Simple_Linear_Regression_using_Scikit_Learn_and_Pyspark.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Regression using Scikit Learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simple Linear Regression Equation\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### y = a0 + a1*X                                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Import Libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time_to_Study</th>\n",
       "      <th>Grades</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>2.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>3.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>1.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Time_to_Study  Grades\n",
       "0              1     1.5\n",
       "1              5     2.7\n",
       "2              7     3.1\n",
       "3              3     2.1\n",
       "4              2     1.8"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Read Student Grades .csv file and divide the data into dependent and independent variables.\n",
    "data = pd.read_csv('Student_Grades_Data.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 2)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = data.iloc[:, :-1].values\n",
    "y = data.iloc[:, 1].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1],\n",
       "       [ 5],\n",
       "       [ 7],\n",
       "       [ 3],\n",
       "       [ 2],\n",
       "       [ 9],\n",
       "       [ 6],\n",
       "       [12],\n",
       "       [11],\n",
       "       [ 2],\n",
       "       [ 4],\n",
       "       [ 8],\n",
       "       [13],\n",
       "       [ 9],\n",
       "       [14],\n",
       "       [10],\n",
       "       [ 6],\n",
       "       [12],\n",
       "       [ 1],\n",
       "       [ 4],\n",
       "       [14],\n",
       "       [10],\n",
       "       [11],\n",
       "       [ 4],\n",
       "       [ 5],\n",
       "       [ 8],\n",
       "       [ 1],\n",
       "       [ 2],\n",
       "       [ 3],\n",
       "       [ 7],\n",
       "       [ 8],\n",
       "       [14],\n",
       "       [ 7],\n",
       "       [ 8],\n",
       "       [ 1],\n",
       "       [ 2],\n",
       "       [ 3],\n",
       "       [ 4],\n",
       "       [ 5],\n",
       "       [ 6],\n",
       "       [ 7],\n",
       "       [ 8],\n",
       "       [ 9],\n",
       "       [10],\n",
       "       [11],\n",
       "       [12],\n",
       "       [13],\n",
       "       [14],\n",
       "       [ 8],\n",
       "       [ 2]], dtype=int64)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.5, 2.7, 3.1, 2.1, 1.8, 3.9, 2.9, 4.5, 4.3, 1.8, 2.4, 3.5, 4.8,\n",
       "       3.9, 5. , 4.1, 2.9, 4.5, 1.5, 2.4, 5. , 4.1, 4.3, 2.4, 2.7, 3.5,\n",
       "       1.5, 1.8, 2.1, 3.1, 3.5, 5. , 3.1, 3.5, 1.5, 1.8, 2.1, 2.4, 2.7,\n",
       "       2.9, 3.1, 3.5, 3.9, 4.1, 4.3, 4.5, 4.8, 5. , 3.5, 1.8])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Split the data into training and test datasets\n",
    "from sklearn.cross_validation import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.1, 3.5, 2.4, 3.5, 3.1, 1.8, 2.7, 5. , 4.3, 1.8, 3.5, 1.8, 1.5,\n",
