{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ordinary Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:00.346699Z",
     "iopub.status.busy": "2026-09-12T23:55:00.346539Z",
     "iopub.status.idle": "2026-09-12T23:55:01.811340Z",
     "shell.execute_reply": "2026-09-12T23:55:01.810903Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:01.821134Z",
     "iopub.status.busy": "2026-09-12T23:55:01.820865Z",
     "iopub.status.idle": "2026-09-12T23:55:04.976243Z",
     "shell.execute_reply": "2026-09-12T23:55:04.975669Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import statsmodels.api as sm\n",
    "\n",
    "np.random.seed(9876789)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS estimation\n",
    "\n",
    "Artificial data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:04.979852Z",
     "iopub.status.busy": "2026-09-12T23:55:04.977962Z",
     "iopub.status.idle": "2026-09-12T23:55:04.987985Z",
     "shell.execute_reply": "2026-09-12T23:55:04.987647Z"
    }
   },
   "outputs": [],
   "source": [
    "nsample = 100\n",
    "x = np.linspace(0, 10, 100)\n",
    "X = np.column_stack((x, x**2))\n",
    "beta = np.array([1, 0.1, 10])\n",
    "e = np.random.normal(size=nsample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our model needs an intercept so we add a column of 1s:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:04.992640Z",
     "iopub.status.busy": "2026-09-12T23:55:04.992052Z",
     "iopub.status.idle": "2026-09-12T23:55:04.999978Z",
     "shell.execute_reply": "2026-09-12T23:55:04.999649Z"
    }
   },
   "outputs": [],
   "source": [
    "X = sm.add_constant(X)\n",
    "y = np.dot(X, beta) + e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.001668Z",
     "iopub.status.busy": "2026-09-12T23:55:05.001512Z",
     "iopub.status.idle": "2026-09-12T23:55:05.028009Z",
     "shell.execute_reply": "2026-09-12T23:55:05.027651Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       1.000\n",
      "Model:                            OLS   Adj. R-squared:                  1.000\n",
      "Method:                 Least Squares   F-statistic:                 4.020e+06\n",
      "Date:                Sat, 12 Sep 2026   Prob (F-statistic):          2.83e-239\n",
      "Time:                        23:55:05   Log-Likelihood:                -146.51\n",
      "No. Observations:                 100   AIC:                             299.0\n",
      "Df Residuals:                      97   BIC:                             306.8\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.3423      0.313      4.292      0.000       0.722       1.963\n",
      "x1            -0.0402      0.145     -0.278      0.781      -0.327       0.247\n",
      "x2            10.0103      0.014    715.745      0.000       9.982      10.038\n",
      "==============================================================================\n",
      "Omnibus:                        2.042   Durbin-Watson:                   2.274\n",
      "Prob(Omnibus):                  0.360   Jarque-Bera (JB):                1.875\n",
      "Skew:                           0.234   Prob(JB):                        0.392\n",
      "Kurtosis:                       2.519   Cond. No.                         144.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = sm.OLS(y, X)\n",
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quantities of interest can be extracted directly from the fitted model. Type ``dir(results)`` for a full list. Here are some examples:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.029759Z",
     "iopub.status.busy": "2026-09-12T23:55:05.029594Z",
     "iopub.status.idle": "2026-09-12T23:55:05.038007Z",
     "shell.execute_reply": "2026-09-12T23:55:05.037653Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters:  [ 1.34233516 -0.04024948 10.01025357]\n",
      "R2:  0.9999879365025871\n"
     ]
    }
   ],
   "source": [
    "print(\"Parameters: \", results.params)\n",
    "print(\"R2: \", results.rsquared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS non-linear curve but linear in parameters\n",
    "\n",
