['TV', 'Newspaper', 'Radio'], y_vars='Sales',size=4, aspect=1, kind='scatter')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(advertising.corr(), cmap=\"YlGnBu\", annot = True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As is visible from the pairplot and the heatmap, the variable `TV` seems to be most correlated with `Sales`. So let's go ahead and perform simple linear regression using `TV` as our feature variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Step 3: Performing Simple Linear Regression\n",
    "\n",
    "Equation of linear regression<br>\n",
    "$y = c + m_1x_1 + m_2x_2 + ... + m_nx_n$\n",
    "\n",
    "-  $y$ is the response\n",
    "-  $c$ is the intercept\n",
    "-  $m_1$ is the coefficient for the first feature\n",
    "-  $m_n$ is the coefficient for the nth feature<br>\n",
    "\n",
    "In our case:\n",
    "\n",
    "$y = c + m_1 \\times TV$\n",
    "\n",
    "The $m$ values are called the model **coefficients** or **model parameters**.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generic Steps in model building using `statsmodels`\n",
    "\n",
    "We first assign the feature variable, `TV`, in this case, to the variable `X` and the response variable, `Sales`, to the variable `y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = advertising['TV']\n",
    "y = advertising['Sales']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Train-Test Split\n",
    "\n",
    "You now need to split our variable into training and testing sets. You'll perform this by importing `train_test_split` from the `sklearn.model_selection` library. It is usually a good practice to keep 70% of the data in your train dataset and the rest 30% in your test dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size = 0.7, test_size = 0.3, random_state = 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74     213.4\n",
       "3      151.5\n",
       "185    205.0\n",
       "26     142.9\n",
       "90     134.3\n",
       "Name: TV, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's now take a look at the train dataset\n",
    "\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74     17.0\n",
       "3      16.5\n",
       "185    22.6\n",
       "26     15.0\n",
       "90     14.0\n",
       "Name: Sales, dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Building a Linear Model\n",
    "\n",
    "You first need to import the `statsmodel.api` library using which you'll perform the linear regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train_lm, X_test_lm, y_train_lm, y_test_lm = train_test_split(X, y, train_size = 0.7, test_size = 0.3, random_state = 100)\n",
    "import statsmodels.api as sm\n",
    "X_train_sm = sm.add_constant(X_train)\n",
    "lr = sm.OLS(y_train, X_train_sm)\n",
    "lr_model=lr.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    6.948683\n",
       "TV       0.054546\n",
       "dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_model.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x286c4a39250>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x286c4a5ccd0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#y=mx+c ... y(pred) = -4 + 1*X_train\n",
    "\n",
    "plt.plot(X_train, -4 + 1*X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the `statsmodels` library fits a line on the dataset which passes through the origin. But in order to have an intercept, you need to manually use the `add_constant` attribute of `statsmodels`. And once you've added the constant to your `X_train` dataset, you can go ahead and fit a regression line using the `OLS` (Ordinary Least Squares) attribute of `statsmodels` as shown below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add a constant to get an intercept\n",
