Challenge(Q1,2,3),4. Linear Regression - 19BAI1047.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Shaswat Panda\n",
    "### 19BAI1047\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/run/media/supastazz/Random ヾ(≧▽≦*)o/codingfolder/CSE1015_Lab\n"
     ]
    }
   ],
   "source": [
    "!pwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "chal = pd.read_excel(\"data_chall.xlsx\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "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>Sample Number</th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>Y2</th>\n",
       "      <th>Z1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>50</td>\n",
       "      <td>6</td>\n",
       "      <td>30</td>\n",
       "      <td>4.855400</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>50</td>\n",
       "      <td>6</td>\n",
       "      <td>45</td>\n",
       "      <td>4.966500</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>50</td>\n",
       "      <td>6</td>\n",
       "      <td>60</td>\n",
       "      <td>5.793300</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>50</td>\n",
       "      <td>6</td>\n",
       "      <td>75</td>\n",
       "      <td>6.282900</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>50</td>\n",
       "      <td>8</td>\n",
       "      <td>30</td>\n",
       "      <td>5.064000</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>60</td>\n",
       "      <td>200</td>\n",
       "      <td>10</td>\n",
       "      <td>75</td>\n",
       "      <td>9.534520</td>\n",
       "      <td>37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>61</td>\n",
       "      <td>200</td>\n",
       "      <td>12</td>\n",
       "      <td>30</td>\n",
       "      <td>8.084280</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61</th>\n",
       "      <td>62</td>\n",
       "      <td>200</td>\n",
       "      <td>12</td>\n",
       "      <td>45</td>\n",
       "      <td>8.952733</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>63</td>\n",
       "      <td>200</td>\n",
       "      <td>12</td>\n",
       "      <td>60</td>\n",
       "      <td>8.861120</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>63</th>\n",
       "      <td>64</td>\n",
       "      <td>200</td>\n",
       "      <td>12</td>\n",
       "      <td>75</td>\n",
       "      <td>10.126740</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>64 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Sample Number   X1  X2  X3         Y2  Z1\n",
       "0               1   50   6  30   4.855400  18\n",
       "1               2   50   6  45   4.966500  19\n",
       "2               3   50   6  60   5.793300  20\n",
       "3               4   50   6  75   6.282900  27\n",
       "4               5   50   8  30   5.064000  19\n",
       "..            ...  ...  ..  ..        ...  ..\n",
       "59             60  200  10  75   9.534520  37\n",
       "60             61  200  12  30   8.084280  39\n",
       "61             62  200  12  45   8.952733  44\n",
       "62             63  200  12  60   8.861120  43\n",
       "63             64  200  12  75  10.126740  38\n",
       "\n",
       "[64 rows x 6 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "var1 = chal['X1'].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 50,  50,  50,  50,  50,  50,  50,  50,  50,  50,  50,  50,  50,\n",
       "        50,  50,  50, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100,\n",
       "       100, 100, 100, 100, 100, 100, 150, 150, 150, 150, 150, 150, 150,\n",
       "       150, 150, 150, 150, 150, 150, 150, 150, 150, 200, 200, 200, 200,\n",
       "       200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "var2 = chal['X2'].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6,  6,  6,  6,  8,  8,  8,  8, 10, 10, 10, 10, 12, 12, 12, 12,  6,\n",
       "        6,  6,  6,  8,  8,  8,  8, 10, 10, 10, 10, 12, 12, 12, 12,  6,  6,\n",
       "        6,  6,  8,  8,  8,  8, 10, 10, 10, 10, 12, 12, 12, 12,  6,  6,  6,\n",
       "        6,  8,  8,  8,  8, 10, 10, 10, 10, 12, 12, 12, 12])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [0., 1.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(var1,var2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "var3 = chal['X3'].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([30, 45, 60, 75, 30, 45, 60, 75, 30, 45, 60, 75, 30, 45, 60, 75, 30,\n",
       "       45, 60, 75, 30, 45, 60, 75, 30, 45, 60, 75, 30, 45, 60, 75, 30, 45,\n",
       "       60, 75, 30, 45, 60, 75, 30, 45, 60, 75, 30, 45, 60, 75, 30, 45, 60,\n",
       "       75, 30, 45, 60, 75, 30, 45, 60, 75, 30, 45, 60, 75])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [0., 1.]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(var1,var3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0.],\n",
       "       [0., 1.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(var2,var3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "y2 = chal['Y2'].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.37471011],\n",
       "       [0.37471011, 1.        ]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(var1,y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.39209061],\n",
       "       [0.39209061, 1.        ]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(var2,y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.66235199],\n",
       "       [0.66235199, 1.        ]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(var3,y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "y2 = chal['Y2'].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "z1 = chal['Z1'].to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([18, 19, 20, 27, 19, 24, 21, 23, 20, 20, 21, 24, 21, 22, 29, 25, 24,\n",
       "       24, 26, 27, 29, 27, 29, 27, 27, 29, 31, 32, 31, 31, 32, 33, 32, 33,\n",
       "       32, 36, 35, 33, 32, 38, 32, 33, 33, 33, 34, 35, 38, 38, 33, 34, 34,\n",