    "We simulate artificial data with a non-linear relationship between x and y:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.041972Z",
     "iopub.status.busy": "2026-09-12T23:55:05.041823Z",
     "iopub.status.idle": "2026-09-12T23:55:05.053015Z",
     "shell.execute_reply": "2026-09-12T23:55:05.052653Z"
    }
   },
   "outputs": [],
   "source": [
    "nsample = 50\n",
    "sig = 0.5\n",
    "x = np.linspace(0, 20, nsample)\n",
    "X = np.column_stack((x, np.sin(x), (x - 5) ** 2, np.ones(nsample)))\n",
    "beta = [0.5, 0.5, -0.02, 5.0]\n",
    "\n",
    "y_true = np.dot(X, beta)\n",
    "y = y_true + sig * np.random.normal(size=nsample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.054834Z",
     "iopub.status.busy": "2026-09-12T23:55:05.054689Z",
     "iopub.status.idle": "2026-09-12T23:55:05.078610Z",
     "shell.execute_reply": "2026-09-12T23:55:05.077829Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.933\n",
      "Model:                            OLS   Adj. R-squared:                  0.928\n",
      "Method:                 Least Squares   F-statistic:                     211.8\n",
      "Date:                Sat, 12 Sep 2026   Prob (F-statistic):           6.30e-27\n",
      "Time:                        23:55:05   Log-Likelihood:                -34.438\n",
      "No. Observations:                  50   AIC:                             76.88\n",
      "Df Residuals:                      46   BIC:                             84.52\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "x1             0.4687      0.026     17.751      0.000       0.416       0.522\n",
      "x2             0.4836      0.104      4.659      0.000       0.275       0.693\n",
      "x3            -0.0174      0.002     -7.507      0.000      -0.022      -0.013\n",
      "const          5.2058      0.171     30.405      0.000       4.861       5.550\n",
      "==============================================================================\n",
      "Omnibus:                        0.655   Durbin-Watson:                   2.896\n",
      "Prob(Omnibus):                  0.721   Jarque-Bera (JB):                0.360\n",
      "Skew:                           0.207   Prob(JB):                        0.835\n",
      "Kurtosis:                       3.026   Cond. No.                         221.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res = sm.OLS(y, X).fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract other quantities of interest:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.084187Z",
     "iopub.status.busy": "2026-09-12T23:55:05.084041Z",
     "iopub.status.idle": "2026-09-12T23:55:05.093767Z",
     "shell.execute_reply": "2026-09-12T23:55:05.093280Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters:  [ 0.46872448  0.48360119 -0.01740479  5.20584496]\n",
      "Standard errors:  [0.02640602 0.10380518 0.00231847 0.17121765]\n",
      "Predicted values:  [ 4.77072516  5.22213464  5.63620761  5.98658823  6.25643234  6.44117491\n",
      "  6.54928009  6.60085051  6.62432454  6.6518039   6.71377946  6.83412169\n",
      "  7.02615877  7.29048685  7.61487206  7.97626054  8.34456611  8.68761335\n",
      "  8.97642389  9.18997755  9.31866582  9.36587056  9.34740836  9.28893189\n",
      "  9.22171529  9.17751587  9.1833565   9.25708583  9.40444579  9.61812821\n",
      "  9.87897556 10.15912843 10.42660281 10.65054491 10.8063004  10.87946503\n",
      " 10.86825119 10.78378163 10.64826203 10.49133265 10.34519853 10.23933827\n",
      " 10.19566084 10.22490593 10.32487947 10.48081414 10.66779556 10.85485568\n",
      " 11.01006072 11.10575781]\n"
     ]
    }
   ],
   "source": [
    "print(\"Parameters: \", res.params)\n",
    "print(\"Standard errors: \", res.bse)\n",
    "print(\"Predicted values: \", res.predict())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a plot to compare the true relationship to OLS predictions. Confidence intervals around the predictions are built using the ``wls_prediction_std`` command."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.101093Z",
     "iopub.status.busy": "2026-09-12T23:55:05.100945Z",
     "iopub.status.idle": "2026-09-12T23:55:05.537228Z",