    "X_train_sm = sm.add_constant(X_train)\n",
    "\n",
    "# Fit the resgression line using 'OLS'\n",
    "lr = sm.OLS(y_train, X_train_sm).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "const    6.948683\n",
       "TV       0.054546\n",
       "dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print the parameters, i.e. the intercept and the slope of the regression line fitted\n",
    "lr.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Sales   R-squared:                       0.816\n",
      "Model:                            OLS   Adj. R-squared:                  0.814\n",
      "Method:                 Least Squares   F-statistic:                     611.2\n",
      "Date:                Fri, 09 Aug 2024   Prob (F-statistic):           1.52e-52\n",
      "Time:                        00:43:59   Log-Likelihood:                -321.12\n",
      "No. Observations:                 140   AIC:                             646.2\n",
      "Df Residuals:                     138   BIC:                             652.1\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.9487      0.385     18.068      0.000       6.188       7.709\n",
      "TV             0.0545      0.002     24.722      0.000       0.050       0.059\n",
      "==============================================================================\n",
      "Omnibus:                        0.027   Durbin-Watson:                   2.196\n",
      "Prob(Omnibus):                  0.987   Jarque-Bera (JB):                0.150\n",
      "Skew:                          -0.006   Prob(JB):                        0.928\n",
      "Kurtosis:                       2.840   Cond. No.                         328.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Performing a summary operation lists out all the different parameters of the regression line fitted\n",
    "print(lr.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Looking at some key statistics from the summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values we are concerned with are - \n",
    "1. The coefficients and significance (p-values)\n",
    "2. R-squared\n",
    "3. F statistic and its significance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 1. The coefficient for TV is 0.054, with a very low p value\n",
    "The coefficient is statistically significant. So the association is not purely by chance. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2. R - squared is 0.816\n",
    "Meaning that 81.6% of the variance in `Sales` is explained by `TV`\n",
    "\n",
    "This is a decent R-squared value."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. F statistic has a very low p value (practically low)\n",
    "Meaning that the model fit is statistically significant, and the explained variance isn't purely by chance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "The fit is significant. Let's visualize how well the model fit the data.\n",
    "\n",
    "From the parameters that we get, our linear regression equation becomes:\n",
    "\n",
    "$ Sales = 6.948 + 0.054 \\times TV $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train, y_train)\n",
    "plt.plot(X_train, 6.948 + 0.054*X_train, 'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 4: Residual analysis \n",
    "To validate assumptions of the model, and hence the reliability for inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Distribution of the error terms\n",