       "       32, 38, 39, 37, 42, 41, 36, 38, 37, 39, 44, 43, 38])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.55381959],\n",
       "       [0.55381959, 1.        ]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(y2,z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.       , 0.8942364],\n",
       "       [0.8942364, 1.       ]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(var1,z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.25428523],\n",
       "       [0.25428523, 1.        ]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(var2,z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.13773783],\n",
       "       [0.13773783, 1.        ]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(var3,z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f363b98a130>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(var1,y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f363b8ff7f0>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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   ],
   "source": [
    "plt.scatter(var2,y2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f363b840070>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
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   "execution_count": 34,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(var1,z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f363b7fd910>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(var2,z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f363b75b7f0>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
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       "    <path d=\"M 26.925 226.15838 \n",
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       "    <path d=\"M 26.925 8.71838 \n",
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       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(var3,z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f363b733940>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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   ],
   "source": [
    "plt.scatter(y2,z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple Linear Regression "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = chal[['X1','X2','X3']]\n",
    "Y = chal['Y2']\n",
    "Z = chal['Z1']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.3, random_state=103)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
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       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>150</td>\n",
       "      <td>12</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>100</td>\n",
       "      <td>8</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>100</td>\n",
       "      <td>12</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>50</td>\n",
       "      <td>12</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>150</td>\n",
       "      <td>10</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>100</td>\n",
       "      <td>8</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>150</td>\n",
       "      <td>12</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>100</td>\n",
       "      <td>8</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>100</td>\n",
       "      <td>12</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>200</td>\n",
       "      <td>6</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>50</td>\n",
       "      <td>8</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>200</td>\n",
       "      <td>10</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>100</td>\n",
       "      <td>10</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>100</td>\n",
       "      <td>6</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>50</td>\n",
       "      <td>10</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>50</td>\n",
       "      <td>8</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     X1  X2  X3\n",
       "1    50   6  45\n",
       "55  200   8  75\n",
       "15   50  12  75\n",
       "61  200  12  45\n",
       "41  150  10  45\n",
       "38  150   8  60\n",
       "39  150   8  75\n",
       "50  200   6  60\n",
       "14   50  12  60\n",
       "63  200  12  75\n",
       "46  150  12  60\n",
       "11   50  10  75\n",
       "40  150  10  30\n",
       "53  200   8  45\n",
       "5    50   8  45\n",
       "52  200   8  30\n",
       "0    50   6  30\n",
       "54  200   8  60\n",
       "37  150   8  45\n",
       "17  100   6  45\n",
       "29  100  12  45\n",
       "8    50  10  30\n",
       "59  200  10  75\n",
       "10   50  10  60\n",
       "33  150   6  45\n",
       "13   50  12  45\n",
       "58  200  10  60\n",
       "26  100  10  60\n",
       "45  150  12  45\n",
       "20  100   8  30\n",
       "31  100  12  75\n",
       "12   50  12  30\n",
       "43  150  10  75\n",
       "23  100   8  75\n",
       "44  150  12  30\n",
       "21  100   8  45\n",
       "28  100  12  30\n",
       "49  200   6  45\n",
       "6    50   8  60\n",
       "57  200  10  45\n",
       "27  100  10  75\n",
       "19  100   6  75\n",
       "9    50  10  45\n",
       "7    50   8  75"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1      4.966500\n",
       "55     9.315850\n",
       "15     9.099100\n",
       "61     8.952733\n",
       "41     7.191133\n",
       "38     7.148000\n",
       "39     9.213267\n",
       "50     6.834840\n",
       "14     7.713600\n",
       "63    10.126740\n",
       "46     8.605340\n",
       "11     8.891850\n",
       "40     6.988440\n",
       "53     7.234333\n",
       "5      5.196200\n",
       "52     6.261340\n",
       "0      4.855400\n",
       "54     7.324250\n",
       "37     7.122467\n",
       "17     6.960600\n",
       "29     8.109800\n",
       "8      5.781000\n",
       "59     9.534520\n",
       "10     6.612200\n",
       "33     7.076500\n",
       "13     7.054800\n",
       "58     7.751060\n",
       "26     7.385900\n",
