Simple linear regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import the relevant libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('1.01. Simple linear regression.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>79</td>\n",
       "      <td>1936</td>\n",
       "      <td>3.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>80</td>\n",
       "      <td>1810</td>\n",
       "      <td>3.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>81</td>\n",
       "      <td>1987</td>\n",
       "      <td>3.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>82</td>\n",
       "      <td>1962</td>\n",
       "      <td>3.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>83</td>\n",
       "      <td>2050</td>\n",
       "      <td>3.81</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>84 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     SAT   GPA\n",
       "0   1714  2.40\n",
       "1   1664  2.52\n",
       "2   1760  2.54\n",
       "3   1685  2.74\n",
       "4   1693  2.83\n",
       "..   ...   ...\n",
       "79  1936  3.71\n",
       "80  1810  3.71\n",
       "81  1987  3.73\n",
       "82  1962  3.76\n",
       "83  2050  3.81\n",
       "\n",
       "[84 rows x 2 columns]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .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>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>84.000000</td>\n",
       "      <td>84.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>1845.273810</td>\n",
       "      <td>3.330238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>104.530661</td>\n",
       "      <td>0.271617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>1634.000000</td>\n",
       "      <td>2.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>1772.000000</td>\n",
       "      <td>3.190000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>1846.000000</td>\n",
       "      <td>3.380000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>1934.000000</td>\n",
       "      <td>3.502500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>2050.000000</td>\n",
       "      <td>3.810000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SAT        GPA\n",
       "count    84.000000  84.000000\n",
       "mean   1845.273810   3.330238\n",
       "std     104.530661   0.271617\n",
       "min    1634.000000   2.400000\n",
       "25%    1772.000000   3.190000\n",
       "50%    1846.000000   3.380000\n",