       "       1.5, 1.5])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Fit the Simple Linear Regression Model\n",
    "from sklearn.linear_model import LinearRegression\n",
    "LinReg = LinearRegression()\n",
    "LinReg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a0 = 1.3045041899441348\n",
      "a1 = [0.2704027]\n"
     ]
    }
   ],
   "source": [
    "#Print the \n",
    "print(f'a0 = {LinReg.intercept_}')\n",
    "print(f'a1 = {LinReg.coef_}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.11571229, 3.46772579, 2.38611499, 3.46772579, 3.19732309,\n",
       "       1.84530959, 2.65651769, 5.09014199, 4.27893389, 1.84530959,\n",
       "       3.46772579, 1.84530959, 1.57490689, 1.57490689, 1.57490689])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Predicted grade scores from test dataset\n",
    "y_predict = LinReg.predict(X_test)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.1, 3.5, 2.4, 3.5, 3.1, 1.8, 2.7, 5. , 4.3, 1.8, 3.5, 1.8, 1.5,\n",
       "       1.5, 1.5])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Actual grade scores from test dataset\n",
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
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S2GuvwumwIoIddtihG6M0s3zuPrJMTJwI+Ve+bGratDx8+C/44Q9/WFDfLQOz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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Grades Vs Time to Study visualization on Training Data\n",
    "plt.scatter(X_train, y_train, color='Blue')\n",
    "plt.plot(X_train, LinReg.predict(X_train), color='Black')\n",
    "plt.title('Grades Vs Time to Study (On Training Data)')\n",
    "plt.xlabel('Time to Study')\n",
    "plt.ylabel('Grades')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JISKcEMxqjJOCbTJJRYeV/vSnP/VAslmNcveRdZrPV2TW82RWKUjaUdIMSXMl\nvSDp9DLLjJa0QtKc9HZOVvFY13nnnXdaJIRnn33WCcGsB8iyUtgAnBURsyUNAWZJ+nNEvFiy3EMR\ncViGcVgXcnVg1rNlVilExKKImJ3eXwXMBXbIan+WrbvuuqtFQli7dq0TglkPU5UxBUl1wF7AE2Vm\n7y/pGeAt4PsR8UKZ9ScCEwGGp7+UteopTQZ77703s2bNyikaM8tS5kcfSdoMuAk4IyJWlsyeDYyI\niD2BXwK3lttGREyNiFERMWro0KHZBmzNvva1r5U9zNQJwaznyjQpSOpPkhCmR8TNpfMjYmVErE7v\n3wn0l7RNljFZ+yICSVx33XXNbVdccYW7isx6gSyPPhJwJTA3Ii5sZZlt0+WQtG8az9tZxWRllFwI\nRxJ9+hS/LCKCE088MZ/4zKyqshxTOBA4BnhO0py07cfAcICImAIcCZwiaQPwHnB0+Oto9RRcCOdN\nYFh9fdHsN954g7q6ulxCM7N8ZJYUIuJhkrMmt7XMpcClWcVg7UgvhFPuSXJuNuudfJqLXuyu+voW\nCWEjEGV+i2BmvYOTQi8liXEF0/8CBOkLwof9mvVaTgq9zMSJE1seZgrc0DQxaBBMnlztsMysm/AJ\n8XqJjRs30q9f8dN9//33c/BbbyVjC/PnJxXC5Mm+EI5ZL+ak0Au0e74iJwEzS7n7qAerr69vkRDe\neecdH1lkZq1ypdBDlSaDESNGMG/evHyCMbOa4Uqhh7nuuutaJITGxkYnBDOriJNCDyKJr33ta83T\nkydPbj6PkZlZJdx91AOMHz+e22+/vajN4wZm1hlOCjVs7dq1DBgwoKht5syZfOYzn8kpIjOrdU4K\nNcqXxTSzLHhMocbMnTu3RUJYvXq1E4KZdQknhe6u4HoHkthtt92aZx1wwAFEBIMHD84vPjPrUdx9\n1J2l1zu4saGBo0pmuTIwsyy4UujOJk1CJQlhChAjRuQVkZn1cE4K3dQpp5yCSq6EFsBJkJy8zsws\nA+4+6mbee+89Bg0aVNQ2H9ixsMHXOzCzjLhS6EYGDx5clBA+se22xKBBxQnB1zswswxllhQk7Shp\nhqS5kl6QdHqZZSTpEkmvSXpW0t5ZxdOdvfTSS0iioaGhuW3dunW8vGgRTJ0KI0aAlPydOtWnujaz\nzGRZKWwAzoqIXYH9gNMk7VayzOeBndPbROCyDOPpliSx6667Nk+fc845RAT9+/dPGiZMgHnzoLEx\n+euEYGYZymxMISIWAYvS+6skzQV2AF4sWGw8MC2S4ysfl7SlpO3SdXu0adOmcdxxxxW1+TBTM8tb\nVQaaJdUBewFPlMzaAVhQML3K8XZfAAAKpElEQVQwbStKCpImklQSDK/xQdaIoE+f4gJtxowZjB49\nOp+AzMwKZD7QLGkz4CbgjIhYWTq7zCotvi5HxNSIGBURo4YOHZpFmFVx1FFHtUgIEeGEYGbdRqaV\ngqT+JAlhekTcXGaRhRQfbTkMeCvLmPKwcuVKtthii6K2xYsX8+EPfziniMzMysvy6CMBVwJzI+LC\nVha7HTg2PQppP2BFTxtPkFSUEA466CAiwgnBzLqlLCuFA4FjgOckzUnbfgwMB4iIKcCdwDjgNaAB\nOCHDeKpq9uzZLa5rsHHjxhbdR2Zm3UmWRx89TPkxg8JlAjgtqxjyUnpq64suuogzzjgjp2jMzCrn\n01x0oUsuuYTTTy/+jZ4PMzWzWuKk0AXKHWb65JNPss8+++QUkZlZ57iDexM98MADLQ8zHTPGCcHM\napKTQietXbuWHXbYgYMPPhiAjwPrSH9kcd99MHZsjtGZmXWOk0InXHnllQwYMIC33kp+UvEw8CrQ\nv3Ch++7LITIzs03jMYUOWLp0adHvC4466iiuv+GGtg+xMjOrIa4UKnTWWWcVJYTXX3+d3//+904I\nZtajOCm048UXX0QSF16Y/Cj7ggsuICLYaaedkgXGjCm/YmvtZmbdmLuPWtHY2MjYsWOZMWNGc9vy\n5ctbnMOIe+9NBpULxxDGjEnazcxqjCuFMu6++2769u3bnBBuvPFGIqJlQmhy770Q8f7NCcHMapQr\nhQINDQ1sv/32rFixAoCRI0fy1FNP0a+fHyYz6x1cKaQuvfRSBg8e3JwQnnrqKZ5++mknBDPrVXr9\nJ96iRYvYfvvtm6ePP/54rrrqqhwjMjPLT6+uFE4++eSihLBgwQInBDPr1XplUpgzZw6SuPzyywG4\n8MILiQiGDRuWc2RmZvnqVd1HGzduZP/99+epp54CYODAgSxdupTBgwfnHJmZWffQayqFxsZG+vXr\n15wQ/vjHP9LQ0OCEYGZWoNdUChs2bOCAAw4A4KGHHvJlMc3Mysjsk1HSbyQtkfR8K/NHS1ohaU56\nOyerWAA+MG4cjzz6KI88+ih9+vb1qa3NzMrI8uvy1cCh7SzzUESMTG/nZxZJ6WkowNc8MDMrI7Ok\nEBEPAu9ktf0Oae3aBr7mgZlZkbw71veX9IykuyTt3tpCkiZKmilp5tKlS6sZn5lZr5JnUpgNjIiI\nPYFfAre2tmBETI2IURExaujQoVUL0Myst8ktKUTEyohYnd6/E+gvaZtMduZrHpiZVSS3pCBpW0lK\n7++bxvJ2Jju7996WCcDXPDAzayGz3ylIug4YDWwjaSHwb6TXto+IKcCRwCmSNgDvAUdHRGQVjxOA\nmVn7MksKEfHVduZfClya1f7NzKzj8j76yMzMuhEnBTMza+akYGZmzZwUzMysmZOCmZk1U5ZHgWZB\n0lKgPu84WrENsCzvIDrJsVdfrcYNjj0vmxL7iIho95QQNZcUujNJMyNiVN5xdIZjr75ajRsce16q\nEbu7j8zMrJmTgpmZNXNS6FpT8w5gEzj26qvVuMGx5yXz2D2mYGZmzVwpmJlZMycFMzNr5qTQBSTt\nKGmGpLmSXpB0et4xdYSkvpKelvSnvGPpCElbSvqDpJfSx37/vGOqlKTvpa+V5yVdJ2lA3jG1RtJv\nJC2R9HxB21aS/izp1fTvh/KMsTWtxP7z9DXzrKRbJG2ZZ4zllIu7YN73JUVWFyVzUugaG4CzImJX\nYD/gNEm75RxTR5wOzM07iE64GPifiPgksCc18j9I2gH4LjAqIj4F9AWOzjeqNl0NHFrSdjZwX0Ts\nDNyXTndHV9My9j8Dn4qIPYBXgB9VO6gKXE3LuJG0I/CPwPysduyk0AUiYlFEzE7vryL5cNoh36gq\nI2kY8AXg13nH0hGSNgc+B1wJEBHrImJ5vlF1SD9goKR+wCDgrZzjaVVEPAi8U9I8HrgmvX8NcERV\ng6pQudgj4p6I2JBOPg4Mq3pg7WjlMQe4CPgBkNkRQk4KXUxSHbAX8ES+kVTsFyQvssa8A+mgjwJL\ngavSrq9fSxqcd1CViIg3gf8i+ba3CFgREffkG1WHfSQiFkHypQj4cM7xdNY3gLvyDqISkg4H3oyI\nZ7Lcj5NCF5K0GXATcEZErMw7nvZIOgxYEhGz8o6lE/oBewOXRcRewLt03y6MImn/+3hgJ2B7YLCk\nr+cbVe8jaRJJ1+/0vGNpj6RBwCTgnKz35aTQRST1J0kI0yPi5rzjqdCBwOGS5gHXA4dIujbfkCq2\nEFgYEU0V2R9IkkQtGAu8ERFLI2I9cDNwQM4xddRiSdsBpH+X5BxPh0g6DjgMmJDpteG7zsdIvkQ8\nk75fhwGzJW3b1TtyUugCkkTStz03Ii7MO55KRcSPImJYRNSRDHTeHxE18Y01Iv4GLJC0S9o0Bngx\nx5A6Yj6wn6RB6WtnDDUySF7gduC49P5xwG05xtIhkg4FfggcHhENecdTiYh4LiI+HBF16ft1IbB3\n+j7oUk4KXeNA4BiSb9pz0tu4vIPqBb4DTJf0LDAS+EnO8VQkrW7+AMwGniN5H3bbUy9Iug54DNhF\n0kJJ3wR+BvyjpFdJjob5WZ4xtqaV2C8FhgB/Tt+rU3INsoxW4q7OvmujcjIzs2pwpWBmZs2cFMzM\nrJmTgpmZNXNSMDOzZk4KZmbWzEnBap6krQsOBf6bpDcLph/NYH8jO3rIcfqbhOmSnkvPjPqwpM3S\nM72e2okYRtfaWW2tNvTLOwCzTRURb5P8TgFJ5wKrI+K/MtzlSGAUcGcH1jkdWBwRnwZIf3S3HtgG\nOBX4VVcHadYZrhSsR5O0Ov07WtJfJN0g6RVJP5M0QdKT6bf3j6XLDZV0k6Sn0tuBJdv7AHA+8JW0\nEvlKem2BW9Pz8z8uaY8yoWwHvNk0EREvR8Rakh99fSzd1s9LKwBJl0o6Pr1/aHodgIeBf07b+qTX\nNBhaMP1aVufat57PScF6kz1JvrF/muQX6J+IiH1JThv+nXSZi4GLImIf4