{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ordinary Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:04:45.481328Z",
     "iopub.status.busy": "2026-07-28T19:04:45.481173Z",
     "iopub.status.idle": "2026-07-28T19:04:46.899315Z",
     "shell.execute_reply": "2026-07-28T19:04:46.898491Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:04:46.905690Z",
     "iopub.status.busy": "2026-07-28T19:04:46.905364Z",
     "iopub.status.idle": "2026-07-28T19:04:50.847908Z",
     "shell.execute_reply": "2026-07-28T19:04:50.845151Z"
    }
   },
   "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": "2026-07-28T19:04:50.851763Z",
     "iopub.status.busy": "2026-07-28T19:04:50.851392Z",
     "iopub.status.idle": "2026-07-28T19:04:50.858133Z",
     "shell.execute_reply": "2026-07-28T19:04:50.857488Z"
    }
   },
   "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": "2026-07-28T19:04:50.860066Z",
     "iopub.status.busy": "2026-07-28T19:04:50.859857Z",
     "iopub.status.idle": "2026-07-28T19:04:50.863989Z",
     "shell.execute_reply": "2026-07-28T19:04:50.863433Z"
    }
   },
   "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": "2026-07-28T19:04:50.867368Z",
     "iopub.status.busy": "2026-07-28T19:04:50.867189Z",
     "iopub.status.idle": "2026-07-28T19:04:50.890261Z",
     "shell.execute_reply": "2026-07-28T19:04:50.889728Z"
    }
   },
   "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:                Tue, 28 Jul 2026   Prob (F-statistic):          2.83e-239\n",
      "Time:                        19:04:50   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": "2026-07-28T19:04:50.895519Z",
     "iopub.status.busy": "2026-07-28T19:04:50.895179Z",
     "iopub.status.idle": "2026-07-28T19:04:50.901873Z",
     "shell.execute_reply": "2026-07-28T19:04:50.901423Z"
    }
   },
   "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": "2026-07-28T19:04:50.911530Z",
     "iopub.status.busy": "2026-07-28T19:04:50.911340Z",
     "iopub.status.idle": "2026-07-28T19:04:50.920189Z",
     "shell.execute_reply": "2026-07-28T19:04:50.919730Z"
    }
   },
   "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": "2026-07-28T19:04:50.927222Z",
     "iopub.status.busy": "2026-07-28T19:04:50.927044Z",
     "iopub.status.idle": "2026-07-28T19:04:50.949205Z",
     "shell.execute_reply": "2026-07-28T19:04:50.948736Z"
    }
   },
   "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:                Tue, 28 Jul 2026   Prob (F-statistic):           6.30e-27\n",
      "Time:                        19:04:50   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": "2026-07-28T19:04:50.955570Z",
     "iopub.status.busy": "2026-07-28T19:04:50.955197Z",
     "iopub.status.idle": "2026-07-28T19:04:50.962906Z",
     "shell.execute_reply": "2026-07-28T19:04:50.962439Z"
    }
   },
   "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": "2026-07-28T19:04:50.964499Z",
     "iopub.status.busy": "2026-07-28T19:04:50.964332Z",
     "iopub.status.idle": "2026-07-28T19:04:51.326199Z",
     "shell.execute_reply": "2026-07-28T19:04:51.325734Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f93bbc5de80>"
      ]
     },
     "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": "2026-07-28T19:04:51.332602Z",
     "iopub.status.busy": "2026-07-28T19:04:51.332382Z",
     "iopub.status.idle": "2026-07-28T19:04:51.344250Z",
     "shell.execute_reply": "2026-07-28T19:04:51.343742Z"
    }
   },
   "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": "2026-07-28T19:04:51.348207Z",
     "iopub.status.busy": "2026-07-28T19:04:51.348020Z",
     "iopub.status.idle": "2026-07-28T19:04:51.354879Z",
     "shell.execute_reply": "2026-07-28T19:04:51.354449Z"
    }
   },
   "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": "2026-07-28T19:04:51.361221Z",
     "iopub.status.busy": "2026-07-28T19:04:51.361038Z",
     "iopub.status.idle": "2026-07-28T19:04:51.381050Z",
     "shell.execute_reply": "2026-07-28T19:04:51.380602Z"
    }
   },
   "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:                Tue, 28 Jul 2026   Prob (F-statistic):           5.69e-38\n",
      "Time:                        19:04:51   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": "2026-07-28T19:04:51.392265Z",
     "iopub.status.busy": "2026-07-28T19:04:51.392074Z",
     "iopub.status.idle": "2026-07-28T19:04:51.800255Z",