     "shell.execute_reply": "2026-09-12T23:55:05.536654Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe544f04050>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_ols = res.get_prediction()\n",
    "iv_l = pred_ols.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u = pred_ols.summary_frame()[\"obs_ci_upper\"]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(x, y, \"o\", label=\"data\")\n",
    "ax.plot(x, y_true, \"b-\", label=\"True\")\n",
    "ax.plot(x, res.fittedvalues, \"r--.\", label=\"OLS\")\n",
    "ax.plot(x, iv_u, \"r--\")\n",
    "ax.plot(x, iv_l, \"r--\")\n",
    "ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS with dummy variables\n",
    "\n",
    "We generate some artificial data. There are 3 groups which will be modelled using dummy variables. Group 0 is the omitted/benchmark category."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.539142Z",
     "iopub.status.busy": "2026-09-12T23:55:05.538984Z",
     "iopub.status.idle": "2026-09-12T23:55:05.552452Z",
     "shell.execute_reply": "2026-09-12T23:55:05.551654Z"
    }
   },
   "outputs": [],
   "source": [
    "nsample = 50\n",
    "groups = np.zeros(nsample, int)\n",
    "groups[20:40] = 1\n",
    "groups[40:] = 2\n",
    "# dummy = (groups[:,None] == np.unique(groups)).astype(float)\n",
    "\n",
    "dummy = pd.get_dummies(groups).values\n",
    "x = np.linspace(0, 20, nsample)\n",
    "# drop reference category\n",
    "X = np.column_stack((x, dummy[:, 1:]))\n",
    "X = sm.add_constant(X, prepend=False)\n",
    "\n",
    "beta = [1.0, 3, -3, 10]\n",
    "y_true = np.dot(X, beta)\n",
    "e = np.random.normal(size=nsample)\n",
    "y = y_true + e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspect the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.556219Z",
     "iopub.status.busy": "2026-09-12T23:55:05.556058Z",
     "iopub.status.idle": "2026-09-12T23:55:05.570027Z",
     "shell.execute_reply": "2026-09-12T23:55:05.569657Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         0.         0.         1.        ]\n",
      " [0.40816327 0.         0.         1.        ]\n",
      " [0.81632653 0.         0.         1.        ]\n",
      " [1.2244898  0.         0.         1.        ]\n",
      " [1.63265306 0.         0.         1.        ]]\n",
      "[ 9.28223335 10.50481865 11.84389206 10.38508408 12.37941998]\n",
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
      " 1 1 1 2 2 2 2 2 2 2 2 2 2]\n",
      "[[ True False False]\n",
      " [ True False False]\n",
      " [ True False False]\n",
      " [ True False False]\n",
      " [ True False False]]\n"
     ]
    }
   ],
   "source": [
    "print(X[:5, :])\n",
    "print(y[:5])\n",
    "print(groups)\n",
    "print(dummy[:5, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.571568Z",
     "iopub.status.busy": "2026-09-12T23:55:05.571425Z",
     "iopub.status.idle": "2026-09-12T23:55:05.598090Z",
     "shell.execute_reply": "2026-09-12T23:55:05.597653Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.978\n",
      "Model:                            OLS   Adj. R-squared:                  0.976\n",
      "Method:                 Least Squares   F-statistic:                     671.7\n",
      "Date:                Sat, 12 Sep 2026   Prob (F-statistic):           5.69e-38\n",
      "Time:                        23:55:05   Log-Likelihood:                -64.643\n",
      "No. Observations:                  50   AIC:                             137.3\n",
      "Df Residuals:                      46   BIC:                             144.9\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "x1             0.9999      0.060     16.689      0.000       0.879       1.121\n",
      "x2             2.8909      0.569      5.081      0.000       1.746       4.036\n",
      "x3            -3.2232      0.927     -3.477      0.001      -5.089      -1.357\n",
      "const         10.1031      0.310     32.573      0.000       9.479      10.727\n",
      "==============================================================================\n",
      "Omnibus:                        2.831   Durbin-Watson:                   1.998\n",