       "45     7.762120\n",
       "20     6.937600\n",
       "31     9.665860\n",
       "12     6.594200\n",
       "43     9.438567\n",
       "23     9.232500\n",
       "44     7.871333\n",
       "21     6.960900\n",
       "28     7.702450\n",
       "49     6.969200\n",
       "6      5.914400\n",
       "57     7.225680\n",
       "27     9.387400\n",
       "19     9.164200\n",
       "9      5.895767\n",
       "7      8.649900\n",
       "Name: Y2, dtype: float64"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept: 1.254961992847159\n"
     ]
    }
   ],
   "source": [
    "print('intercept:', regressor.intercept_)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope: [0.00722792 0.25443675 0.05795036]\n"
     ]
    }
   ],
   "source": [
    "print('slope:', regressor.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'copy_X': True,\n",
       " 'fit_intercept': True,\n",
       " 'n_jobs': None,\n",
       " 'normalize': False,\n",
       " 'positive': False}"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regressor.get_params()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8.36053841, 5.60428066, 7.48925517, 6.61999979, 6.11315416,\n",
       "       8.50801609, 7.49229696, 8.5734426 , 7.12988722, 6.98139561,\n",
       "       7.34279142, 9.23080771, 6.26063184, 6.98342346, 5.39036254,\n",
       "       7.4902691 , 5.96567647, 9.73866728, 8.21204679, 5.24288485])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = regressor.predict(X_test) \n",
    "y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>150</td>\n",
       "      <td>10</td>\n",
       "      <td>60</td>\n",
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       "    <tr>\n",
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       "      <td>150</td>\n",
       "      <td>6</td>\n",
       "      <td>30</td>\n",
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       "      <th>3</th>\n",
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       "      <td>75</td>\n",
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       "      <td>60</td>\n",
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       "      <th>36</th>\n",
       "      <td>150</td>\n",
       "      <td>8</td>\n",
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       "      <th>60</th>\n",
       "      <td>200</td>\n",
       "      <td>12</td>\n",
       "      <td>30</td>\n",
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       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>200</td>\n",
       "      <td>6</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>100</td>\n",
       "      <td>10</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>100</td>\n",
       "      <td>6</td>\n",
       "      <td>60</td>\n",
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       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>150</td>\n",
       "      <td>6</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>62</th>\n",
       "      <td>200</td>\n",
       "      <td>12</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>100</td>\n",
       "      <td>10</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>200</td>\n",
       "      <td>10</td>\n",
       "      <td>30</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>50</td>\n",
       "      <td>8</td>\n",
       "      <td>30</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>100</td>\n",
       "      <td>8</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>200</td>\n",
       "      <td>6</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>150</td>\n",
       "      <td>12</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>150</td>\n",
       "      <td>6</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>100</td>\n",
       "      <td>6</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     X1  X2  X3\n",
       "42  150  10  60\n",
       "32  150   6  30\n",
       "3    50   6  75\n",
       "2    50   6  60\n",
       "36  150   8  30\n",
       "30  100  12  60\n",
       "60  200  12  30\n",
       "51  200   6  75\n",
       "25  100  10  45\n",
       "18  100   6  60\n",
       "34  150   6  60\n",
       "62  200  12  60\n",
       "24  100  10  30\n",
       "56  200  10  30\n",
       "4    50   8  30\n",
       "22  100   8  60\n",
       "48  200   6  30\n",
       "47  150  12  75\n",
       "35  150   6  75\n",
       "16  100   6  30"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42    7.329667\n",
       "32    7.073000\n",
       "3     6.282900\n",
       "2     5.793300\n",
       "36    6.117820\n",
       "30    8.555750\n",
       "60    8.084280\n",
       "51    9.136967\n",
       "25    7.018700\n",
       "18    7.086350\n",
       "34    6.822700\n",
       "62    8.861120\n",
       "24    6.958450\n",
       "56    6.974480\n",
       "4     5.064000\n",
       "22    7.244300\n",
       "48    6.993700\n",
       "47    9.768640\n",
       "35    9.263050\n",
       "16    6.949200\n",
       "Name: Y2, dtype: float64"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(y_pred, y_test, color='red') \n",
    "plt.title(\"Challenging question\")\n",
    "  \n",
    "plt.xlabel(\"y_pred\") \n",
    "plt.ylabel(\"y_test\") \n",
    "plt.show() \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import statsmodels.api as sm\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "x = sm.add_constant(X_train)\n",
    "model = sm.OLS(y_train, x).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     Y2   R-squared:                       0.768\n",
      "Model:                            OLS   Adj. R-squared:                  0.751\n",
      "Method:                 Least Squares   F-statistic:                     44.20\n",
      "Date:                Sun, 21 Mar 2021   Prob (F-statistic):           9.05e-13\n",
      "Time:                        10:33:23   Log-Likelihood:                -42.621\n",
      "No. Observations:                  44   AIC:                             93.24\n",