    "We need to check if the error terms are also normally distributed (which is infact, one of the major assumptions of linear regression), let us plot the histogram of the error terms and see what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = lr.predict(X_train_sm)\n",
    "res = (y_train - y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "sns.distplot(res, bins = 15)\n",
    "fig.suptitle('Error Terms', fontsize = 15)                  # Plot heading \n",
    "plt.xlabel('y_train - y_train_pred', fontsize = 15)         # X-label\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The residuals are following the normally distributed with a mean 0. All good!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Looking for patterns in the residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train,res)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are confident that the model fit isn't by chance, and has decent predictive power. The normality of residual terms allows some inference on the coefficients.\n",
    "\n",
    "Although, the variance of residuals increasing with X indicates that there is significant variation that this model is unable to explain."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the regression line is a pretty good fit to the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Step 5: Predictions on the Test Set\n",
    "\n",
    "Now that you have fitted a regression line on your train dataset, it's time to make some predictions on the test data. For this, you first need to add a constant to the `X_test` data like you did for `X_train` and then you can simply go on and predict the y values corresponding to `X_test` using the `predict` attribute of the fitted regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Add a constant to X_test\n",
    "X_test_sm = sm.add_constant(X_test)\n",
    "\n",
    "# Predict the y values corresponding to X_test_sm\n",
    "y_pred = lr.predict(X_test_sm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "126     7.374140\n",
       "104    19.941482\n",
       "99     14.323269\n",
       "92     18.823294\n",
       "111    20.132392\n",
       "dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Looking at the RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.019296008966233"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Returns the mean squared error; we'll take a square root\n",
    "np.sqrt(mean_squared_error(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Checking the R-squared on the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7921031601245658"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r_squared = r2_score(y_test, y_pred)\n",
    "r_squared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Visualizing the fit on the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_test, y_test)\n",
    "y_test_pred = lr.predict(X_test_sm)\n",
    "plt.plot(X_test,y_test_pred, 'r')\n",
    "# plt.plot(X_test, 6.948 + 0.054 * X_test, 'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression using `linear_model` in `sklearn`\n",
    "\n",
    "Apart from `statsmodels`, there is another package namely `sklearn` that can be used to perform linear regression. We will use the `linear_model` library from `sklearn` to build the model. Since, we hae already performed a train-test split, we don't need to do it again.\n",
    "\n",