      "Prob(Omnibus):                  0.243   Jarque-Bera (JB):                1.927\n",
      "Skew:                          -0.279   Prob(JB):                        0.382\n",
      "Kurtosis:                       2.217   Cond. No.                         96.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "res2 = sm.OLS(y, X).fit()\n",
    "print(res2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Draw a plot to compare the true relationship to OLS predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:05.599731Z",
     "iopub.status.busy": "2026-09-12T23:55:05.599568Z",
     "iopub.status.idle": "2026-09-12T23:55:06.003765Z",
     "shell.execute_reply": "2026-09-12T23:55:06.003354Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_ols2 = res2.get_prediction()\n",
    "iv_l = pred_ols2.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u = pred_ols2.summary_frame()[\"obs_ci_upper\"]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(x, y, \"o\", label=\"Data\")\n",
    "ax.plot(x, y_true, \"b-\", label=\"True\")\n",
    "ax.plot(x, res2.fittedvalues, \"r--.\", label=\"Predicted\")\n",
    "ax.plot(x, iv_u, \"r--\")\n",
    "ax.plot(x, iv_l, \"r--\")\n",
    "legend = ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Joint hypothesis test\n",
    "\n",
    "### F test\n",
    "\n",
    "We want to test the hypothesis that both coefficients on the dummy variables are equal to zero, that is, $R \\times \\beta = 0$. An F test leads us to strongly reject the null hypothesis of identical constant in the 3 groups:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.010262Z",
     "iopub.status.busy": "2026-09-12T23:55:06.010103Z",
     "iopub.status.idle": "2026-09-12T23:55:06.020709Z",
     "shell.execute_reply": "2026-09-12T23:55:06.020364Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 0 0]\n",
      " [0 0 1 0]]\n",
      "<F test: F=145.49268198027997, p=1.2834419617282373e-20, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "R = [[0, 1, 0, 0], [0, 0, 1, 0]]\n",
    "print(np.array(R))\n",
    "print(res2.f_test(R))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also use formula-like syntax to test hypotheses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.022540Z",
     "iopub.status.busy": "2026-09-12T23:55:06.022392Z",
     "iopub.status.idle": "2026-09-12T23:55:06.030742Z",
     "shell.execute_reply": "2026-09-12T23:55:06.030378Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=145.49268198027954, p=1.2834419617283094e-20, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "print(res2.f_test(\"x2 = x3 = 0\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Small group effects\n",
    "\n",
    "If we generate artificial data with smaller group effects, the T test can no longer reject the Null hypothesis: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.036990Z",
     "iopub.status.busy": "2026-09-12T23:55:06.036839Z",
     "iopub.status.idle": "2026-09-12T23:55:06.045014Z",
     "shell.execute_reply": "2026-09-12T23:55:06.044654Z"
    }
   },
   "outputs": [],
   "source": [
    "beta = [1.0, 0.3, -0.0, 10]\n",
    "y_true = np.dot(X, beta)\n",
    "y = y_true + np.random.normal(size=nsample)\n",
    "\n",
    "res3 = sm.OLS(y, X).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.052903Z",
     "iopub.status.busy": "2026-09-12T23:55:06.052751Z",
     "iopub.status.idle": "2026-09-12T23:55:06.058561Z",
     "shell.execute_reply": "2026-09-12T23:55:06.058214Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.2249111925408884, p=0.3031864410631284, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "print(res3.f_test(R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.065020Z",
     "iopub.status.busy": "2026-09-12T23:55:06.064845Z",
     "iopub.status.idle": "2026-09-12T23:55:06.074161Z",
     "shell.execute_reply": "2026-09-12T23:55:06.073653Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.2249111925408889, p=0.3031864410631284, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "print(res3.f_test(\"x2 = x3 = 0\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multicollinearity\n",
    "\n",
