Evaluation Metrics - Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import Image\n",
    "from IPython.core.display import HTML \n",
    "#Image(url= \"https://miro.medium.com/proxy/0*zX9jlpZ8k0CuEpFE.jpg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean Squared Error (MSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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Cuw3Nj8SPyrxD9i/w+nij9qL4b2LpuU6tHIwPovzf0qX9t3X/APhJP2rPiZd5JxrE0Iz/ALDbf6V1/wDwTY08al+2L4EBxiGSaXn2jb/GgD+gUJhQO1OoooAKKKKACqOtaxbaDpd3qN4/lWtrC88r7ScIoyTxV6mSxJPGySKHRhhlYZDD0I9KAPjPx3/wVY+Dng0skI1jVXx8jwWLKhPoS2MV7F+yr+1NoH7VngO88SaHay6c1pdPaz2VwQZIyACCcdiDWF+2r8D/AAz8QP2afHls2g2IvrLSp76ymit0SSOWJDINpAzyFI/Gvh//AIImeI5IfFXxJ0BpD5ctrb3aR9gyuyk/+PD9KAP1mZ2BAAGfevjqX/gpx8Prb9o1vhbcWN3BEL4aX/bb4EP2kvsxjrszxu96+xVXdyTn0r8u/wBtD9h3w5pv7RXw817wfdzQ+IPGviqP7Ro/G1I1/ez3CHqAMZP1oA/UdTuUH1GaWmRDESA9Qop9ABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFADWO0ZryH43ftT+Bf2f5be38V3lyl5cRGWK3tbZ5WZR9BXr5GaoahoWnam6Ne2FreOoIVriFZCo9ASOKAPifRf8Agrb8L/Enj7RvDmn6Zqgj1C7W0N7dReUsRY4BIPOM19yQyiaMOpDIwBVh0I9a/E3/AIKr/DXTPhX+0loet6FZxadFqtrFeGKBdqiRH5IA4HIr9hfg9rR8RfCzwpqRbc1zpsEhPuUFAHJftPftIaH+zB8N5PFmt2018rSi3t7SDAeWQ84yaz/2WP2q/DP7VfgmbXvD8clnPay+Td2E/wDrIW7dPWtf9pT4BeG/2jPhpeeFvE7vb2YIuEuovvwMv8Qr5g/4JZ/BhvhbpXxMuLe8a80e41t7OwuCuPOSE7S4/EEfhQB96g5FLTUGFAp1ABRRRQAhGRXy9/wUo8NjxD+x544QKGktUiulJ7bXAJ/ImvqKvGf2ybEaj+y58S4Su7/iSztj6DNAH8345xX7rf8ABJ/x6/i39k/TbGaQPNol3LY4zkqgbKD8ARX4UtjnHTpX60/8ETteM3hT4haOW4iu4blUz03Jgn/x2gD9PAc0tIvSloAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAI3YggAf5/wAiviT4XN/wur/got488U/8fGj+AdJTRLRuq/aJT+8x2yAT+dfXnxD8WWngXwTrniG+kWG00yzlupXZsABVJ/pXzF/wTQ8L3I+B2p+O9Sj26t451m61qZmHPlsxEY9xigD0H9uvw8fFH7JPxKtRGZZE0p7qNep3RkP/AE/Svzs/4Is+JTYfGvxfoxbEd9o+9RnqySA5/Kv1i+K2gr4l+GPivSiN/wBs0y4hCn1aNgP51+An7IXxt1H9nP40Prljpsmp6lJaXOnw2MIyzzOCiDHs2D+FAH6wfti/F/XPHHirTfgB8Nblv+Eq8QEf2xqEDf8AIMsv+WhJHRmr6O+C3wk0P4HfDnSPCGgwLFZafEFaT+KaQ8vI3qSea8g/Yt/Z4vfhh4cv/GXjJ/t/xL8Wyfb9WupeXgVjuSBfQKOozXvPjzxPa+CvBut67fyrFbadZyXDyOeAFUk/yoA/E7/gqF8Q5fip+1vJoVhJ9oj0WODS4VT5szMcuMfVgPwr9iv2cvh1H8KPgj4L8Koio2naZCkuBjMhXc+ffJr8Tf2T/D1z+03+3Jpmp3sZmiutZm128yOBGrmQA57fdFfvwiBCMf40AOfOODiuQ1r4j2WjfEXw74OdJJNS1qG4uI2XGIo4lyS31OB+Nde5wPrXwj4q+OVhbf8ABUXw34durlI7W10CTTEdnwBcTDeB9SAKAPu1RuGT1rifjD8IfDnxt8Caj4T8S2S3WnXkZUNjLwv2dT2I612yDGadtGTx1oA/m+/aN+CHiD9lH42Xvh6aeWKWzmF1pmoxnBkhzlHBHccZr9yP2JfjTdfHj9nHwr4mvz/xM/KNrdn+9JGdpP44zXwH/wAFsJdNfx94Bhh2nVUsZTMBjPllvlz37H86+zf+CbHw7v8A4d/sneFrfU4mhvL8vfmJhgqrtlR+VAH1QOnrXwp/wV3+KK+Cv2cIvDkMm278R3iQ7AefKQbm/DoK+6wMDA7V+K//AAWA+KH/AAmXx+0nwjZy+dDoNmFaNDnM8pBI+uMCgD37/gi78Lv7N8AeL/HVxCBJqV2thbOV5KR8uQfTdX6USL8vAzzXiH7FnwyHwj/Zp8DeH2i8q6Fit1cgjB82X5mz78ivcSM0AeAfD/4Zxf8ADV/xF8dvp/2djp9npcM5UjzcLudge/YfhXvbyLEygsFLNwCetR3tzBp9rJcTypbwRgvJI5CqAB1JNfJfgL44/wDDTP7VlxYeGrl5fAngO3c3N3E52Xl9Jwo44ZVAJoA+u0OR606mR85Pc80+gAooooAKQ9KWkIzQB8t/tJfCf9oTxr48ivvhf8RLDwt4fFqkbWV1GWcy87m6dOR+VeT/APDOn7ZX/RaNF/8AAb/7GvvzaPSjaPSgD4D/AOGdP2yv+i0aL/4Df/Y0f8M6ftlf9Fo0X/wG/wDsa+/No9KNo9KAPgP/AIZ0/bK/6LRov/gN/wDY19BfsvfD/wCMPgLT9di+K/jG08W3M80bWMlpEEWFMYYHgHORn0r3raPSkKKcZAOORQAJggkHIJp1IAAOOKWgAooooAKa5wuePxp1J1oA+Y/Ff/BOn4E+NfFGq6/q/hJ7jVNVupb27n+1uu+WRiznAOBliTWX/wAOv/2d/wDoTX/8DpP8a+sMCjFAHyf/AMOv/wBnf/oTX/8AA6T/ABr0/wCB/wCyp8N/2c7vVbrwHojaTNqcaR3Ra4aQOqklR83TGTXsOKMCgBE7+lOoooAKKKq3l5FYW0txcSrBBEpd5HYBVUDkknpQBleMfGOl+A/DWo67rl4ljpljE0000h2gKMnj3r4Q8DaFrf8AwUO+MMXjfxLbTWHwV8Nzsmj6XKpX+05QeJWH8S5FZPxX+Irft6fGn/hXeh65Fo3wk8NTh9d1JrgRHUpVP+rjJYZWvujwfqHgfwL4c0/Q9E1PSbDSrCJYYLeK4QBUAx/e7nmgDs7Gyh060gtbWFYLeFRGkaDAVQMAAVO5IHHriue/4WD4aH/Mf038LpP8a5P4gftI/Df4aaJcapr3jDS7aCBS5VLhXdsdlUHJJoA7f/hKNOOvnRBeRHVFg+1G1z84izgMfY4rWU5zXw9+w38YX/aa+OfxY+JEcLwaNbx2+j6XE/8ADCuST9T1r7hXvxigB1MYZyPWn1HI20MfQZoA/mp/adaR/wBof4itKAJDrt2Wx6mQ16//AMExf+TxPBx77Z//AEUa4H9tfw8fDP7VHxKsipUHWJ5gD2DEsP511f8AwTh1A6Z+2L4AbdhZZ5Ij/wACiagD+g6iiigAooooAKKKKAOf8f6d/bHgjxDYgbjc6dcQhSM5LRsP61+O/wDwR51M6V+1L4h04sV+1aPPHtPqkqn+hr9o54hNGykZDDFfiF+wBOfA/wDwURl0n7ivdalp5UDuC3H/AI7QB+1mva5Z+GdHvNU1C6Sz0+yhaeeaQgKiAZJJ+gP4184fs8eH9Q+NHxM1b46+JbaSC1nibTPCNhKMG1sA2WuSOzynv1x6U74n6nc/tOfEv/hWGgTsngXRJUn8WanCfkuGBBSxRu5PBbHbjtX0xpmm2ulafbWdpBHb21vGsUUUYwqKBgAfhxQBaU5UHGPaloooAKKKKAGucLXyH8a/2svi/wDDv4karoPhv4KX/irRrUqIdVhm2rNkZOB7dK+vSM0mxQc4GaAPgr/hun49/wDRuOqf+BB/wo/4bp+Pf/RuOqf+BB/wr72wPQUYHoKAPgn/AIbp+Pf/AEbjqn/gQf8ACj/hun49/wDRuOqf+BB/wr72wPQUYHoKAPJP2cvip4t+LfgSXWfGHg648Daol00I0+4fcWQYw/4165TfLX+6Pyp1ABRRRQAUyX7pHrT6a3b60AflN/wWy0VUvvhxquwZ2TQFh167sfrX3f8AsY62PEH7L/w7vAeW0qJTz3AxXyR/wWr0Jrn4UeCNUUYFtqckbEf7UZx/KvSP2L/jXpPw9/YQ8MeINSl882iNaW9ohzJcThiEjQdSScUAepftUePtWv4tN+Fng5y3i3xXmCWaM5+wWfSWVj2OMgZr174X/DvS/hb4F0fwzpMYS00+ERhscyN/E59STk/jXmf7OHwv1awbUfiF41XzPG/iP95LE4yLG3PKQJ6YHX3Ne7KcqCKAADApaKKACiiigAry39qQBv2cviSCMj+wLz/0Sxr1KvJf2tLv7D+zR8S5iQAug3Q594yv9aAP5si5IxX6gf8ABEct/b3xK67fItefxevzBKEFgcfL1/Ov1i/4ImaG0fhz4i6uVAD3MFsDjrhScfrQB+oKcg/U06mqMZp1ABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABXK/Ezxyvw48H3/AIgbSdS1wWig/YNJhM1xLkgYVR1611VFAH5hftuftHfFX47fDy68C+A/hH4x0zStRIW/v73T2jkkiByYlHvgZ9q9R/Yz/aP8U+F/h54I+HPin4QeLtLvrNY9MXUYNPJtcZOJHJPyjBFfdlFAFW6i823nTG4OhTHr1Ffmz+w3+wPc+H/jj4x+IfjrS2gttN1m7j0KyuFBEx81ttx9NuCv1r9MKKAOT+I3jdfh14Q1DX20jUNc+yIGFjpMHnXMvb5Ur88P21/2kfin8cvhzdeB/AHwj8Y6Zpuo4S/v76wZZnjB5RVHQHpX6d0UAfh5+w5p3xR/ZX+LcvibVvhB4n1bT7u0azk8jT2MkQYg7lH4Cv1/+DXxa/4W9o13qY8Ma74WEE/ki3160NvLJx95Qeor0SigCK4kWKJnY4Cgk8Z7elfj34y/Yw+OH7Q3xs8WfGHwuINGVdZkk0tr+fyp5FhbYrKvYHbxX7DsMjGOtNiiWIbUUIP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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "image/jpeg": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PATH = \"C:/Users/arock.000/Downloads/\"\n",
    "Image(filename = PATH + \"MSE.jpg\", width=600, height=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2519999999999999"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error \n",