    "There's one small step that we need to add, though. When there's only a single feature, we need to add an additional column in order for the linear regression fit to be performed successfully."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train_lm, X_test_lm, y_train_lm, y_test_lm = train_test_split(X, y, train_size = 0.7, test_size = 0.3, random_state = 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(140,)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_lm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_lm = X_train_lm.values.reshape(-1,1)\n",
    "X_test_lm = X_test_lm.values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(140, 1)\n",
      "(140,)\n",
      "(60, 1)\n",
      "(60,)\n"
     ]
    }
   ],
   "source": [
    "print(X_train_lm.shape)\n",
    "print(y_train_lm.shape)\n",
    "print(X_test_lm.shape)\n",
    "print(y_test_lm.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Representing LinearRegression as lr(Creating LinearRegression Object)\n",
    "lm = LinearRegression()\n",
    "\n",
    "# Fit the model using lr.fit()\n",
    "lm.fit(X_train_lm, y_train_lm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.9486832000013585\n",
      "[0.05454575]\n"
     ]
    }
   ],
   "source": [
    "print(lm.intercept_)\n",
    "print(lm.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = lm.predict(X_test_lm)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x286ca83de90>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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g/ZJLLtGGDRtM7+N2u+V2u8NZBgBENbodiHVhDR8JCQnq06ePPv3004D1PXv2qGPHjuH8VgBgO3Pf+UTPF34WtE7wQKwJOXxUVlZq3759/uvFxcXavn27UlNTlZGRofvuu0833nijrrnmGg0ePFirVq3SW2+9pYKCgnDWDQC2YtbtuKR9st6552oLqgGsFfI5HwUFBRo8eHDQem5urhYuXChJevHFF5Wfn6/Dhw+rW7dumjVrlsaOHdugr89LbQE4DWMWxIJQnr+bdMJpcyB8AHCKn7+6Ve98VBq0TvCAE1l2wikA4O/Muh2jerXXMz/ubUE1QHQhfABAmDFmAc6M8AEAYTLiqfX6pLQiaJ3gAQQifABAGJh1O36e3VkPjOhuQTVAdCN8AEATMWYBQkP4AIBG6jJ9paprg18wSPAAzozwAQCNYNbt+NXYHrq5f6fIFwPYDOEDAELEmAVoGsIHADQQn0QLhAfhAwAawCx4vHDzFRreI82CagB7I3wAwBkYhqHMvJVB63Q7gMYjfABAPRizAM2D8AEAJsyCx5KJA9Q74zwLqgGchfABAP+its5Q5wcZswDNifABAP/AmAWIDMIHAMg8eKz7ZbYy27S2oBrA2QgfAGLaiVO1uuThVUHrdDuA5kP4ABCzGLMA1iB8AIhJZsFj8/RrdUGS24JqgNhC+AAQU76p9OmKx94LWqfbAUQO4QNAzGDMAkQHwgeAmGAWPD5+dLhaJfBnEIg0/tUBcLSD31Rp0H8XBK3T7QCsQ/gA4FiMWYDoRPgA4EhmwWPf7By1iI+zoBoA/4p/hQAcZXvJMdPgcWDuKIIHECXofABwDMYsgD0QPgA4glnwKM4fKZfLZUE1AM6EHiQAW/vz7i/rHbMQPIDoROcDgG0xZgHsifABwJbq63YAiH6MXQDYyp+2HiZ4ADZH5wOAbZiFjiR3C+2cNdyCagA0FuEDgC3Q7QCcg/ABIKotWLtXT6zeE7RO8ADsi/ABIGqZdTuy0s/Vm5O+b0E1AMKF8AEgKjFmAZyL8AEgqjz61sd68S/FQesED8A5CB8AooZZt2P8VRnKH9fLgmoANBfCB4CowJgFiB0hv8nY+vXrNXr0aHk8HrlcLi1btqzeY++44w65XC499dRTTSgRgJPd/vIWggcQY0IOH1VVVcrKytKCBQvOeNyyZcv017/+VR6Pp9HFAXC2TtNWaPXHXwas/XJYV4IH4HAhj11ycnKUk5NzxmM+//xzTZ48We+++65GjeKPCIBgdDuA2BX2cz7q6up0880367777lOPHj3OerzP55PP5/Nf93q94S4JQBT54XMbteXg0aB1ggcQO8IePubNm6cWLVro7rvvbtDx+fn5mjVrVrjLABCFzLod//3Dy/QfV6ZbUA0Aq4Q1fGzdulW//vWvVVRUJJfL1aD75OXlaerUqf7rXq9X6en8IQKchjELgO+ENXy8//77KisrU0ZGhn+ttrZW9957r5566ikdOHAg6D5ut1tutzucZQCIIlc+9p6+rvQFrRM8gNgV1vBx880369prrw1YGz58uG6++Wbdeuut4fxWAGzArNux+L/6asDFbSyoBkC0CDl8VFZWat++ff7rxcXF2r59u1JTU5WRkaHzzz8/4PiWLVsqLS1N3bp1a3q1AGzBMAxl5q0MWqfbAUBqRPjYsmWLBg8e7L/+3fkaubm5WrhwYdgKA2BPZt0OieAB4J9CDh/Z2dkyDKPBx5ud5wHAmcyCx4q7B6qHJ8WCagBEKz7bBUCT1dUZuuhBxiwAGobwAaBJGLMACBXhA0CjmQWP9+8frPTUVhZUA8AuCB8AQuarqVW3h1YFrdPtANAQhA8AIWHMAqCpCB8AGswseBTNGKrU1gkWVAPArggfAM6q/ES1smatDlqn2wGgMQgfAM6IMQuAcCN8AKiXWfD4+NHhapXAnw4AjcdfEABBvvSeVN85fw5ap9sBIBwIHwACMGYB0NwIHwD8zILHvtk5ahEfZ0E1AJyKvygAtK+s0jR4HJg7iuABIOzofAAxjjELgEgjfAAxzCx4FOePlMvlsqAaALGCfioQg3YcPlbvmIXgAaC50fkAYoxZ6GgZ79Le2SMtqAZALCJ8ADGkvm4HAEQSYxcgBhTu+YrgASBq0PkAHM4sdPTpdJ7+eOcAC6oBAMIH4Gh0OwBEI8YugAMtKTpM8AAQteh8AA5jFjrGXX6h5t/4b5EvBgBMED4AB6HbAcAOGLsADvBC4WcEDwC2QecDsDmz0DExu7PuH9HdgmoA4OwIH4CN0e0AYEeED8CGZr21Sy/95UDQOsEDgB0QPgCbMet2zBrTQ7kDOkW+GABoBMIHYCOMWQA4AeEDsIE7Xtmid3d9GbRO8ABgR4QPIMqZdTuemdBboy5rb0E1ANB0hA8gijFmAeBEhA8gCo16+n3tOuINWid4AHACwgcQZcy6Ha/d1k/9O59vQTUAEH6EDyCKMGYBEAsIH0AU6PXIu6rw1QStEzwAOBHhA7CYWbdj5d1X61JPsgXVAEDzI3wAFjEMQ5l5K4PW6XYAcDrCB2ABs26HRPAAEBviQr3D+vXrNXr0aHk8HrlcLi1btsx/W3V1tR544AH16tVLrVu3lsfj0U9+8hMdOXIknDUDtmYWPDZOG0LwABAzQg4fVVVVysrK0oIFC4JuO378uIqKijRjxgwVFRVpyZIl2rNnj8aMGROWYgE7q66tq/fVLJ5zEy2oCACs4TIMw2j0nV0uLV26VNdff329x2zevFlXXXWVDh48qIyMjLN+Ta/Xq5SUFJWXlys5mRPu4AyMWQA4XSjP381+zkd5eblcLpfOPfdc09t9Pp98Pp//utcb/K6OgJ2ZBY/tDw/Vua0SLKgGAKwX8tglFCdPntS0adM0YcKEelNQfn6+UlJS/Jf09PTmLAmImOOnauodsxA8AMSyZgsf1dXVuummm1RXV6dnn3223uPy8vJUXl7uv5SUlDRXSUDEdJq2Qpc+/G7QOmMWAGimsUt1dbV+9KMfqbi4WGvXrj3j7MftdsvtdjdHGYAlzLodux8docSEeAuqAYDoE/bw8V3w2Lt3r9atW6fzz+fDsBAbvq06pd6/WhO0TrcDAAKFHD4qKyu1b98+//Xi4mJt375dqamp8ng8+uEPf6iioiK9/fbbqq2tVWlpqSQpNTVVCQnMueFMvJoFABou5JfaFhQUaPDgwUHrubm5mjlzpjIzM03vt27dOmVnZ5/16/NSW9iNWfDYNztHLeKb9XxuAIgqzfpS2+zsbJ0przThbUMAW/n82Al9f+7aoHW6HQBwZny2C9AIZt2OhPg47ZmdY0E1AGAvhA8gRGbBozh/pFwulwXVAID9MJQGGmj/V5X1vmkYwQMAGo7OB9AAZqHjqsxU/e8d/S2oBgDsjfABnEV93Q4AQOMwdgHqsePwMYIHADQDOh+ACbPQMf6qdOWPu8yCagDAWQgfwGnodgBA82LsAvzDhr1fEzwAIALofAAy73bcNeRi3TusmwXVAICzET4Q8+h2AEBkMXZBzHp7xxGCBwBYgM4HYpJZ6Hh0bA/9pH+nyBcDADGG8IGYQ7cDAKzF2AUxY9HGAwQPAIgCdD4QE8xCx2/GX67RWR4LqgGA2Eb4gOPR7QCA6MLYBY71xuZDBA8AiEJ0PuBIZqHjlZ9dpau7XGBBNQCAf0X4gOPQ7QCA6MbYBY7xfOFnBA8AsAE6H3AEs9Dx3tRBurjt9yyoBgBwJoQP2B7dDgCwF8IHbGvOyt36f+v3B60TPAAguhE+YEtm3Y6N04bIc26iBdUAAEJB+ICtGIahzLyVQet0OwDAPggfsI2573yi5ws/C1oneACAvRA+YAtmY5aiGUOV2jrBgmoAAE1B+EBUq60z1PlBxiwA4CSED0StB/60Q29sKQlY6+FJ1oq7r7aoIgBAOBA+EJXMxiwfPzpcrRJ4yAKA3fGXHFHlVE2duj70TtA6YxYAcA7CB6LGzxZu1p8/KQtYy+52gRbeepVFFQEAmgPhA1HBbMyy57EcJbTgsw8BwGn4yw5LnThVW+9nsxA8AMCZ6HzAMmOf+Ys+LDkWsHZD7w568kdZ1hQEAIgIwgcsYdbt+GzOSMXHuSyoBgAQSfS1EVHlJ6rrHbMQPAAgNtD5QMQMyP+zjpSfDFi7/ZqL9ODISyyqCABgBcIHIsKs21GcP1IuF90OAIg1IY9d1q9fr9GjR8vj8cjlcmnZsmUBtxuGoZkzZ8rj8SgxMVHZ2dnatWtXuOqFzXxV4at3zELwAIDYFHL4qKqqUlZWlhYsWGB6++OPP6758+drwYIF2rx5s9LS0jR06FBVVFQ0uVjYy0V5K9Rn9nsBa/eP6Ma7lQJAjAt57JKTk6OcnBzT2wzD0FNPPaXp06dr3LhxkqRFixapXbt2Wrx4se64446mVQvbqK/bAQBAWF/tUlxcrNLSUg0bNsy/5na7NWjQIG3cuNH0Pj6fT16vN+AC+/rSe5LgAQA4o7CecFpaWipJateuXcB6u3btdPDgQdP75Ofna9asWeEsAxbpN+fPKvUGvppl9g966sd9O1pUEQAgGjXL+3ycfiKhYRj1nlyYl5en8vJy/6WkpKQ5SkIz6zRtRVDwODB3FMEDABAkrJ2PtLQ0SX/vgLRv396/XlZWFtQN+Y7b7Zbb7Q5nGYigg99UadB/FwStM2YBANQnrOEjMzNTaWlpWrNmjS6//HJJ0qlTp1RYWKh58+aF81shCnR+cKVq64yAtYW39lF2t7YWVQQAsIOQw0dlZaX27dvnv15cXKzt27crNTVVGRkZmjJliubMmaMuXbqoS5cumjNnjlq1aqUJEyaEtXBYi5NKAQCNFXL42LJliwYPHuy/PnXqVElSbm6uFi5cqPvvv18nTpzQxIkTdfToUfXt21erV69WUlJS+KqGZT4trdDwp9YHrRM8AAAN5TIMwzj7YZHj9XqVkpKi8vJyJScnW10O/oVZt+NPd/bXlZ1SLagGABBNQnn+5rNd0CCMWQAA4dIsL7WFc+z5soLgAQAIKzofqNflj67W0ePVAWsr7h6oHp4UiyoCADgB4QOm6HYAAJoLYxcE2HH4WFDwyOqQQvAAAIQNnQ/4mXU7/jJtiC48N9GCagAATkX4gCTGLACAyGHsEuM27f8mKHhc0/UCggcAoNnQ+YhhZt2OzdOv1QVJfNAfAKD5ED5iFGMWAIBVGLvEmHWflgUFjzFZHoIHACBi6HzEELNux4cPD1NKq5YWVAMAiFWEjxhgGIYy81YGrdPtAABYgbGLw63Y8UVQ8PjPfhkEDwCAZeh8OJjZmGXXrOFq7ebXDgCwDs9CDlRXZ+iiBxmzAACiE2MXh/nfzSVBwWPS4M4EDwBA1KDz4SBmY5ZPfjVC57SMt6AaAADMET4cgDELAMBOCB829+6uUt3xytaAtQUTLtd1l3ksqggAgDMjfNiY2ZjlszkjFR/nsqAaAAAahvBhQzW1dbp4+jtB64xZAAB2QPiwmTe3f657Xt8esPbiLVdqSPd21hQEAECICB82YjZm2T9npOIYswAAbIT3+bABX01tUPBIcrfQgbmjCB4AANuh8xHlXvvbIeUt2Rmwtvi2vhrQuY1FFQEA0DSEjyhmNmYpzh8pl4tuBwDAvhi7RKETp4LHLB3OS9SBuaMIHgAA26PzEWV+9/5+PbZid8DakokD1DvjPIsqAgAgvAgfUcRszMJ7dwAAnIaxSxSoOFkdFDwubZ9M8AAAOBKdD4s9/ee9mr9mT8Da23cNVM8LUyyqCACA5kX4sBBjFgBALGLsYoGjVaeCgke/i1IJHgCAmEDnI8Ly39mtFwr3B6y9N/UaXdw2yaKKAACILMJHBDFmAQCAsUtElFWcDAoeQy9tR/AAAMQkOh/NbPrSnfrDXw8