      "Df Residuals:                      40   BIC:                             100.4\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.2550      0.613      2.048      0.047       0.017       2.493\n",
      "X1             0.0072      0.002      4.122      0.000       0.004       0.011\n",
      "X2             0.2544      0.048      5.247      0.000       0.156       0.352\n",
      "X3             0.0580      0.006      9.250      0.000       0.045       0.071\n",
      "==============================================================================\n",
      "Omnibus:                        1.851   Durbin-Watson:                   1.786\n",
      "Prob(Omnibus):                  0.396   Jarque-Bera (JB):                1.203\n",
      "Skew:                          -0.069   Prob(JB):                        0.548\n",
      "Kurtosis:                       2.202   Cond. No.                         876.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(model.summary())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Linear Regression\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = chal['X1']\n",
    "x2 = chal['X2']\n",
    "x3 = chal['X3']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "X1_train, X1_test, y_train, y_test = train_test_split(x1, Y, test_size=0.3, random_state=103)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "x11 = sm.add_constant(X1_train)\n",
    "model = sm.OLS(y_train, x11).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     Y2   R-squared:                       0.104\n",
      "Model:                            OLS   Adj. R-squared:                  0.083\n",
      "Method:                 Least Squares   F-statistic:                     4.881\n",
      "Date:                Sun, 21 Mar 2021   Prob (F-statistic):             0.0327\n",
      "Time:                        10:39:41   Log-Likelihood:                -72.369\n",
      "No. Observations:                  44   AIC:                             148.7\n",
      "Df Residuals:                      42   BIC:                             152.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.7075      0.450     14.890      0.000       5.798       7.617\n",
      "X1             0.0074      0.003      2.209      0.033       0.001       0.014\n",
      "==============================================================================\n",
      "Omnibus:                        6.480   Durbin-Watson:                   1.603\n",
      "Prob(Omnibus):                  0.039   Jarque-Bera (JB):                2.462\n",
      "Skew:                           0.209   Prob(JB):                        0.292\n",
      "Kurtosis:                       1.919   Cond. No.                         314.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2_train, X2_test, y_train, y_test = train_test_split(x1, Y, test_size=0.3, random_state=103)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "x22 = sm.add_constant(X2_train)\n",
    "model = sm.OLS(y_train, x22).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     Y2   R-squared:                       0.104\n",
      "Model:                            OLS   Adj. R-squared:                  0.083\n",
      "Method:                 Least Squares   F-statistic:                     4.881\n",
      "Date:                Sun, 21 Mar 2021   Prob (F-statistic):             0.0327\n",
      "Time:                        10:40:32   Log-Likelihood:                -72.369\n",
      "No. Observations:                  44   AIC:                             148.7\n",
      "Df Residuals:                      42   BIC:                             152.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.7075      0.450     14.890      0.000       5.798       7.617\n",
      "X1             0.0074      0.003      2.209      0.033       0.001       0.014\n",
      "==============================================================================\n",
      "Omnibus:                        6.480   Durbin-Watson:                   1.603\n",
      "Prob(Omnibus):                  0.039   Jarque-Bera (JB):                2.462\n",
      "Skew:                           0.209   Prob(JB):                        0.292\n",
      "Kurtosis:                       1.919   Cond. No.                         314.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "X3_train, X3_test, y_train, y_test = train_test_split(x1, Y, test_size=0.3, random_state=103)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "x33 = sm.add_constant(X3_train)\n",
    "model = sm.OLS(y_train, x33).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     Y2   R-squared:                       0.104\n",
      "Model:                            OLS   Adj. R-squared:                  0.083\n",
      "Method:                 Least Squares   F-statistic:                     4.881\n",
      "Date:                Sun, 21 Mar 2021   Prob (F-statistic):             0.0327\n",
      "Time:                        10:41:28   Log-Likelihood:                -72.369\n",
      "No. Observations:                  44   AIC:                             148.7\n",
      "Df Residuals:                      42   BIC:                             152.3\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          6.7075      0.450     14.890      0.000       5.798       7.617\n",
      "X1             0.0074      0.003      2.209      0.033       0.001       0.014\n",
      "==============================================================================\n",
      "Omnibus:                        6.480   Durbin-Watson:                   1.603\n",
      "Prob(Omnibus):                  0.039   Jarque-Bera (JB):                2.462\n",
      "Skew:                           0.209   Prob(JB):                        0.292\n",
      "Kurtosis:                       1.919   Cond. No.                         314.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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