    "  \n",
    "# Given values \n",
    "Y_true = [1,1,2,3,5]  # Y_true = Y (original values) \n",
    "  \n",
    "# calculated values \n",
    "Y_pred = [0.8,1.2,1.9,3.9,4.4]  # Y_pred = Y' \n",
    "  \n",
    "# Calculation of Mean Squared Error (MSE) \n",
    "mean_squared_error(Y_true,Y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Scikit-Learn ](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mean Absolute Error (MAE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "image/jpeg": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PATH = \"C:/Users/arock.000/Downloads/\"\n",
    "Image(filename = PATH + \"MAE.jpg\", width=600, height=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_absolute_error\n",
    "\n",
    "# Given values\n",
    "y_true = [4, 0.5, -2, 9]\n",
    "\n",
    "# calculated values \n",
    "y_pred = [5.5, 0.0, -2, 8]\n",
    "\n",
    "# Calculation of Mean Absolute Error (MAE)\n",
    "mean_absolute_error(y_true, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Scikit-Learn ](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_absolute_error.html#sklearn.metrics.mean_absolute_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Root Mean Squared Error (RMSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 8,
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PATH = \"C:/Users/arock.000/Downloads/\"\n",
    "Image(filename = PATH + \"RMSE.png\", width=600, height=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5019960159204452"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import sqrt\n",
    "\n",
    "# Given values \n",
    "Y_true = [1,1,2,3,5]  # Y_true = Y (original values) \n",
    "  \n",
    "# calculated values \n",
    "Y_pred = [0.8,1.2,1.9,3.9,4.4]  # Y_pred = Y' \n",
    "  \n",
    "# Calculation of Root Mean Squared Error (RMSE) \n",
    "sqrt(mean_squared_error(Y_true, Y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Stackoverflow](https://stackoverflow.com/questions/17197492/is-there-a-library-function-for-root-mean-square-error-rmse-in-python)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# R² Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 11,
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PATH = \"C:/Users/arock.000/Downloads/\"\n",
    "Image(filename = PATH + \"R2.png\", width=600, height=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9486081370449679"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import r2_score\n",
    "\n",
    "# Given values \n",
    "y_true = [3, -0.5, 2, 7]\n",
    "\n",
    "# calculated values\n",
    "y_pred = [2.5, 0.0, 2, 8]\n",
    "\n",
    "# Calculation of R Square (r2_score) \n",