FrK2/b7Ayzm9lUUUAAFiL8NGMGLMAABCMsUszOHLsRFDwGNf7QoIHAABqhvBRU1Ojhx56SJmZmUpMTNRFF12kRx99VHV1deH+VlHpnte3acDctQFrH+QN0fwf/Zs1BQEAEGXCPnaZN2+enn/+eS1atEg9evTQli1bdOuttyolJUX33HNPuL9dVGHMAgDA2YU9fHzwwQcaO3asRo36+5Nup06d9Nprr2nLli3h/lZR48DXVcp+oiBgLbd/R80a29OaggAAiGJhDx8DBw7U888/rz179qhr16768MMPtWHDBj311FOmx/t8Pvl8Pv91r9cb7pKa1U8XbtbaT8oC1rY8dK3afM9tUUUAAES3sIePBx54QOXl5erevbvi4+NVW1ur2bNna/z48abH5+fna9asWeEuIyIYswAAELqwn3D6xhtv6NVXX9XixYtVVFSkRYsW6YknntCiRYtMj8/Ly1N5ebn/UlJSEu6Swm7PlxVBwWPS4M4EDwAAGsBlGIYRzi+Ynp6uadOmadKkSf61xx57TK+++qo++eSTs97f6/UqJSVF5eXlSk5ODmdpYTFv1Sd6ruCzgLUPHx6mlFYtLaoIAADrhfL8Hfaxy/HjxxUXF9hQiY+Pd8RLbZcUHQ4KHnQ7AAAITdjDx+jRozV79mxlZGSoR48e2rZtm+bPn6+f/vSn4f5WEXP8VI0eeXOX/rj1sH/tV9f31M39OlpYFQAA9hT2sUtFRYVmzJihpUuXqqysTB6PR+PHj9fDDz+shISEs94/2sYue76s0KQ/FGlvWaXiXNI9/95Vk4dcrPg4l9WlAQAQNUJ5/g57+GiqaAkfhmHoj1sO6+HlH+lkdZ3aJrn165suV//O51tWEwAA0crScz6coMpXo4eWfaSl2z6XJF3dpY3+58Z/4707AAAIA8LHaXZ/4dWkPxRp/9dVio9zaerQrvr5oM6KY8wCAEBYED7+wTAMLf7bIc1662OdqqlTWvI5+s2Ey9WnU6rVpQEA4CiED0kVJ6uVt2Sn3t7xhSRpSPe2euI/spTa+uwnyAIAgNDEfPj46PNyTV5cpAPfHFeLOJfuH9FN/zXwIsYsAAA0k5gNH4Zh6OUPDmr2it06VVunC89N1G8mXK7eGedZXRoAAI4Wk+Gj/ES1HvjTDq3aVSpJGnppOz3xwyzeIh0AgAiIufCxveSYJi8u0uGjJ9Qy3qW8nEt06/c7yeVizAIAQCTETPgwDEO/31Cseas+UXWtofTURC0Y31tZ6edaXRoAADElZsLHzs/L9diK3ZKkkb3SNPeGy5R8DmMWAAAiLWbCx2UdztWUa7vo/NYJ+s9+HRmzAABgkZgJH5I05dquVpcAAEDMi7O6AAAAEFsIHwAAIKIIHwAAIKIIHwAAIKIIHwAAIKIIHwAAIKIIHwAAIKIIHwAAIKIIHwAAIKIIHwAAIKIIHwAAIKIIHwAAIKIIHwAAIKKi7lNtDcOQJHm9XosrAQAADfXd8/Z3z+NnEnXho6KiQpKUnp5ucSUAACBUFRUVSklJOeMxLqMhESWC6urqdOTIESUlJcnlcgXd7vV6lZ6erpKSEiUnJ1tQYWxi363Bvkcee24N9j3ywr3nhmGooqJCHo9HcXFnPqsj6jofcXFx6tChw1mPS05O5gFqAfbdGux75LHn1mDfIy+ce362jsd3OOEUAABEFOEDAABElO3Ch9vt1iOPPCK32211KTGFfbcG+x557Lk12PfIs3LPo+6EUwAA4Gy263wAAAB7I3wAAICIInwAAICIInwAAICIsl34ePbZZ5WZmalzzjlHV1xxhd5//32rS3KMmTNnyuVyBVzS0tL8txuGoZkzZ8rj8SgxMVHZ2dnatWuXhRXb0/r16zV69Gh5PB65XC4tW7Ys4PaG7LPP59Ndd92lNm3aqHXr1hozZowOHz4cwZ/CXs6257fcckvQY79fv34Bx7DnocnPz1efPn2UlJSktm3b6vrrr9enn34acAyP9fBryL5Hw+PdVuHjjTfe0JQpUzR9+nRt27ZNV199tXJycnTo0CGrS3OMHj166IsvvvBfdu7c6b/t8ccf1/z587VgwQJt3rxZaWlpGjp0qP/zeNAwVVVVysrK0oIFC0xvb8g+T5kyRUuXLtXrr7+uDRs2qLKyUtddd51qa2sj9WPYytn2XJJGjBgR8NhfuXJlwO3seWgKCws1adIkbdq0SWvWrFFNTY2GDRumqqoq/zE81sOvIfsuRcHj3bCRq666yrjzzjsD1rp3725MmzbNooqc5ZFHHjGysrJMb6urqzPS0tKMuXPn+tdOnjxppKSkGM8//3yEKnQeScbSpUv91xuyz8eOHTNatmxpvP766/5jPv/8cyMuLs5YtWpVxGq3q9P33DAMIzc31xg7dmy992HPm66srMyQZBQWFhqGwWM9Uk7fd8OIjse7bTofp06d0tatWzVs2LCA9WHDhmnjxo0WVeU8e/fulcfjUWZmpm666Sbt379fklRcXKzS0tKA/Xe73Ro0aBD7H0YN2eetW7equro64BiPx6OePXvyu2iCgoICtW3bVl27dtVtt92msrIy/23sedOVl5dLklJTUyXxWI+U0/f9O1Y/3m0TPr7++mvV1taqXbt2Aevt2rVTaWmpRVU5S9++ffXyyy/r3Xff1W9/+1uVlpZqwIAB+uabb/x7zP43r4bsc2lpqRISEnTeeefVewxCk5OToz/84Q9au3atnnzySW3evFlDhgyRz+eTxJ43lWEYmjp1qgYOHKiePXtK4rEeCWb7LkXH4z3qPtX2bFwuV8B1wzCC1tA4OTk5/v/u1auX+vfvr86dO2vRokX+k5HY/8hozD7zu2i8G2+80f/fPXv21JVXXqmOHTtqxYoVGjduXL33Y88bZvLkydqxY4c2bNgQdBuP9eZT375Hw+PdNp2PNm3aKD4+Pih1lZWVBSVnhEfr1q3Vq1cv7d271/+qF/a/eTVkn9PS0nTq1CkdPXq03mPQNO3bt1fHjh21d+9eSex5U9x1111avny51q1bpw4dOvjXeaw3r/r23YwVj3fbhI+EhARdccUVWrNmTcD6mjVrNGDAAIuqcjafz6fdu3erffv2yszMVFpaWsD+nzp1SoWFhex/GDVkn6+44gq1bNky4JgvvvhCH330Eb+LMPnmm29UUlKi9u3bS2LPG8MwDE2ePFlLlizR2rVrlZmZGXA7j/XmcbZ9N2PJ4z0sp61GyOuvv260bNnS+P3vf298/PHHxpQpU4zWrVsbBw4csLo0R7j33nuNgoICY//+/camTZuM6667zkhKSvLv79y5c42UlBRjyZIlxs6dO43x48cb7du3N7xer8WV20tFRYWxbds2Y9u2bYYkY/78+ca2bduMgwcPGobRsH2+8847jQ4dOhjvvfeeUVRUZAwZMsTIysoyampqrPqxotqZ9ryiosK49957jY0bNxrFxcXGunXrjP79+xsXXnghe94EP//5z42UlBSjoKDA+OKLL/yX48eP+4/hsR5+Z9v3aHm82yp8GIZhPPPMM0bHjh2NhIQEo3fv3gEvH0LT3HjjjUb79u2Nli1bGh6Pxxg3bpyxa9cu/+11dXXGI488YqSlpRlut9u45pprjJ07d1pYsT2tW7fOkBR0yc3NNQyjYft84sQJY/LkyUZqaqqRmJhoXHfddcahQ4cs+Gns4Ux7fvz4cWPYsGHGBRdcYLRs2dLIyMgwcnNzg/aTPQ+N2X5LMl566SX/MTzWw+9s+x4tj3fXP4oFAACICNuc8wEAAJyB8AEAACKK8AEAACKK8AEAACKK8AEAACKK8AEAACKK8AEAACKK8AEAACKK8AEAACKK8AEAACKK8AEAACKK8AEAACLq/wMSkMEvOfyXtAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_test_lm,y_pred)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equationwe get is the same as what we got before!\n",