    "The Longley dataset is well known to have high multicollinearity. That is, the exogenous predictors are highly correlated. This is problematic because it can affect the stability of our coefficient estimates as we make minor changes to model specification. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.075793Z",
     "iopub.status.busy": "2026-09-12T23:55:06.075640Z",
     "iopub.status.idle": "2026-09-12T23:55:06.101015Z",
     "shell.execute_reply": "2026-09-12T23:55:06.100653Z"
    }
   },
   "outputs": [],
   "source": [
    "from statsmodels.datasets.longley import load_pandas\n",
    "\n",
    "y = load_pandas().endog\n",
    "X = load_pandas().exog\n",
    "X = sm.add_constant(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit and summary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.102813Z",
     "iopub.status.busy": "2026-09-12T23:55:06.102649Z",
     "iopub.status.idle": "2026-09-12T23:55:06.137613Z",
     "shell.execute_reply": "2026-09-12T23:55:06.137222Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 TOTEMP   R-squared:                       0.995\n",
      "Model:                            OLS   Adj. R-squared:                  0.992\n",
      "Method:                 Least Squares   F-statistic:                     330.3\n",
      "Date:                Sat, 12 Sep 2026   Prob (F-statistic):           4.98e-10\n",
      "Time:                        23:55:06   Log-Likelihood:                -109.62\n",
      "No. Observations:                  16   AIC:                             233.2\n",
      "Df Residuals:                       9   BIC:                             238.6\n",
      "Df Model:                           6                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const      -3.482e+06    8.9e+05     -3.911      0.004    -5.5e+06   -1.47e+06\n",
      "GNPDEFL       15.0619     84.915      0.177      0.863    -177.029     207.153\n",
      "GNP           -0.0358      0.033     -1.070      0.313      -0.112       0.040\n",
      "UNEMP         -2.0202      0.488     -4.136      0.003      -3.125      -0.915\n",
      "ARMED         -1.0332      0.214     -4.822      0.001      -1.518      -0.549\n",
      "POP           -0.0511      0.226     -0.226      0.826      -0.563       0.460\n",
      "YEAR        1829.1515    455.478      4.016      0.003     798.788    2859.515\n",
      "==============================================================================\n",
      "Omnibus:                        0.749   Durbin-Watson:                   2.559\n",
      "Prob(Omnibus):                  0.688   Jarque-Bera (JB):                0.684\n",
      "Skew:                           0.420   Prob(JB):                        0.710\n",
      "Kurtosis:                       2.434   Cond. No.                     4.86e+09\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 4.86e+09. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "ols_model = sm.OLS(y, X)\n",
    "ols_results = ols_model.fit()\n",
    "print(ols_results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Condition number\n",
    "\n",
    "One way to assess multicollinearity is to compute the condition number. Values over 20 are worrisome (see Greene 4.9). The first step is to normalize the independent variables to have unit length: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.144008Z",
     "iopub.status.busy": "2026-09-12T23:55:06.143859Z",
     "iopub.status.idle": "2026-09-12T23:55:06.150770Z",
     "shell.execute_reply": "2026-09-12T23:55:06.150346Z"
    }
   },
   "outputs": [],
   "source": [
    "norm_x = X.values\n",
    "for i, name in enumerate(X):\n",
    "    if name == \"const\":\n",
    "        continue\n",
    "    norm_x[:, i] = X[name] / np.linalg.norm(X[name])\n",
    "norm_xtx = np.dot(norm_x.T, norm_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we take the square root of the ratio of the biggest to the smallest eigen values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.152319Z",
     "iopub.status.busy": "2026-09-12T23:55:06.152183Z",
     "iopub.status.idle": "2026-09-12T23:55:06.159696Z",
     "shell.execute_reply": "2026-09-12T23:55:06.159209Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(56240.86930207108+0j)\n"