    "r2_score(y_true, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Scikit-Learn](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.r2_score.html#sklearn.metrics.r2_score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Adjusted R²"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PATH = \"C:/Users/arock.000/Downloads/\"\n",
    "Image(filename = PATH + \"Adjusted R2.png\", width=600, height=400)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "summary()\n",
      "                             OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.518\n",
      "Model:                            OLS   Adj. R-squared:                  0.507\n",
      "Method:                 Least Squares   F-statistic:                     46.27\n",
      "Date:                Tue, 13 Oct 2020   Prob (F-statistic):           3.83e-62\n",
      "Time:                        11:06:13   Log-Likelihood:                -2386.0\n",
      "No. Observations:                 442   AIC:                             4794.\n",
      "Df Residuals:                     431   BIC:                             4839.\n",
      "Df Model:                          10                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const        152.1335      2.576     59.061      0.000     147.071     157.196\n",
      "x1           -10.0122     59.749     -0.168      0.867    -127.448     107.424\n",
      "x2          -239.8191     61.222     -3.917      0.000    -360.151    -119.488\n",
      "x3           519.8398     66.534      7.813      0.000     389.069     650.610\n",
      "x4           324.3904     65.422      4.958      0.000     195.805     452.976\n",
      "x5          -792.1842    416.684     -1.901      0.058   -1611.169      26.801\n",
      "x6           476.7458    339.035      1.406      0.160    -189.621    1143.113\n",
      "x7           101.0446    212.533      0.475      0.635    -316.685     518.774\n",
      "x8           177.0642    161.476      1.097      0.273    -140.313     494.442\n",
      "x9           751.2793    171.902      4.370      0.000     413.409    1089.150\n",
      "x10           67.6254     65.984      1.025      0.306     -62.065     197.316\n",
      "==============================================================================\n",
      "Omnibus:                        1.506   Durbin-Watson:                   2.029\n",
      "Prob(Omnibus):                  0.471   Jarque-Bera (JB):                1.404\n",
      "Skew:                           0.017   Prob(JB):                        0.496\n",
      "Kurtosis:                       2.726   Cond. No.                         227.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "pvalues\n",
      " [1.00967888e-208 8.66999818e-001 1.04142931e-004 4.29955755e-014\n",
      " 1.02381891e-006 5.79473491e-002 1.60389213e-001 6.34720696e-001\n",
      " 2.73455652e-001 1.55602146e-005 3.05998348e-001]\n",
      "tvalues\n",
      " [59.0614273  -0.16757045 -3.91718415  7.81319639  4.9584347  -1.90116324\n",