    "\n",
    "$ Sales = 6.948 + 0.054* TV $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sklearn linear model is useful as it is compatible with a lot of sklearn utilites (cross validation, grid search etc.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Addressing some common questions/doubts on Simple Linear Regression\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q: Why is it called 'R-squared'?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on what we learnt so far, do you see it? Can you answer this?\n",
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ".\n",
    "\n",
    ".\n",
    " \n",
    ".\n",
    "\n",
    ".\n",
    " \n",
    "  #### Drumroll...\n",
    "  \n",
    ".\n",
    " \n",
    ".\n",
    "\n",
    ".\n",
    "\n",
    "."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.         0.90321277]\n",
      " [0.90321277 1.        ]]\n"
     ]
    }
   ],
   "source": [
    "corrs = np.corrcoef(X_train, y_train)\n",
    "print(corrs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8157933136480384"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrs[0,1] ** 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correlation (Pearson) is also called **\"r\"** or **\"Pearson's R\"**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q: What is a good RMSE? Is there some RMSE that I should aim for?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "\n",
    "<br>\n",
    "\n",
    "You should be able to answer this by now!\n",
    "\n",
    "\n",
    "<br>\n",
    "\n",
    "\n",
    "<br>\n",
    "\n",
    "\n",
    "\n",
    "Look at \"Sharma ji ka beta\"; he could answer this in a moment. How lucky is Sharma ji to have such a smart kid!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ".\n",
    "\n",
    ".\n",
    " \n",
    ".\n",
    "\n",
    ".\n",
    " \n",
    "  #### Drumroll...\n",
    "  \n",
    ".\n",
    " \n",
    ".\n",
    "\n",
    ".\n",
    "\n",
    "."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " \n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The RMSE:\n",
    " - depends on the units of the Y variables\n",
    " - is NOT a normalized measure\n",
    " \n",
    "While it can't really tell you of the gooodness of the particular model, it can help you compare models. \n",
    "\n",
    "A better measure is R squared, which is normalized."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q: Does scaling have an impact on the model? When should I scale?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While the true benefits of scaling will be apparent during future modules, at this juncture we can discuss if it has an impact on the model.\n",
    "\n",
    "We'll rebuild the model after scaling the predictor and see what changes.\n",
    "\n",
    "The most popular methods for scaling:\n",
    "1. Min-Max Scaling\n",
    "2. Standard Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size = 0.7, test_size = 0.3, random_state = 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### SciKit Learn has these scaling utilities handy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler, MinMaxScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# One aspect that you need to take care of is that the 'fit_transform' can be performed on 2D arrays only. So you need to\n",
