Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "69cd2fd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import statsmodels.api as sm\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_absolute_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b3243d1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('bmh')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0f187dfc",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('seaborn-darkgrid')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dbe972c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pd.read_csv('http://bit.ly/w-data')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "492a05f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Hours</th>\n",
       "      <th>Scores</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.5</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.1</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.2</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8.5</td>\n",
       "      <td>75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.5</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.5</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>9.2</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.5</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8.3</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2.7</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>7.7</td>\n",
       "      <td>85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>5.9</td>\n",
       "      <td>62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.5</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>3.3</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.1</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>8.9</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2.5</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.9</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>6.1</td>\n",
       "      <td>67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>7.4</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>2.7</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>4.8</td>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>3.8</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>6.9</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>7.8</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Hours  Scores\n",
       "0     2.5      21\n",
       "1     5.1      47\n",
       "2     3.2      27\n",
       "3     8.5      75\n",
       "4     3.5      30\n",
       "5     1.5      20\n",
       "6     9.2      88\n",
       "7     5.5      60\n",
       "8     8.3      81\n",
       "9     2.7      25\n",
       "10    7.7      85\n",
       "11    5.9      62\n",
       "12    4.5      41\n",
       "13    3.3      42\n",
       "14    1.1      17\n",
       "15    8.9      95\n",
       "16    2.5      30\n",
       "17    1.9      24\n",
       "18    6.1      67\n",
       "19    7.4      69\n",
       "20    2.7      30\n",
       "21    4.8      54\n",
       "22    3.8      35\n",
       "23    6.9      76\n",
       "24    7.8      86"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ae2d3e9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Scores')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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z1btGCCGKi4vFiBEjRLdu3URBQYEwGAxixYoVIjg4WDRv3lz069dP7N692/j4kjde09PTxahRo0SLFi1Ep06dxNSpU8VXX30levXqJYR4dNNs4sSJwtfXV6xevbrUjVchhLh8+bJ49913hZ+fnwgMDBRRUVHGXhSPb7w+vmEohCiz/T//+U/RvXt34evrK3r27Gm82SdE2Rt+j28SPr6h9+SN17CwMDFlyhTh5+cn3nrrrVLbPmnJkiUiLCxMzJw5U7Rs2VIEBQWJDRs2lHrM7t27Rf/+/YWvr68IDg4Wy5cvN/ZIefK8CCFEamqqUKvVYuPGjcZ99OjRQ4SFhZXa782bN8Vf//pX4e/vL9q0aSM+/PBDkZWVZfb6ym6EPqmy83j//n0xffp00bZtW9GqVSsxYcIEceXKFePjz507J4YMGSJ8fX3FwIEDjT2LSt54ffJcV/S6lmQwGERMTIwICAgQ/v7+4u233xbbt28XPj4+4rfffjPr+d66dUu8//77omXLlqJXr17in//8Z7k3XoUQYvPmzaJPnz6iefPmomvXrmL58uXGdbdv3xbh4eHC399fBAQEiFmzZhmPU1hYKObPny86dOggWrRoIUaPHi1Onjxp3NbU32dlr2VFWWyZSgh+k4QsKzIyEgUFBWbfTyAi6bC5hohIwVjkiYgUjM01REQKxit5IiIFY5EnIlIw2X3jNScnr/IH/T8nJwfodPIbQ5y5zCfHTIA8c8kxEyDPXHLMBEibq149N5PLbfpK3sFBnvGZy3xyzATIM5ccMwHyzCXHTIB1csnzTBARkUWwyBMRKRiLPBGRgrHIExEpGIs8EZGCya4LJRGRrbuV9xDrTmThToEeni6OCPWvjxfdyp/YR0os8kREFnQr7yFm7rqEm3mFxmUXc7SY10sNLxfTU0JKic01REQWtO5EVqkCDwA38wqx7kSWVfKwyBMRWdCdAv1TLZcaizwRkQV5upievLy85VJjkScisqBQ//p4yc251LKX3JwR6m/5eYHNwRuvREQW9KJbLczrpWbvGiIipXrRrRY+DWpi7RgA2FxDRKRoLPJERArGIk9EpGAs8kRECibZjVedTofp06cjMzMTderUQVRUFFQqFSIjI6FSqeDt7Y3o6GjY2fF9hohIKpIV+Y0bN8LFxQUbN27ElStXEBMTA0dHR4SHhyMwMBBRUVHYu3cvevbsKVUEIqIaT7LL6LS0NAQFBQEAvLy8kJ6ejtTUVAQEBAAAgoKCcOTIEakOT0REkPBKvmnTpti/fz969OiBU6dOITs7G3Xr1oVKpQIAuLq6Ii8vr8x2Tk4OZk926+hoDxcrjOpWGeYynxwzAfLMJcdMgDxzyTETYJ1ckhX5IUOGID09HaGhoWjdujV8fX3xxx9/GNdrtVq4u7uX2U6nK4JOZ94xXFycUFBg5oOfIeYynxwzAfLMJcdMgDxzyTETIG0uV1dnk8slK/JnzpxBmzZtMGPGDJw5cwa///47XnjhBWg0GgQGBuLgwYNo3769VIcnIrIZUk4yIlmRb9iwIb755husXr0abm5umDdvHgoKCjB79mwsWrQIXl5e6N27t1SHJyKyCRVNMmKJQq8SQohq78WCcnLKttOXpyZ+JKsOOeaSYyZAnrnkmAmQZy45ZgJM5/rHwXQkX7lT5rHBXp5PNf5NvXpuJpezkzoRkRVJPckIizwRkRVJPckIizwRkRVJPckIx5MnIpsiZU8Ua5B6khEWeSKyGVL3RLEWKScZYZEnIlkreeV+K78Qf+SX7p1yM68Q605kyWYmJrlhkSci2TJ15W6KpXqiKBFvvBKRbK07kVVpgQcs1xNFiVjkiUi2zLlCt2RPFCVicw0RyVZ5V+h/qeOEF+s4K6J3jdRY5IlItkL96+NijrZUk81Lbs4235vmWWKRJyLZkroPeU3AIk9EsiZlH/KagDdeiYgUjEWeiEjB2FxDRDWW0sbBMYVFnohqJKWOg/MkNtcQUY1k6tu0j8fBURLJruT1ej0iIyORlZUFOzs7xMTEwMHBAZGRkVCpVPD29kZ0dDTs7Pg+Q0TPntQzMsmFZEX+wIEDKCoqwoYNG3D48GF8/fXX0Ov1CA8PR2BgIKKiorB371707NlTqghEROWSekYmuZDsMrpx48YwGAwoLi5Gfn4+HBwckJqaioCAAABAUFAQjhw5ItXhiYgqJPWMTHIh2ZW8i4sLsrKy0LdvX9y9excrV67EsWPHoFKpAACurq7Iy8srs52TkwMcHMx773F0tIeLi5NFc1sCc5lPjpkAeeaSYyZAnrnMyeTl4oSvBvpiteZ33NbqUNfVCWGBr+Jl99pWzWVpkhX5tWvXonPnzvjkk09w8+ZNjB07Fnr9f9u6tFot3N3dy2yn0xVBpyuz2CQXFycUFJj54GeIucwnx0yAPHPJMRMgz1zmZvJwsMfHnRqXWiblc5HyXLm6OptcLllzjbu7O9zc3AAAzz33HIqKitCsWTNoNBoAwMGDB9G2bVupDk9ERABUQgghxY61Wi1mzJiBnJwc6PV6hIaGonnz5pg9ezb0ej28vLwwd+5c2Nvbl9ouJ6dsE0555HgFATDX05BjJkCeueSYCZBnLjlmAqTNVa+em8nlkhX5qmKRl44cc8kxEyDPXHLMBMgzlxwzAdYp8uykTkSkYCzyREQKxrFriMgsNWEwLyVikSeiSlU0mJeXzPrIU2ks8kRUqYoG85rTp+z3XZRAKZ9cWOSJqFI1ZTCvx5Q0DDFvvBJRpWrKYF6PKWkYYhZ5IqpUTRnM6zElfXJhcw0RVepFt1qY10utiDZqcyjpkwuLPBGZ5UW3Wvg0qIm1YzwTof71cTFHW6rJxlY/ubDIExE9QUmfXFjkiYhMUMonF954JSJSMBZ5IiIFY5EnIlIwFnkiIgVjkSciUjDJetckJSVh8+bNAIDCwkKcP38eiYmJ+OKLL6BSqeDt7Y3o6GjY2fF9hohIKpJV2JCQEMTHxyM+Ph6+vr6YNWsWli1bhvDwcCQmJkIIgb1790p1eCIiwjNorjlz5gzS0tIwfPhwpKamIiAgAAAQFBSEI0eOSH14IqIaTfIvQ8XFxWHy5MkAACEEVCoVAMDV1RV5eWUn7XZycoCDg3nvPY6O9nCR4YQFzGU+OWYC5JlLjpmAquW6cf8BVmt+R65WhxdcnRAW+Cpedq9t1UzPgjVySVrk79+/jytXrqB9+/YAUKr9XavVwt297GQDOl0RdGZOZl4TZ2SvDjnmkmMmQJ655JgJePpcpsZqT72VZ9Gx2pVyrp6Gq6uzyeWSNtccO3YMHTt2NP7crFkzaDQaAMDBgwfRtm1bKQ9PRDKkpLHabYGkRT4jIwMNGjQw/hwREYGlS5di+PDh0Ov16N27t5SHJyIZUtJY7bZA0uaa9957r9TPjRs3RkJCgpSHJCKZU9JY7baAo1AS2Rhbn2BaSWO12wIWeSIbooQJppU0VrstYJEnsiEV3bS0pbHPlTJWuy3gmAJENoQ3LelpscgT2RDetKSnxSJPZENC/evjJbfSX3rhTUuqCNvkiWwIb1rS02KRJ7IxvGlJT4PNNURECsYiT0SkYCzyREQKxiJPRKRgvPFKJEOmxqfxkuEkGCR/LPJEMlPe+DRfDfSFh4O9FZORLWJzDZHMlDc+zWrN71ZKRLbMrCKfnp6Of//73xBCIDw8HD169MAvv/widTaiGqm8cWhua+U3nR3Jn1lFPjo6Gs7OzkhOTkZ2djbmzZuHxYsXS52NqEYqbxyauq5sk6enZ1abfGFhIQYMGICYmBj07dsXgYGB0OsrH/UuLi4O+/btg16vx8iRIxEQEIDIyEioVCp4e3sjOjq61OTeREpS1ck9yptUIyzwVSnjkkKZVWF1Oh1yc3ORnJyMjh07Ijc3F4WFhRVuo9FocOLECXz//feIj4/HrVu3EBsbi/DwcCQmJkIIgb1791rkSRDJzeObp8lX7uD0rTwkX7mDmbsu4Vbew0q3fTw+TbCXJ1q86IZgL0/M66XGy+61n0FyUhqzruSHDx+Obt26oW/fvnjttdcQHByMDz/8sMJtDh06BLVajcmTJyM/Px+ffvopNm7ciICAAABAUFAQDh8+jJ49e1b/WRDJTHUn9+D4NGQpZhX5UaNGYcSIEcamlc2bN+P555+vcJu7d+/ixo0bWLlyJa5fv45JkyZBCAGVSgUAcHV1RV5eXpntnJwc4OBgXhOOo6M9XGTYd5i5zCfHTED1c/35sMjk8nsPi6q8X6WeKynIMRNgnVxmFXmtVouvvvoK6enp+Oabb7B48WJERETA1dW13G08PDzg5eUFJycneHl5wdnZGbdu3Sq1T3d39zLb6XRF0JnZicDFxQkFBfLrccBc5pNjJqD6uTxqmf7Teq6WQ5X3q9RzJQU5ZgKkzeXq6mxyuVmXzHPnzoWbmxtu374NZ2dn5OfnIyoqqsJt2rRpg5SUFAghkJ2djQcPHqBDhw7QaDQAgIMHD6Jt27ZP+TSIbAMn9yC5MOtK/vz584iNjcWBAwdQu3ZtfPnll+jXr1+F23Tr1g3Hjh3D0KFDIYRAVFQUGjRogNmzZ2PRokXw8vJC7969LfIkiOSGk3uQXJhV5J/s5mgwGMzq+vjpp5+WWZaQkGBmNCLbxpunJAdmFfl27dph4cKFePjwIVJSUrB+/XoEBgZKnY2IiKrJrDb5qVOnwsXFBW5ubli8eDF8fHxMXqUTEZG8mHUlv2TJEnzyySeYPHmy1HmIiMiCzLqST05OljgGERFJwawr+QYNGiAsLAytW7cu1Tf+3XfflSwYERFVn1lF3sPDAwCQlZUlZRYiIrIws4p8bGwsgEdFvqioCA0bNpQ0FBERWYZZRf7atWv48MMP8ccff6C4uBjPP/884uLi0KQJ+wATEcmZWUX+888/x3vvvYfBgwcDADZt2oTPPvsM69atkzQckaVVdYx3IltlVu+a27dvGws8AAwZMgR3796VLBSRFKozxjuRrTKryBsMBvz555/Gn+/cuSNVHiLJVDTGO5FSmdVc884772D48OHo27cvVCoVfv75Z4wdO1bqbEQWVd4E2eUtJ1ICs2eGatiwIVJSUlBcXIw5c+agQ4cOUmcjsqjyJsgubzmREpjVXJOdnY0dO3Zg2rRpGDZsGOLj45GTkyN1NiKL4hjvVBOZVeQjIiLg5eUFAKhfvz4CAgIwY8YMSYMRWVp5E2Szdw0pmVnNNXfv3kVoaCgAwNnZGePGjcOWLVukzEUkCY7xTjWN2b1rsrOzjT/n5uZCCCFZKCIisgyzruTHjRuHQYMGoUuXLgCAo0ePcjx5IiIbUGmRF0Jg0KBBaN68Ofbs2QM7OzuMHz8ePj4+le580KBBcHNzA/BoJMsPPvgAkZGRUKlU8Pb2RnR0tFnTCBIRUdVUWGHT0tLwxhtvICUlBY0aNcK2bdvw008/4b333sPhw4cr3HFh4aMvncTHxyM+Ph6xsbGIjY1FeHg4EhMTIYTA3r17LfdMiIiojAqL/D/+8Q+Eh4ejW7du2L59O1QqFbZv346NGzdi6dKlFe74woULePDgAcLCwhAaGoqTJ08iNTUVAQEBAICgoCAcOXLEcs+EiIjKqLC55ubNmxgwYAAAQKPR4I033oCdnR1eeukl5OfnV7jjWrVqYfz48Rg2bBiuXr2KCRMmQAgBlUoFAHB1dUVeXl6Z7ZycHODgYF4TjqOjPVxcnMx67LPEXOaTYyZAnrnkmAmQZy45ZgKsk6vCIl+yvfzEiROYNWuW8efHzTHlady4MRo2bAiVSoXGjRvDw8MDqampxvVarRbu7u5lttPpiqDTmRfexcUJBQVmPvgZYi7zyTETIM9ccswEyDOXHDMB0uZydXU2ubzCS+bnnnsOFy5cwG+//YacnBy0a9cOAHD8+HH8z//8T4UH/OGHHzB//nwAj74xm5+fj06dOkGj0QAADh48iLZt2z71EyEiIvNVeCX/8ccfY9y4ccjPz8fUqVPh4uKCb7/9FitXrsSyZcsq3PHQoUMxffp0jBw5EiqVCl988QWef/55zJ49G4sWLYKXlxd69+5t0SdDRESlqUQl32rS6XR4+PChsWnl+PHj8PT0RKNGjSQJlJNTtp2+PDXxI1l1yDGXHDMBj3Jdyb4vqwlG5Hyu5JZLjpkAaXPVq+dmcnml/eSdnJzg5PTfGwWtW7e2XCoimbpx/wFm7rpUavz5izlajnVDNoffRCIyYbXmd04wQorAIk9kQq7W9EdqTjBCtoZFnsiEF1xN92XmBCNka1jkiUwIC3yVE4yQIpg1CiVRTfOye23M66WWVe8aoqpgkScqBycYISVgcw0RkYKxyBMRKRiLPBGRgrHIExEpGIs8EZGCsXcNlXIr7yG7DRIpCIs8Gd3Ke8hBuYgUhs01ZLTuRBYH5SJSGF7Jk1F5g2/JfVAuNjERlY9FnozKG3xLzoNysYmJqGKSNtfcvn0bXbt2RXp6Oq5du4aRI0di1KhRiI6ORnFxsZSHpioI9a9vc4NysYmJqGKSFXm9Xo+oqCjUqvXoaio2Nhbh4eFITEyEEAJ79+6V6tBURS+61cK8XmoEe3mixYtuCPbylP0Vsa02MRE9K5I11yxYsAAjRozAqlWrAACpqakICAgAAAQFBeHw4cPo2bOnVIenKrK1QblssYmJ6FmSpMgnJSXB09MTXbp0MRZ5IQRUKhUAwNXVFXl5pifsdnJygIODeR8wHB3t4eJienIHa2Iu81U30/sdG+FSbgFu3H9oXPayey2837FRtfarxHMlFTnmkmMmwDq5JCnymzZtgkqlwtGjR3H+/HlERETgzp07xvVarRbu7u4mt9XpiqAzczLzmjgje3XIMVd1M3k42GNuT+8yvWs8HOyrtV8lniupyDGXHDMB0uZydXU2uVySIr9+/Xrj/8eMGYM5c+Zg4cKF0Gg0CAwMxMGDB9G+fXspDk01kK01MRE9S8/sy1ARERFYunQphg8fDr1ej969ez+rQxMR1ViS95OPj483/j8hIUHqwxERUQkc1oCISMFY5ImIFIxFnohIwVjkiYgUjEWeiEjBOAolSYZDABNZH4s8SYJDABPJA5trSBIcAphIHljkSRIcAphIHljkSRIcAphIHljkSRK2OMsUkRLxxitJ4vEsU+xdQ2RdLPIkGQ4BTGR9bK4hIlIwFnkiIgVjkSciUjAWeSIiBZPsxqvBYMCsWbOQkZEBe3t7xMbGQgiByMhIqFQqeHt7Izo6GnZ2fJ8xpaJxX6w1JgzHoiGyPZIV+f379wMANmzYAI1GYyzy4eHhCAwMRFRUFPbu3YuePXtKFcFmVTTuCwCrjAnDsWiIbJNkl9E9evRATEwMAODGjRt44YUXkJqaioCAAABAUFAQjhw5ItXhbVpF475Ya0wYjkVDZJsk7Sfv4OCAiIgI7N69G0uWLMH+/fuhUqkAAK6ursjLyyuzjZOTAxwczHvvcXS0h4uLk0UzW0J1c/35sMjk8nsPiyDK2ebew6JKj1mdXBVlqs5zVeprKAU5ZgLkmUuOmQDr5JL8y1ALFizA1KlT8fbbb6Ow8L9XglqtFu7u7mUer9MVQaczb98uLk4oKDDzwc9QdXN51DL9sjxXzvLH6yo7ZnVyVZSpOs9Vqa+hFOSYCZBnLjlmAqTN5erqbHK5ZM01W7ZsQVxcHACgdu3aUKlUaN68OTQaDQDg4MGDaNu2rVSHt2kVjftirTFhOBYNkW1SCSHKawGoloKCAkyfPh25ubkoKirChAkT0KRJE8yePRt6vR5eXl6YO3cu7O3tS22Xk1O2Cac8Sn63lqJ3TXVzSdG7RsmvoaXJMRMgz1xyzARIm6tePTeTyyUr8lXFIi8dOeaSYyZAnrnkmAmQZy45ZgKsU+Q5QFkNx77vRMrGIl+Dse87kfLx66Y1GPu+Eykfi3wNxnlYiZSPRb4G4zysRMrHNnkbZKmbpaH+9XExR1uqyYZ934mUhUXexljyZinnYSVSPhZ5G1PRzdKqzKfKeViJlI1Fvhqs0cecN0uJ6GmwyFdRRc0mXhKOMsebpUT0NNi7poqs1cecA4UR0dPglXwVWavZhDdLiehpsMhXkTWbTXizlIjMxeaaKmKzCRHZAl7JVxGbTYjIFrDIV4OUzSYcApiILIFFXoY4BDARWQrb5GWIQwATkaVIciWv1+sxY8YMZGVlQafTYdKkSXjttdcQGRkJlUoFb29vREdHw87O+u8xcmwW4bdaichSJCnyW7duhYeHBxYuXIi7d+9i8ODBeP311xEeHo7AwEBERUVh79696NmzpxSHN5tcm0X4rVYishRJLqX79OmDKVOmGH+2t7dHamoqAgICAABBQUE4cuSIFId+KnJtFmH3TCKyFEmu5F1dXQEA+fn5+OijjxAeHo4FCxZApVIZ1+fl5Znc1snJAQ4O5r33ODraw6Ua48T8+bDI5PJ7D4uqtd/q5vJyccJXA32xWvM7bmt1qOvqhLDAV/Gye+0q79MSuaQgx0yAPHPJMRMgz1xyzARYJ5dkvWtu3ryJyZMnY9SoUejfvz8WLlxoXKfVauHu7m5yO52uCDqdecdwcXFCQYGZDzbBo5bpp/9cLYdq7be6uQDAw8EeH3dqXGpZdfdpiVyWJsdMgDxzyTETIM9ccswESJvL1dXZ5HJJmmtyc3MRFhaGadOmYejQoQCAZs2aQaPRAAAOHjyItm3bSnHop8JmESJSOpUQQlh6p3PnzsV//vMfeHl5GZfNnDkTc+fOhV6vh5eXF+bOnQt7e/sy2+bkmG7GMcUS74pS9K6piVcRVSXHTIA8c8kxEyDPXHLMBEibq149N5PLJSny1VGVIi+3bpA18ResquSYCZBnLjlmAuSZS46ZAOsUeZv/xqtcu0ESEcmB9b+NVE1y7QZJRCQHNl/k+e1QIqLy2XyR57dDiYjKZ/NFnt0giYjKZ/M3Xjl5BxFR+Wy+yAOc85SIqDw231xDRETlY5EnIlIwFnkiIgVjkSciUjAWeSIiBZPdAGVERGQ5vJInIlIwFnkiIgVjkSciUjCb/sbrqVOn8OWXXyI+Pt7aUaDX6zFjxgxkZWVBp9Nh0qRJeOONN6wdCwaDAbNmzUJGRgbs7e0RGxuLV1991dqxAAC3b99GSEgIVq9ejSZN5PGN5UGDBsHN7dHkCw0aNEBsbKyVEz0SFxeHffv2Qa/XY+TIkRg2bJi1IyEpKQmbN28GABQWFuL8+fM4fPhwufM3Pwt6vR6RkZHIysqCnZ0dYmJiZPG7pdPpMH36dGRmZqJOnTqIiopCo0aNnsmxbbbI/+///i+2bt2K2rVrWzsKAGDr1q3w8PDAwoULcffuXQwePFgWRX7//v0AgA0bNkCj0SA2NhYrVqywcqpHf4xRUVGoVUs+YwwVFj6al0AOFw0laTQanDhxAt9//z0ePHiA1atXWzsSACAkJAQhISEAgM8++wxDhgyxaoEHgAMHDqCoqAgbNmzA4cOH8fXXX2Pp0qVWzQQAGzduhIuLCzZu3IgrV64gJiYG33777TM5ts0217z66quyePEe69OnD6ZMmWL82dT8tdbQo0cPxMTEAABu3LiBF154wcqJHlmwYAFGjBiBv/zlL9aOYnThwgU8ePAAYWFhCA0NxcmTJ60dCQBw6NAhqNVqTJ48GR988AGCg4OtHamUM2fOIC0tDcOHD7d2FDRu3BgGgwHFxcXIz8+Hg4M8rmPT0tIQFBQEAPDy8kJ6evozO7Y8zkAV9O7dG9evX7d2DCNXV1cAQH5+Pj766COEh4dbN1AJDg4OiIiIwO7du7FkyRJrx0FSUhI8PT3RpUsXrFq1ytpxjGrVqoXx48dj2LBhuHr1KiZMmIAdO3ZYvVDcvXsXN27cwMqVK3H9+nVMmjQJO3bsgEqlsmqux+Li4jB58mRrxwAAuLi4ICsrC3379sXdu3excuVKa0cCADRt2hT79+9Hjx49cOrUKWRnZ8NgMDyTi0GbvZKXo5s3byI0NBQDBw5E//79rR2nlAULFmDnzp2YPXs2CgoKrJpl06ZNOHLkCMaMGYPz588jIiICOTk5Vs0EPLoKHDBgAFQqFRo3bgwPDw9Z5PLw8EDnzp3h5OQELy8vODs7486dO9aOBQC4f/8+rly5gvbt21s7CgBg7dq16Ny5M3bu3Ikff/wRkZGRxmY4axoyZAjq1KmD0NBQ7N+/H76+vs/s0z6LvIXk5uYiLCwM06ZNw9ChQ60dx2jLli2Ii4sDANSuXRsqlcrqTUnr169HQkIC4uPj0bRpUyxYsAD16tWzaiYA+OGHHzB//nwAQHZ2NvLz82WRq02bNkhJSYEQAtnZ2Xjw4AE8PDysHQsAcOzYMXTs2NHaMYzc3d2NN86fe+45FBUVwWAwWDnVoyatNm3aID4+Hj169MArr7zyzI5ts801crNy5Urcv38fy5cvx/LlywE8ujls7RuLvXr1wvTp0zF69GgUFRVhxowZcHZ2rnzDGmjo0KGYPn06Ro4cCZVKhS+++MLqTTUA0K1bNxw7dgxDhw6FEAJRUVFWf6N+LCMjAw0aNLB2DKNx48ZhxowZGDVqFPR6Pf7+97/DxcXF2rHQsGFDfPPNN1i9ejXc3Nwwb968Z3ZsDmtARKRgbK4hIlIwFnkiIgVjkSciUjAWeSIiBWORJyJSMBZ5qlF8fHzKfJEoKSkJEydOtFIiImmxyBMRKZj1v+lBJCN5eXn47LPPcOHCBahUKnTp0gUff/wxHBwc4OPjg6NHj8LT0xMAjD9fvnwZ8+bNg4uLC7RaLRITEzFz5kxcu3YNdnZ28PX1xeeffw47O15T0bPHIk81ztixY0sV3Hv37sHHxwcAMHfuXHh4eOCnn36CXq/HpEmTsHr1arz//vsV7vPy5cvYs2cP6tevjy1btkCr1eLHH3+EwWBAdHQ0MjMz0bBhQ0mfF5EpLPJU43z33XfGq3HgUZv8zp07AQAHDx7E999/D5VKBScnJ4wYMQLfffddpUX+pZdeQv369QE8Gmtm8eLFGDNmDDp27IixY8eywJPV8PMjUQnFxcWlhvAtLi5GUVFRmcfpdLpSP5ccH+WVV17B7t278f777yM/Px/vvvsu9u3bJ11oogqwyBOV0LlzZyQkJEAIAZ1Oh40bNxpHWfT09MSZM2cAANu2bSt3H4mJiZg+fTo6d+6MadOmoXPnzjh37twzyU/0JBZ5ohJmzZqFO3fuoH///ujfvz8aN26MDz74wLju888/x+DBg5Genl7uMMSDBg2CwWDAm2++iZCQEOTl5WHMmDHP8mkQGXEUSiIiBeOVPBGRgrHIExEpGIs8EZGCscgTESkYizwRkYKxyBMRKRiLPBGRgrHIExEp2P8B581wgNB/INIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#ploting the relationship between hours and scores\n",
    "plt.scatter(df['Hours'],df['Scores'])\n",
    "plt.title('Relationship between hours and scores')\n",
    "plt.xlabel('Hours')\n",
    "plt.ylabel('Scores')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9ac6e09f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#spliting the dependent and independent variable\n",
    "x=df[['Hours']]\n",
    "y=df[['Scores']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bcc9e2a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Appling train test split\n",
    "x_train,x_test,y_train,y_test=train_test_split(x,y,test_size=0.75, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "27579c97",
   "metadata": {},
   "outputs": [],
   "source": [
    "#z_score computation\n",
    "def detect_outliers(data):\n",
    "    outliers=[]\n",
    "    threshold=3 #it is a outlier if it is more than 3 standard deviation\n",