      "  1.40618676  0.47543095  1.0965381   4.37039381  1.02487222]\n",
      "rsquared\n",
      " 0.5177494254132934\n",
      "rsquared_adj\n",
      " 0.506560316954205\n",
      "HC0_se\n",
      "HC1_se\n",
      "HC2_se\n",
      "HC3_se\n",
      "aic\n",
      "bic\n",
      "bse\n",
      "centered_tss\n",
      "compare_f_test\n",
      "compare_lm_test\n",
      "compare_lr_test\n",
      "condition_number\n",
      "conf_int\n",
      "conf_int_el\n",
      "cov_HC0\n",
      "cov_HC1\n",
      "cov_HC2\n",
      "cov_HC3\n",
      "cov_kwds\n",
      "cov_params\n",
      "cov_type\n",
      "df_model\n",
      "df_resid\n",
      "diagn\n",
      "eigenvals\n",
      "el_test\n",
      "ess\n",
      "f_pvalue\n",
      "f_test\n",
      "fittedvalues\n",
      "fvalue\n",
      "get_influence\n",
      "get_prediction\n",
      "get_robustcov_results\n",
      "initialize\n",
      "k_constant\n",
      "llf\n",
      "load\n",
      "model\n",
      "mse_model\n",
      "mse_resid\n",
      "mse_total\n",
      "nobs\n",
      "normalized_cov_params\n",
      "outlier_test\n",
      "params\n",
      "predict\n",
      "pvalues\n",
      "remove_data\n",
      "resid\n",
      "resid_pearson\n",
      "rsquared\n",
      "rsquared_adj\n",
      "save\n",
      "scale\n",
      "ssr\n",
      "summary\n",
      "summary2\n",
      "t_test\n",
      "t_test_pairwise\n",
      "tvalues\n",
      "uncentered_tss\n",
      "use_t\n",
      "wald_test\n",
      "wald_test_terms\n",
      "wresid\n",
      "[206.11706979  68.07234761 176.88406035]\n",
      "r2_score 0.5177494254132934\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn import datasets, linear_model\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import statsmodels.api as sm\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "\n",
    "diabetes = datasets.load_diabetes()\n",
    "X = diabetes.data\n",
    "y = diabetes.target\n",
    "X2 = sm.add_constant(X) \n",
    "est = sm.OLS(y, X2)\n",
    "est2 = est.fit()\n",
    "print(\"summary()\\n\",est2.summary())\n",
    "print(\"pvalues\\n\",est2.pvalues)\n",
    "print(\"tvalues\\n\",est2.tvalues)\n",
    "print(\"rsquared\\n\",est2.rsquared)\n",
    "print(\"rsquared_adj\\n\",est2.rsquared_adj)\n",
    "\n",
    "#All the attributes \n",
    "for attr in dir(est2):\n",
    "    if not attr.startswith('_'):\n",
    "        print(attr)\n",
    "\n",
    "predictions = est2.predict(X2)\n",
    "\n",
    "print(est2.predict(X2[:3,:]))\n",
    "\n",
    "from sklearn.metrics import r2_score\n",
    "print(\"r2_score\",r2_score(y,predictions))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Analytics Vidhya](https://discuss.analyticsvidhya.com/t/getting-p-value-r-squared-and-adjusted-r-squared-value-in-python/31528/6)"
   ]
  },
  {
   "cell_type": "code",
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