     ]
    }
   ],
   "source": [
    "eigs = np.linalg.eigvals(norm_xtx)\n",
    "condition_number = np.sqrt(eigs.max() / eigs.min())\n",
    "print(condition_number)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dropping an observation\n",
    "\n",
    "Greene also points out that dropping a single observation can have a dramatic effect on the coefficient estimates: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.162805Z",
     "iopub.status.busy": "2026-09-12T23:55:06.162664Z",
     "iopub.status.idle": "2026-09-12T23:55:06.175112Z",
     "shell.execute_reply": "2026-09-12T23:55:06.174654Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Percentage change 4.55%\n",
      "Percentage change -105.20%\n",
      "Percentage change -3.43%\n",
      "Percentage change 2.92%\n",
      "Percentage change 3.32%\n",
      "Percentage change 97.06%\n",
      "Percentage change 4.64%\n",
      "\n"
     ]
    }
   ],
   "source": [
    "ols_results2 = sm.OLS(y.iloc[:14], X.iloc[:14]).fit()\n",
    "print(\n",
    "    \"Percentage change %4.2f%%\\n\"\n",
    "    * 7\n",
    "    % tuple((ols_results2.params - ols_results.params) / ols_results.params * 100)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also look at formal statistics for this such as the DFBETAS -- a standardized measure of how much each coefficient changes when that observation is left out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.177994Z",
     "iopub.status.busy": "2026-09-12T23:55:06.177854Z",
     "iopub.status.idle": "2026-09-12T23:55:06.187791Z",
     "shell.execute_reply": "2026-09-12T23:55:06.184151Z"
    }
   },
   "outputs": [],
   "source": [
    "infl = ols_results.get_influence()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general we may consider DBETAS in absolute value greater than $2/\\sqrt{N}$ to be influential observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.191977Z",
     "iopub.status.busy": "2026-09-12T23:55:06.191824Z",
     "iopub.status.idle": "2026-09-12T23:55:06.201030Z",
     "shell.execute_reply": "2026-09-12T23:55:06.200660Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.0 / len(X) ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-09-12T23:55:06.202834Z",
     "iopub.status.busy": "2026-09-12T23:55:06.202690Z",
     "iopub.status.idle": "2026-09-12T23:55:06.238023Z",
     "shell.execute_reply": "2026-09-12T23:55:06.237650Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    dfb_const  dfb_GNPDEFL   dfb_GNP  dfb_UNEMP  dfb_ARMED   dfb_POP  dfb_YEAR\n",
      "0   -0.016406    -0.234566 -0.045095  -0.121513  -0.149026  0.211057  0.013388\n",
      "1   -0.020608    -0.289091  0.124453   0.156964   0.287700 -0.161890  0.025958\n",
      "2   -0.008382     0.007161 -0.016799   0.009575   0.002227  0.014871  0.008103\n",
      "3    0.018093     0.907968 -0.500022  -0.495996   0.089996  0.711142 -0.040056\n",
      "4    1.871260    -0.219351  1.611418   1.561520   1.169337 -1.081513 -1.864186\n",
      "5   -0.321373    -0.077045 -0.198129  -0.192961  -0.430626  0.079916  0.323275\n",
      "6    0.315945    -0.241983  0.438146   0.471797  -0.019546 -0.448515 -0.307517\n",
      "7    0.015816    -0.002742  0.018591   0.005064  -0.031320 -0.015823 -0.015583\n",
      "8   -0.004019    -0.045687  0.023708   0.018125   0.013683 -0.034770  0.005116\n",
      "9   -1.018242    -0.282131 -0.412621  -0.663904  -0.715020 -0.229501  1.035723\n",
      "10   0.030947    -0.024781  0.029480   0.035361   0.034508 -0.014194 -0.030805\n",
      "11   0.005987    -0.079727  0.030276  -0.008883  -0.006854 -0.010693 -0.005323\n",
      "12  -0.135883     0.092325 -0.253027  -0.211465   0.094720  0.331351  0.129120\n",
      "13   0.032736    -0.024249  0.017510   0.033242   0.090655  0.007634 -0.033114\n",
      "14   0.305868     0.148070  0.001428   0.169314   0.253431  0.342982 -0.318031\n",
      "15  -0.538323     0.432004 -0.261262  -0.143444  -0.360890 -0.467296  0.552421\n"
     ]
    }
   ],
   "source": [
    "print(infl.summary_frame().filter(regex=\"dfb\"))"
   ]
  }
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