    "    mean=np.mean(data)\n",
    "    std=np.std(data)\n",
    "    \n",
    "    for i in data:\n",
    "        z_score=(i-mean)/std\n",
    "        if np.abs(z_score)>threshold: #np.abs means absolute value that is round off\n",
    "            outliers.append(i)\n",
    "    if len(outliers)==0:\n",
    "        print('There are no outliers')\n",
    "    else:\n",
    "        return outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e32c8bbb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are no outliers\n"
     ]
    }
   ],
   "source": [
    "#checking outliers in train data by z_score\n",
    "detect_outliers(x_train.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "452b81ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Appling LinearREgression \n",
    "regression_model=LinearRegression().fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "90ccf885",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9466908619322414"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#testing train accuracy\n",
    "regression_model.score(x_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ce4fd9c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9478707230647945"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#testing Test accuracy\n",
    "regression_model.score(x_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7178f511",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Regression line')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#ploting the regression line\n",
    "#y=mx+c\n",
    "line=regression_model.coef_*x+regression_model.intercept_\n",
    "plt.scatter(x,y)\n",
    "plt.plot(x,line)\n",
    "plt.xlabel('Hours')\n",
    "plt.ylabel('Score')\n",
    "plt.title('Regression line')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "88d54b04",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred=regression_model.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ff6b31e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Residual')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#checking the spread of residual\n",
    "residual=y_test-y_pred\n",
    "plt.scatter(y_pred,residual)\n",
    "st_line=x_test*0\n",
    "plt.plot(y_pred,st_line)\n",
    "plt.title('Homoscdasticity')\n",
    "plt.xlabel('Y pred')\n",
    "plt.ylabel('Residual')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d2de779e",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train_constant=sm.add_constant(x_train)\n",
    "model=sm.OLS(y_train,x_train_constant).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "800c2d3c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 Scores   R-squared:                       0.947\n",