       "75%    1934.000000   3.502500\n",
       "max    2050.000000   3.810000"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Create your first regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the dependent and the independent variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data['GPA']\n",
    "x1 = data['SAT']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explore the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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8RceIDjZtHti6bagZUfW6PKq9xr2PvzioLI3OuKoMVvXOM6qsT0tt51Xz8nzu6p6STKp2lVxLqXun2nM2D7A1YJQMZ5A5SrmaOX75YklxZVbNeobWdp4AkOdzV9CQTIp6NVw+5tDIFXSzV9tRnzecq/m4xlayPi016y2hJOX53BU0JJNqXQ1vN3pkw2sfNHL8uJ43nKv5uKaTZn1aatZbQknK87lrTEMyqVaW0lM+aA2tfTCyg0FjGqXjNHu1HWXQOo6r+bimk2Z5Wmpaa1VkYQA6z+t0KGhIJjWTmK/Wcxo9TqPlGu7sqXaVRvLFrAxA5znxZMfAQPT1s3NmN2Blo2uEF0mR1i1OiuqoviLV0XlXPlDzBs7Lzp7S9HGLVEdla4RPBJ590/4kXtTMJiVxXBGR4cjzAHRWxNY9ZWZjgBOBM4HJcR5bAlnoixXJM2XHHb5h/7Cb2YEEgeJkoAvoACK308zsYuB4YACY6+5zKvYfDcwOj7sS+Li7rx1uufMmK32xInmW5wHorGgqaJjZW4GPEQSLfcp2LQK+B9wU8ThTgcPCY2wLPGVmC9zdw/3dwLeBg9z9hTDAfAX4fDPlTtNwWwl5SAkhknV5HoDOioaCRvgjfyZwHDCa4Oof4D7gDHd/tpHjufsiMzvU3TeZ2dvD8rxa9pBtgU+7+wvh308CH23kNbIgjlZCK/tiW90NFufrqQtP6snyNOQ8qBs0zGwnYBbwCWAPgkDRD9wA/BD4FbC80YBR4u4bzWw2cC7wU+CFsn39wK1hOcYAFwCXN/M6aYqjldCqvthWd4PF+XrqwhNJ3pBBw8xuBY4guOJ/GfgRMA+42903hY8ZdiHc/SIzuxS4HTgLuKaiHG8lCB6/cffrGzl2OHUsVWtqtAbWrNtAb29XpGPMOqqPK376GzZs3Lx1W+e2I5l1VN+Qx4h6/JL5i5dUDXDzF69k5rS9GjpWq1+v2WM1WkftSHVUX7vUUb2WxtEE3UVfAy5z99fjfPFwau5od3/C3V8zs1sYPEaCme0M3A38EviXRl8jC/dp7FCjlbBDd+fWud31ulX6JozltH+0Nz2mb8LYmvPDm5k7vnrt+prb45qHXn6uQ5WjFWVPY359Ul1oSR23SPcgJKVIdVR2n0ZV9YLGPcChBIPPnzGz/wR+TNDS2BhD+XYHZpvZIQSzp44GvlvaaWYjCVofP3H3r8XweqmoN2MjardKK/pik+4GqzzXocrRqDxMp0yqC01dc9IqQ97c5+4fBCYAXwJWEwxC/wxYZWbXmNlhw3lxd18ILAAeBx4FHnT3eWa20MzeA8wEDgCON7Mnwv++M5zXTEO9xHFZSpOcdGbUKKnFm329rGd1heTe6yx9hqTY6g6Eu/uLwKXApWZ2AHA68BGCWVSfIGgh7G9mB7n7I40WwN2/QtCSKd92RPjPpRQkE+9QrYQs3aWa9JTEeuc0nNfLw3TKpN7rLH2GpNgamnLr7o8Bj5nZOcAM4DTgKOC9wENmtgL4AfBDd9clTkRZ61ZJshtsqHMdTu6fkqxPp0zqvc7aZ0iKq6mreHff7O53uPuJwM7Ap4AlwJ4ErQaPrYRtIA/dKnFpp3OtJqnzb/d6ldYZdhoRd/8rwRTZa8xsIkH3Ve5uwEtTHrpV4tJO51pNUuff7vUqrRM5NbqZjQLGAf2lezQybjeUGr0w0wA1nTQ9qqP6ilRHw06Nbmb7hFNtXwVeBNaZ2Y/NbELMZRWpqjSdtNRnX5pOumTZqpRLJtJ+hgwa4c139wPTgS0E0247gRMIBr53SbyE0vY0nVQkO+q1NL5EkO78fwNj3X08MBb4D2A8Qb4okURpOqlIdtQbCH8/sNDdv1Ha4O4vA18ws8nA4UkWTgQ0nVQkS+oFjZ0IkhRWs5gguaDkTByDyq1MQa6Fc0Syo17Q6ARqJSlcB2wXb3EkaXHkKGp1nqPK6aQjOgaPaWhaqUjrFCJFh0QXx6ByGgPTk/vGb72BrTSDWrOoRFpPQaPNxDGonNbAtGZRiaQvStBozzvjCqrW4HEjg8pxHKMZmkUlkr4oaUS+YmZfqbXTzDZX2Tzg7sNOUSLxi2NQOa2Bac2iEklfvR/2/0YtjUKJI0dRWnmONItKJH1DBg13361F5ZAWiiN9eBopyJWUTyR9DXUhmdno0jrhZrYPsF/FQ7YAN7p7tS4rKZBW3qdRLuvrZYgUXaSgYWafBs4H5gIXh5uPBS4se1gHQVfWrsA3kMLSetQi7atu0AjX5P448DJQbZrKOeH/RxLkqPqSmV3l7mujFMDMLgaOJwg4c919TsX+/YDvAN3Ar4BP5SQ1e2ENNfU1a0EjrRZRo/JSTpEhg4aZfRA4A/g5cLK7r6l8jLt/q+zxfyH4gT8D+D/1XtzMpgKHAfsA2wJPmdkCdy9f+e8HwJnu/pCZzSVIXfLteseW5CQ59fX7dy9n0RMvsmUARnTA1P124dQPTWrqWHlpEeWlnCJQ/z6NTwB/BU6qFjCquB74E8H64XW5+yLg0LDl8DaCIPZqab+Z/R0wxt0fCjddR5CWXVKU1H0a3797Ofc+/uLWO763DMC9j7/I9+9e3tTx8nIzYF7KKQL1g8Y/EGS5jdTVFA6A3w30RS2Au280s9nAU8A9wAtlu3cBXir7+yXgHVGPLclIaj3qRU+82ND2evJyM2BeyikC9cc03kaV5f5CT1I9A+4LBMvCRubuF5nZpcDtBN1P14S7RjD4PpEOghlakYXLFrat3t6u2I85c1oX3V2jueHOp/nz2vXsOG4Mp814F9MO3HVYx621Ku+WgebOo3fcGFavXV91e/nxkqijRkQtZ5qyUo4sa5c6qhc0/kKwCNObuPutwK1VdvUQrPBXV7gy4Gh3f8LdXzOzWwjGN0qeB3Yu+3s8wZKzkWmN8GTWLe6bMJZLPzl50LbhvtaIjuqBY0RHc8c+5pCJVW8GPOaQiVuPl4W1naOUM01ZqKOsK1Idla0RXn1/nef/kaCLqhHTgKidsbsD15pZp5mNAo4mWKcDAHf/I/C6mU0JN50K3NlgeSQnpu5XffXgWtvrmdw3ntNnTNo61tLT3cnpMyZlbnA5L+UUgfotjZ8BXzWzQ9393noHM7Njgb2Ay6O8uLsvNLODgceBzcDN7j7PzBYCF7r7UuCjBIGlG3iMYKlZKaDSLKm4Zk9Bfm4GzEs5RToGBmp33ZjZzsBygoWYTnb3Xw7x2EMIgsxGYJK7/yXmsjZqN2CluqeK0WROiuqoPtVRfUWqo7LuqYlUGdOul3vqJTP7BPBj4OdmdgfBOMbvgLUEA957AscR3CHeAczIQMAQEZEE1L0j3N1vMrMPEdy092HgqCoP6yCYNXWqu98XawlFRCQzIuWecvdfmNlewBEEg9V7EkzHXQOsJOiWuq2UzFBERIopcpZbd99IEBx+llxxREQky7S6XoqUpE5E8kZBIyVKUicieVTv5j5JiJLUiUgeKWikREnqRCSPFDRSklR6cRGRJClopCSp9OIiIknSQHhKSoPdmj0lInmioJEiJakTkbxR95SIiESmoCEiIpEpaIiISGQa08g5pSIRkVZS0MgxpSIRkVZT91SOKRWJiLSagkaOKRWJiLRa6t1TZnYRcGL45wJ3P79i/wHA1cAo4DngY1pONtDT3Vk1QCgViYgkJdWWhplNBw4H9gf2Aw40s2MrHvYt4EJ33xdw4NzWljK7lIpERFot7ZbGS8AX3f0NADN7GphQ8ZiRQHf477cQLDErKBWJiLReqkHD3ZeV/h2uQX4iMKXiYecA/2lm/w94FXhv60qYfUpFIiKtlHZLAwAz6wMWAOe5+zNl28cAc4Hp7v6wmZ0D3AAcGfXYPT3bx13cXOnt7Uq7CJmnOqpPdVRfu9RR6kHDzKYANwNfcPd5Fbv3Bta7+8Ph31cDX23k+P39r7Bly8DwC5pDvb1drF79ctrFyDTVUX2qo/qKVEcjRnQMebGd9kD4rsB84JQqAQPgD8CuZmbh30cDj7SqfCIiMljaLY1zgdHAnL/FBa4CZhLMmFpqZrOAn5hZB/An4ONpFFRERKBjYKCwXTe7ASvVPVWMJnNSVEf1qY7qK1IdlXVPTQSerdyfdktDIlJiQhHJAgWNHFBiQhHJCuWeygElJhSRrFDQyAElJhSRrFDQyIFaCQiVmFBEWk1BIweUmFBEskID4TmgxIQikhUKGjmhxIQikgXqnhIRkcgUNEREJDIFDRERiUxBQ0REIlPQEBGRyBQ0REQkMgUNERGJTEFDREQiU9AQEZHIFDRERCSy1NOImNlFwInhnwvc/fyK/QZcDYwDVgEnufva1pZSREQg5ZaGmU0HDgf2B/YDDjSzY8v2dwC3AZe4+77A48AFaZRVRETSb2m8BHzR3d8AMLOngQll+w8AXnX3u8K