{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression diagnostics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example file shows how to use a few of the ``statsmodels`` regression diagnostic tests in a real-life context. You can learn about more tests and find out more information about the tests here on the [Regression Diagnostics page.](https://www.statsmodels.org/stable/diagnostic.html)\n",
    "\n",
    "Note that most of the tests described here only return a tuple of numbers, without any annotation. A full description of outputs is always included in the docstring and in the online ``statsmodels`` documentation. For presentation purposes, we use the ``zip(name,test)`` construct to pretty-print short descriptions in the examples below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimate a regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Lottery   R-squared:                       0.348\n",
      "Model:                            OLS   Adj. R-squared:                  0.333\n",
      "Method:                 Least Squares   F-statistic:                     22.20\n",
      "Date:                Fri, 20 Mar 2026   Prob (F-statistic):           1.90e-08\n",
      "Time:                        11:18:46   Log-Likelihood:                -379.82\n",
      "No. Observations:                  86   AIC:                             765.6\n",
      "Df Residuals:                      83   BIC:                             773.0\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===================================================================================\n",
      "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "Intercept         246.4341     35.233      6.995      0.000     176.358     316.510\n",
      "Literacy           -0.4889      0.128     -3.832      0.000      -0.743      -0.235\n",
      "np.log(Pop1831)   -31.3114      5.977     -5.239      0.000     -43.199     -19.424\n",
      "==============================================================================\n",
      "Omnibus:                        3.713   Durbin-Watson:                   2.019\n",
      "Prob(Omnibus):                  0.156   Jarque-Bera (JB):                3.394\n",
      "Skew:                          -0.487   Prob(JB):                        0.183\n",
      "Kurtosis:                       3.003   Cond. No.                         702.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.compat import lzip\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.stats.api as sms\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Load data\n",
    "import statsmodels.datasets\n",
    "dat = statsmodels.datasets.get_rdataset(\"Guerry\", \"HistData\", cache=True).data\n",
    "\n",
    "# Fit regression model (using the natural log of one of the regressors)\n",
    "results = smf.ols(\"Lottery ~ Literacy + np.log(Pop1831)\", data=dat).fit()\n",
    "\n",
    "# Inspect the results\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normality of the residuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jarque-Bera test:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Jarque-Bera', np.float64(3.393608024843183)),\n",
       " ('Chi^2 two-tail prob.', np.float64(0.18326831231663213)),\n",
       " ('Skew', np.float64(-0.4865803431122349)),\n",
       " ('Kurtosis', np.float64(3.0034177578816337))]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "name = [\"Jarque-Bera\", \"Chi^2 two-tail prob.\", \"Skew\", \"Kurtosis\"]\n",
    "test = sms.jarque_bera(results.resid)\n",
    "lzip(name, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Omni test:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Chi^2', np.float64(3.713437811597197)),\n",
       " ('Two-tail probability', np.float64(0.15618424580304707))]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "name = [\"Chi^2\", \"Two-tail probability\"]\n",
    "test = sms.omni_normtest(results.resid)\n",
    "lzip(name, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Influence tests\n",
    "\n",
    "Once created, an object of class ``OLSInfluence`` holds attributes and methods that allow users to assess the influence of each observation. For example, we can compute and extract the first few rows of DFbetas by:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.00301154,  0.00290872,  0.00118179],\n",
       "       [-0.06425662,  0.04043093,  0.06281609],\n",
       "       [ 0.01554894, -0.03556038, -0.00905336],\n",
       "       [ 0.17899858,  0.04098207, -0.18062352],\n",
       "       [ 0.29679073,  0.21249207, -0.3213655 ]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.outliers_influence import OLSInfluence\n",
    "\n",
    "test_class = OLSInfluence(results)\n",
    "test_class.dfbetas[:5, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explore other options by typing ``dir(influence_test)``\n",
    "\n",
    "Useful information on leverage can also be plotted:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.regressionplots import plot_leverage_resid2\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "fig = plot_leverage_resid2(results, ax=ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other plotting options can be found on the [Graphics page.](https://www.statsmodels.org/stable/graphics.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multicollinearity\n",
    "\n",
    "Condition number:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(702.179214549006)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.cond(results.model.exog)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Heteroskedasticity tests\n",
    "\n",
    "Breush-Pagan test:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Lagrange multiplier statistic', np.float64(4.893213374094005)),\n",
       " ('p-value', np.float64(0.08658690502352002)),\n",
       " ('f-value', np.float64(2.503715946256461)),\n",
       " ('f p-value', np.float64(0.08794028782672814))]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "name = [\"Lagrange multiplier statistic\", \"p-value\", \"f-value\", \"f p-value\"]\n",
    "test = sms.het_breuschpagan(results.resid, results.model.exog)\n",
    "lzip(name, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Goldfeld-Quandt test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('F statistic', np.float64(1.1002422436378139)),\n",
       " ('p-value', np.float64(0.38202950686925286))]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "name = [\"F statistic\", \"p-value\"]\n",
    "test = sms.het_goldfeldquandt(results.resid, results.model.exog)\n",
    "lzip(name, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearity\n",
    "\n",
    "Harvey-Collier multiplier test for Null hypothesis that the linear specification is correct:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('t value', np.float64(-1.0796490077783811)),\n",
       " ('p value', np.float64(0.283463924755859))]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "name = [\"t value\", \"p value\"]\n",
    "test = sms.linear_harvey_collier(results)\n",
    "lzip(name, test)"
   ]
  }
 ],
 "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": "3.14.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