      "Model:                            OLS   Adj. R-squared:                  0.933\n",
      "Method:                 Least Squares   F-statistic:                     71.03\n",
      "Date:                Sat, 05 Mar 2022   Prob (F-statistic):            0.00109\n",
      "Time:                        14:54:13   Log-Likelihood:                -19.184\n",
      "No. Observations:                   6   AIC:                             42.37\n",
      "Df Residuals:                       4   BIC:                             41.95\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.4276      6.869      0.062      0.953     -18.643      19.498\n",
      "Hours          9.8255      1.166      8.428      0.001       6.589      13.062\n",
      "==============================================================================\n",
      "Omnibus:                          nan   Durbin-Watson:                   1.868\n",
      "Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.570\n",
      "Skew:                          -0.140   Prob(JB):                        0.752\n",
      "Kurtosis:                       1.517   Cond. No.                         14.0\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\hp\\anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 6 samples were given.\n",
      "  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"
     ]
    }
   ],
   "source": [
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e13a6646",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.102025407722985"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_error(y_pred,y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "feffe4c5",
   "metadata": {},
   "source": [
    "# prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9a38eac9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9.25]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#the predicton score if a stdent study for 9.25 Hours\n",
    "hours=np.array(9.25)\n",
    "hours=hours.reshape(-1,1)\n",
    "hours"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d58aa292",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\hp\\anaconda3\\lib\\site-packages\\sklearn\\base.py:450: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[91.31374661]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regression_model.predict(hours)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ceaa164f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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