/vw6MbW0RRUSkJNWg4e7LSv82s70IuqmmlD1kT2CVmc0laI08DXy2pYUUEZGt0m5pAGBmfcAC4Dx3f6Zs1zbANOD97r7UzL4KzAFmRT12T8/2MZY0f3p7u9IuQuapjupTHdXXLnWUetAwsynAzcAX3H1exe5VwDPuvjT8+0bgpkaO39//Clu2DAy/oDnU29vF6tUvp12MTFMd1ac6qq9IdTRiRMeQF9tpD4TvCswHTqkSMAAeBHrNbN/w7w8Dj7aqfCIiMljaLY1zgdHAnGBmLQBXATOBC8MuqWOBa81sO+B54NRUSioiIqkPhH8e+HyVXVeVPebXwMEtK5SIiNSUdktDhCXLVnHLohX0r9tAT3cnx03dQ+uhi2SUgoakasmyVVx/53Le2LQFgP51G7j+zuUAChwiGaTcU5KqWxat2BowSt7YtIVbFq1IqUQiMhS1NFpEXTDV9a/b0NB2EUmXWhotUOqCKf0QlrpglixblXLJ0tfT3dnQdhFJl4JGC6gLprbjpu7BqG0GfwxHbTOC46bukVKJRGQo6p5qAXXB1FbqolPXnUg+KGi0QE93Z9UAoS6YwOS+8QoSIjmh7qkWUBeMiBSFWhotoC4YESkKBY0WUReMiBSBuqdERCQyBQ0REYlMQUNERCJT0BARkcgUNEREJDIFDRERiUxBQ0REIlPQEBGRyFK/uc/MLgJODP9c4O7n13jckcAV7j6xZYUTEZFBUg0aZjYdOBzYHxgA7jKzY9391orH7QR8E+hofSmLSwtDiUij0u6eegn4oru/4e4bgaeBCVUe9x1gdktLVnBaGEpEmpFqS8Pdl5X+bWZ7EXRTTSl/jJl9DngMeKi1pSu2oRaGUmtDRGpJfUwDwMz6gAXAee7+TNn2vYF/Aj4AvKOZY/f0bB9LGfOqt7er6vY1NRaAWrNuQ83nFFW7nW8zVEf1tUsdpR40zGwKcDPwBXefV7H7BGBnYCkwCtjFzO539/dFPX5//yts2TIQW3nzpLe3i9WrX666b4caC0Pt0N1Z8zlFNFQdSUB1VF+R6mjEiI4hL7ZTHdMws12B+cApVQIG7n6Ru7/T3fcDjgBebCRgSG1aGEpEmpF2S+NcYDQwx8xK264CZgIXuvvStApWdFoYSkSa0TEwUNium92AleqeKkaTOSmqo/pUR/UVqY7KuqcmAs++aX+rCyQiIvmloCEiIpEpaIiISGQKGiIiEpmChoiIRJb2lNskjYRgJkA7a/fzj0J1VJ/qqL6i1FHZeYystr/IU24PAe5PuxAiIjn1PmBx5cYiB41O4CCCTLqbUy6LiEhejCRI3/QI8KZcQ0UOGiIiEjMNhIuISGQKGiIiEpmChoiIRKagISIikSloiIhIZAoaIiISmYKGiIhEVuQ0IoVlZt3Ag8BRwN8DXy/b/Xbg1+5+lJntB3wH6AZ+BXzK3TeZ2QTgB8DbAAc+6u6vtPIcklZeR+7+rJkdDlxGcOPSY8CZ7v5Grbows7HAD4HdgdXAie6+Ko1zSUqVOpoFnE9wM+wvgS8O9Xkpeh2Z2UXAieGfC9z9fDObDswBxgA/dvd/Cx/bNt81tTRyxszeS3Br/zsB3H2hu+8XrqP+j8A64F/Ch/8A+Iy7vxPoAM4Kt18JXOnuk4ClwJdbeAqJq6yj0FzgJHffG3gLcFq4vVZdfA24393fBVwLfKsVZW+VyjqyYL3lrwEfcPd3A9sCnwCI+PMAAAW7SURBVAsf3nZ1FAaHw4H9gf2AA83sZOC7wNHAu4CDzGxG+JS2+a4paOTPWcCngRer7LsMuMrdnzGzvwPGuPtD4b7rgBPMbFvg/cBN5dsTLXHrVaujkUC3mY0kWJd+fZ26OJLgKhrgRmBG+PiiqKyjfYAl7v5S+PcdwDFtXEcvEbS03nD3jcDTBAH2GXdf6e6bCALFCe32XVP3VM64+5kAwYXh35jZXsA04Mxw0y4EH/ySl4B3ADsC68IPffn2wqhRR2cD9xG0xFYSfJGHqout9Rd2M6wDeqkerHOnSh39BphjZrsSnOPxwHjatI7cfVnp3+F360Tgcqp/p9rqu6aWRnH8M0EzuJRgbARQnlisA9hSZTvh9sIys/HAJcDeBInYHiLolx6qLirzXHdQ4Hpy998DFwC3EWSHfhJ4gzavIzPrA34OnAf8F9G+U4X+riloFMcxwLyyv58n+IEsGU9wBfgn4K1hNw3hY3J/ZVjH+4DfufsKd99C0P8+jaHr4gWCOsPMtgG6gP5WFrqVzGw08LC77+/u/0Bw/ito4zoysynAPcAF7n49tb9TbfVdU9AoADPbkaBPdWVpm7v/EXg9/OADnArcGfbP3g98JNx+GnBnK8ubgt8BB5vZTuHfRwOP1KmLhfxtsPwjBAO+G1tU3jRsB9xjZl1mNgr4LMHsoLaso7Cbbj5wiruXLsZ+HeyyPcNAcArBd6qtvmsa0yiG3Qmudip9FLg2nFr5GPAf4fazgevN7N+A/wZObkkpU+LuT5vZl4F7zWwT8AeC7jyoXRdfBq4zs2XAXwjqsrDcvd/MZhN03W0L/MjdfxTubsc6OpdgwsScsnGfq4BZwM3hvoX8bZC7bb5rWk9DREQiU/eUiIhEpqAhIiKRKWiIiEhkChoiIhKZgoaIiESmKbciTTKzmQRTdw8G3gqsAR4G5rr7bUM8718J7lBfA+xSdhd/+WOeJ8hYHMWX3f1rDRZfpCkKGiJNMLPLgc8AzwI/A/5M8CN/JDDTzK5193+u8fRTgdeAHYDjCJL9VZpDkGa7ZAeCG+5WAjdUPPZXzZ2FSON0n4ZIg8xsGnAvwU1eJ5UlpMPM3hru2x84xt1/VvHcAwlSZP87wdoV97v7ByK85p7AM8A97j49plMRaZjGNEQad1T4/yvKAwaAu/+VIPEfBK2ISqW0GzcT5DU61Mx2T6SUIglQ0BBpXGnNiHfX2H8/QSrt/1u+MUzqdxLwP8ATwI8JMqJ+IpliisRPQUOkcT8P//9NM7vczCaXZTLF3de7+0/d/YmK580gWPbzp+4+ANwKbABmlT9fJMsUNEQa5O53AN8GRhEMhj8IrDGzBWb2BTOrtdBOqWvqxvA4fyVIercLcESypRaJh4KGSBPc/WyCsY27gI0EM52OIOiS+i8z+4aZbf1+mdlY4MPAH4ElZYcqZZI9E5EcUNAQaZK7L3D3GQTTYY8kmCb7B4IxjwuAb5Q9/ESgE5gXdk2V3EGwBO0RZla+kI9IJmnKrUiMzKw0sH0N8Dqwo7u/ZmaLgSlDPhm+5O7fqLZDU24lKxQ0RBoQLrLzKODuftQQj7sbOBwwYBPB0qkvELQsKnURrAK3AtiroiVSOp6ChmSC7ggXaYC7rwtv4JtuZju5+/8M8fAtwCrgnPDvq2ql+zCzg4E9CdYuvzfGIovESmMaIo27gmB84qZq4xBhTqrpwK3uvg74WLjrR5WPLXNd+H8NiEumqXtKpEHhPRXzgOMJckjdDfyeYAD8vQRjF8uB9xN0T90PPOjuNcc0wmm6fwTeIEhiuLZiv7qnJBPU0hBpkLtvdvcTCNKE3AUcBHyeoJUwGvhfwAHuvpogOSHAD+oc83ngF+HzPzbUY0XSpJaGiIhEppaGiIhEpqAhIiKRKWiIiEhkChoiIhKZgoaIiESmoCEiIpEpaIiISGQKGiIiEpmChoiIRKagISIikf1/+fKTggbZzPAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "plt.xlabel('SAT',fontsize=20)\n",
    "plt.ylabel('GPA',fontsize=20)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regression itself"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\nimis\\Anaconda3\\lib\\site-packages\\numpy\\core\\fromnumeric.py:2389: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>GPA</td>       <th>  R-squared:         </th> <td>   0.406</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.399</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   56.05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 27 Jun 2020</td> <th>  Prob (F-statistic):</th> <td>7.20e-11</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>14:58:07</td>     <th>  Log-Likelihood:    </th> <td>  12.672</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    84</td>      <th>  AIC:               </th> <td>  -21.34</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    82</td>      <th>  BIC:               </th> <td>  -16.48</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.2750</td> <td>    0.409</td> <td>    0.673</td> <td> 0.503</td> <td>   -0.538</td> <td>    1.088</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SAT</th>   <td>    0.0017</td> <td>    0.000</td> <td>    7.487</td> <td> 0.000</td> <td>    0.001</td> <td>    0.002</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>12.839</td> <th>  Durbin-Watson:     </th> <td>   0.950</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.002</td> <th>  Jarque-Bera (JB):  </th> <td>  16.155</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.722</td> <th>  Prob(JB):          </th> <td>0.000310</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.590</td> <th>  Cond. No.          </th> <td>3.29e+04</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.29e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                    GPA   R-squared:                       0.406\n",
       "Model:                            OLS   Adj. R-squared:                  0.399\n",
       "Method:                 Least Squares   F-statistic:                     56.05\n",
       "Date:                Sat, 27 Jun 2020   Prob (F-statistic):           7.20e-11\n",
       "Time:                        14:58:07   Log-Likelihood:                 12.672\n",
       "No. Observations:                  84   AIC:                            -21.34\n",
       "Df Residuals:                      82   BIC:                            -16.48\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const          0.2750      0.409      0.673      0.503      -0.538       1.088\n",
       "SAT            0.0017      0.000      7.487      0.000       0.001       0.002\n",
       "==============================================================================\n",
       "Omnibus:                       12.839   Durbin-Watson:                   0.950\n",
       "Prob(Omnibus):                  0.002   Jarque-Bera (JB):               16.155\n",
       "Skew:                          -0.722   Prob(JB):                     0.000310\n",
       "Kurtosis:                       4.590   Cond. No.                     3.29e+04\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 3.29e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sm.add_constant(x1)\n",
    "result = sm.OLS(y,x).fit()\n",
    "result.summary()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "yhat= 0.0017*x1+0.2750\n",
    "fig = plt.plot(x1,yhat , lw=4,c='red',label = 'regression')\n",
    "plt.xlabel('SAT',fontsize=20)\n",
    "plt.ylabel('GPA',fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
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