MuUnFI8ItaRnJTs9xEx\nMiJ+D5wHPJ2en//HwLQy+/4N8ENJj0m6QNLOafvZwF/Tbf2f1gJXchGeK4AvAv8AbJvG0whcC0xI\nFx0LPBMRyyp9UMwKOSlYb/JUeu2LtcBfgabTVT8H1KX3xwKXSppDcn6fzSUNaWe7BwG/BYiI+4Gt\nJW1RuEBEzCE53ffPga2ApyTt2oHYP0lyEr1X0xO4FZ648DfAsen9bwBXdWC7ZkU8pmC9ydqC+40F\n0428/17oA+wfEe91YLsq09bi/DERsZrkjKg3S2oExpGcWbfQBoq/rBVeprPsOWkiYoGkxZIOAT7L\n+1WDWYe5UjArdg/w7aYJSSPLLLOK5IRqTR4k/SCWNBpYVno9DUkHptdRaBqX2A2oL7OtemA3SR9M\nq40xaftLwE5NYx/AV0ti+jVJ9XBDRGys7F81a8lJwazYd4FR6aDxi8DJZZaZQfLBPUfSV4Bzm9Yh\nGTg+rsw6HwP+Iuk54GlgJnBTeuTUI+lhqj+PiAXADcCzJBd/eRogItYAE4E70oHm+pLt3w5shruO\nbBP5LKlmPYCkUSQD5P+QdyxW2zymYFbjJJ0NnILHEqwLuFIwM7NmHlMwM7NmTgpmZtbMScHMzJo5\nKZiZWTMnBTMza/b/Abkmga3WYG4gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Grades Vs Time to Study visualization on Test Data\n",
    "plt.scatter(X_test, y_test, color='Red')\n",
    "plt.plot(X_train, LinReg.predict(X_train), color='Black')\n",
    "plt.title('Grades Vs Time to Study (On Test Data)')\n",
    "plt.xlabel('Time to Study')\n",
    "plt.ylabel('Grades')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.00853119])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Predicting Grade of a student when he studied for 10 Hrs. Example of how to pass an external value,\n",
    "#Independent of Test or Training Dataset\n",
    "\n",
    "Predict_Grade = LinReg.predict(10)\n",
    "Predict_Grade"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R-Square Error: 0.997283498148368\n"
     ]
    }
   ],
   "source": [
    "#Model Evaluation using R-Square\n",
    "from sklearn import metrics\n",
    "r_square = metrics.r2_score(y_test, y_predict)\n",
    "print('R-Square Error:', r_square)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adjusted R-Square Error: 0.9971679023248944\n"
     ]
    }
   ],
   "source": [
    "#For Illustration Purpose Only. \n",
    "#Considering Multiple Linear Equation with two Variables : grade = a0 + a1*time_to_study + a2*class_participation\n",
    "#Model Evaluation using Adjusted R-Square. \n",
    "# Here n = no. of observations and p = no. of independent variables\n",
    "\n",
    "n = 50\n",
    "p = 2\n",
    "Adj_r_square = 1-(1-r_square)*(n-1)/(n-p-1)\n",
    "print('Adjusted R-Square Error:', Adj_r_square)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error: 0.003099226779173007\n"
     ]
    }
   ],
   "source": [
    "#Model Evaluation using Mean Square Error (MSE)\n",
    "print('Mean Squared Error:', metrics.mean_squared_error(y_test, y_predict))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root Mean Squared Error: 0.055670699467251235\n"
     ]
    }
   ],
   "source": [
    "#Model Evaluation using Root Mean Square Error (RMSE)\n",
    "print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y_test, y_predict)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Absolute Error: 0.0492721911855992\n"
     ]
    }
   ],
   "source": [
    "#Model Evaluation using Mean Absolute Error (MAE)\n",
    "print('Mean Absolute Error:', metrics.mean_absolute_error(y_test, y_predict))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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