    "# reshape your 'X_train_scaled' and 'y_trained_scaled' data in order to perform the standardisation.\n",
    "X_train_scaled = X_train.reshape(-1,1)\n",
    "y_train_scaled = y_train.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(140, 1)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_scaled.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a scaler object using StandardScaler()\n",
    "scaler = StandardScaler()\n",
    "#'Fit' and transform the train set; and transform using the fit on the test set later\n",
    "X_train_scaled = scaler.fit_transform(X_train_scaled)\n",
    "y_train_scaled = scaler.fit_transform(y_train_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean and sd for X_train_scaled: 2.5376526277146434e-17 0.9999999999999999\n",
      "mean and sd for y_train_scaled: -2.5376526277146434e-16 1.0\n"
     ]
    }
   ],
   "source": [
    "print(\"mean and sd for X_train_scaled:\", np.mean(X_train_scaled), np.std(X_train_scaled))\n",
    "print(\"mean and sd for y_train_scaled:\", np.mean(y_train_scaled), np.std(y_train_scaled))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's fit the regression line following exactly the same steps as done before\n",
    "X_train_scaled = sm.add_constant(X_train_scaled)\n",
    "\n",
    "lr_scaled = sm.OLS(y_train_scaled, X_train_scaled).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.91433544e-16,  9.03212773e-01])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check the parameters\n",
    "lr_scaled.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you might notice, the value of the parameters have changed since we have changed the scale."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the statistics of the model, to see if any other aspect of the model has changed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.816\n",
      "Model:                            OLS   Adj. R-squared:                  0.814\n",
      "Method:                 Least Squares   F-statistic:                     611.2\n",
      "Date:                Thu, 13 Sep 2018   Prob (F-statistic):           1.52e-52\n",
      "Time:                        22:39:46   Log-Likelihood:                -80.233\n",
      "No. Observations:                 140   AIC:                             164.5\n",
      "Df Residuals:                     138   BIC:                             170.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const      -2.914e-16      0.037  -7.98e-15      1.000      -0.072       0.072\n",
      "x1             0.9032      0.037     24.722      0.000       0.831       0.975\n",
      "==============================================================================\n",
      "Omnibus:                        0.027   Durbin-Watson:                   2.196\n",
      "Prob(Omnibus):                  0.987   Jarque-Bera (JB):                0.150\n",
      "Skew:                          -0.006   Prob(JB):                        0.928\n",
      "Kurtosis:                       2.840   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": [
    "print(lr_scaled.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model statistics and goodness of fit remain unchanged.\n",
    "\n",
    "##### So why scale at all?\n",
    "- Helps with interpretation (we'll be able to appreciate this better in later modules)\n",
    "- Faster convergence of gradient descent"
   ]
  }
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