     "shell.execute_reply": "2026-07-28T19:04:51.799564Z"
    }
   },
   "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": "2026-07-28T19:04:51.806337Z",
     "iopub.status.busy": "2026-07-28T19:04:51.806105Z",
     "iopub.status.idle": "2026-07-28T19:04:51.821753Z",
     "shell.execute_reply": "2026-07-28T19:04:51.816516Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 0 0]\n",
      " [0 0 1 0]]\n",
      "<F test: F=145.49268198027985, p=1.2834419617282554e-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": "2026-07-28T19:04:51.826377Z",
     "iopub.status.busy": "2026-07-28T19:04:51.826176Z",
     "iopub.status.idle": "2026-07-28T19:04:51.837889Z",
     "shell.execute_reply": "2026-07-28T19:04:51.837299Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=145.49268198028003, p=1.2834419617282254e-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": "2026-07-28T19:04:51.843168Z",
     "iopub.status.busy": "2026-07-28T19:04:51.842975Z",
     "iopub.status.idle": "2026-07-28T19:04:51.848985Z",
     "shell.execute_reply": "2026-07-28T19:04:51.848480Z"
    }
   },
   "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": "2026-07-28T19:04:51.854183Z",
     "iopub.status.busy": "2026-07-28T19:04:51.853983Z",
     "iopub.status.idle": "2026-07-28T19:04:51.864147Z",
     "shell.execute_reply": "2026-07-28T19:04:51.863525Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.2249111925408935, p=0.30318644106312703, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "print(res3.f_test(R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-28T19:04:51.871293Z",
     "iopub.status.busy": "2026-07-28T19:04:51.871085Z",
     "iopub.status.idle": "2026-07-28T19:04:51.882045Z",
     "shell.execute_reply": "2026-07-28T19:04:51.877033Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.2249111925408938, p=0.3031864410631269, 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": "2026-07-28T19:04:51.885276Z",
     "iopub.status.busy": "2026-07-28T19:04:51.885087Z",
     "iopub.status.idle": "2026-07-28T19:04:51.920489Z",
     "shell.execute_reply": "2026-07-28T19:04:51.919741Z"
    }
   },
   "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": "2026-07-28T19:04:51.926288Z",
     "iopub.status.busy": "2026-07-28T19:04:51.926074Z",
     "iopub.status.idle": "2026-07-28T19:04:51.963376Z",
     "shell.execute_reply": "2026-07-28T19:04:51.962748Z"
    }
   },
   "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:                Tue, 28 Jul 2026   Prob (F-statistic):           4.98e-10\n",
      "Time:                        19:04:51   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": "2026-07-28T19:04:51.966668Z",
     "iopub.status.busy": "2026-07-28T19:04:51.966466Z",
     "iopub.status.idle": "2026-07-28T19:04:51.977674Z",
     "shell.execute_reply": "2026-07-28T19:04:51.976569Z"
    }
   },
   "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": "2026-07-28T19:04:51.985280Z",
     "iopub.status.busy": "2026-07-28T19:04:51.985038Z",
     "iopub.status.idle": "2026-07-28T19:04:51.994981Z",
     "shell.execute_reply": "2026-07-28T19:04:51.989586Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "56240.86912116517\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": "2026-07-28T19:04:51.997079Z",
     "iopub.status.busy": "2026-07-28T19:04:51.996896Z",
     "iopub.status.idle": "2026-07-28T19:04:52.015083Z",
     "shell.execute_reply": "2026-07-28T19:04:52.014364Z"
    }
   },
   "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": "2026-07-28T19:04:52.017319Z",
     "iopub.status.busy": "2026-07-28T19:04:52.017130Z",
     "iopub.status.idle": "2026-07-28T19:04:52.026652Z",
     "shell.execute_reply": "2026-07-28T19:04:52.025499Z"
    }
   },
   "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": "2026-07-28T19:04:52.033295Z",
     "iopub.status.busy": "2026-07-28T19:04:52.033074Z",
     "iopub.status.idle": "2026-07-28T19:04:52.040739Z",
     "shell.execute_reply": "2026-07-28T19:04:52.037872Z"
    }
   },
   "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": "2026-07-28T19:04:52.042442Z",
     "iopub.status.busy": "2026-07-28T19:04:52.042261Z",
     "iopub.status.idle": "2026-07-28T19:04:52.072395Z",
     "shell.execute_reply": "2026-07-28T19:04:52.071921Z"
    }
   },
   "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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