{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ordinary Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-27T07:05:56.891909Z",
     "iopub.status.busy": "2026-08-27T07:05:56.891709Z",
     "iopub.status.idle": "2026-08-27T07:05:57.478729Z",
     "shell.execute_reply": "2026-08-27T07:05:57.477874Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-27T07:05:57.481435Z",
     "iopub.status.busy": "2026-08-27T07:05:57.480550Z",
     "iopub.status.idle": "2026-08-27T07:05:59.824580Z",
     "shell.execute_reply": "2026-08-27T07:05:59.823285Z"
    }
   },
   "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": "2026-08-27T07:05:59.826744Z",
     "iopub.status.busy": "2026-08-27T07:05:59.826415Z",
     "iopub.status.idle": "2026-08-27T07:05:59.836359Z",
     "shell.execute_reply": "2026-08-27T07:05:59.835918Z"
    }
   },
   "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": "2026-08-27T07:05:59.840846Z",
     "iopub.status.busy": "2026-08-27T07:05:59.840653Z",
     "iopub.status.idle": "2026-08-27T07:05:59.843974Z",
     "shell.execute_reply": "2026-08-27T07:05:59.843025Z"
    }
   },
   "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": "2026-08-27T07:05:59.848595Z",
     "iopub.status.busy": "2026-08-27T07:05:59.848403Z",
     "iopub.status.idle": "2026-08-27T07:05:59.869631Z",
     "shell.execute_reply": "2026-08-27T07:05:59.869162Z"
    }
   },
   "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:                Thu, 27 Aug 2026   Prob (F-statistic):          2.83e-239\n",
      "Time:                        07:05:59   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": "2026-08-27T07:05:59.874739Z",
     "iopub.status.busy": "2026-08-27T07:05:59.874544Z",
     "iopub.status.idle": "2026-08-27T07:05:59.881322Z",
     "shell.execute_reply": "2026-08-27T07:05:59.880903Z"
    }
   },
   "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": "2026-08-27T07:05:59.885984Z",
     "iopub.status.busy": "2026-08-27T07:05:59.885798Z",
     "iopub.status.idle": "2026-08-27T07:05:59.892859Z",
     "shell.execute_reply": "2026-08-27T07:05:59.891896Z"
    }
   },
   "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": "2026-08-27T07:05:59.894594Z",
     "iopub.status.busy": "2026-08-27T07:05:59.894415Z",
     "iopub.status.idle": "2026-08-27T07:05:59.916378Z",
     "shell.execute_reply": "2026-08-27T07:05:59.915954Z"
    }
   },
   "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:                Thu, 27 Aug 2026   Prob (F-statistic):           6.30e-27\n",
      "Time:                        07:05:59   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": "2026-08-27T07:05:59.919090Z",
     "iopub.status.busy": "2026-08-27T07:05:59.918386Z",
     "iopub.status.idle": "2026-08-27T07:05:59.926840Z",
     "shell.execute_reply": "2026-08-27T07:05:59.925885Z"
    }
   },
   "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": "2026-08-27T07:05:59.928559Z",
     "iopub.status.busy": "2026-08-27T07:05:59.928378Z",
     "iopub.status.idle": "2026-08-27T07:06:00.349325Z",
     "shell.execute_reply": "2026-08-27T07:06:00.348161Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f92324b8c20>"
      ]
     },
     "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": "2026-08-27T07:06:00.353177Z",
     "iopub.status.busy": "2026-08-27T07:06:00.352422Z",
     "iopub.status.idle": "2026-08-27T07:06:00.364082Z",
     "shell.execute_reply": "2026-08-27T07:06:00.363656Z"
    }
   },
   "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": "2026-08-27T07:06:00.369287Z",
     "iopub.status.busy": "2026-08-27T07:06:00.366503Z",
     "iopub.status.idle": "2026-08-27T07:06:00.377548Z",
     "shell.execute_reply": "2026-08-27T07:06:00.376997Z"
    }
   },
   "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": "2026-08-27T07:06:00.379785Z",
     "iopub.status.busy": "2026-08-27T07:06:00.379586Z",
     "iopub.status.idle": "2026-08-27T07:06:00.401630Z",
     "shell.execute_reply": "2026-08-27T07:06:00.401161Z"
    }
   },
   "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:                Thu, 27 Aug 2026   Prob (F-statistic):           5.69e-38\n",
      "Time:                        07:06:00   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": "2026-08-27T07:06:00.406626Z",
     "iopub.status.busy": "2026-08-27T07:06:00.406421Z",
     "iopub.status.idle": "2026-08-27T07:06:00.767612Z",
     "shell.execute_reply": "2026-08-27T07:06:00.766869Z"
    }
   },
   "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": "2026-08-27T07:06:00.774561Z",
     "iopub.status.busy": "2026-08-27T07:06:00.774221Z",
     "iopub.status.idle": "2026-08-27T07:06:00.785409Z",
     "shell.execute_reply": "2026-08-27T07:06:00.782900Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 0 0]\n",
      " [0 0 1 0]]\n",
      "<F test: F=145.49268198027963, p=1.2834419617282974e-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": "2026-08-27T07:06:00.787608Z",
     "iopub.status.busy": "2026-08-27T07:06:00.787425Z",
     "iopub.status.idle": "2026-08-27T07:06:00.797581Z",
     "shell.execute_reply": "2026-08-27T07:06:00.797161Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=145.49268198027949, p=1.2834419617283214e-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": "2026-08-27T07:06:00.800781Z",
     "iopub.status.busy": "2026-08-27T07:06:00.800598Z",
     "iopub.status.idle": "2026-08-27T07:06:00.804378Z",
     "shell.execute_reply": "2026-08-27T07:06:00.803933Z"
    }
   },
   "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": "2026-08-27T07:06:00.813858Z",
     "iopub.status.busy": "2026-08-27T07:06:00.813668Z",
     "iopub.status.idle": "2026-08-27T07:06:00.820790Z",
     "shell.execute_reply": "2026-08-27T07:06:00.819817Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.224911192540883, p=0.30318644106313, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "print(res3.f_test(R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-27T07:06:00.822568Z",
     "iopub.status.busy": "2026-08-27T07:06:00.822388Z",
     "iopub.status.idle": "2026-08-27T07:06:00.832893Z",
     "shell.execute_reply": "2026-08-27T07:06:00.831912Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.2249111925408838, p=0.30318644106312975, 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": "2026-08-27T07:06:00.836557Z",
     "iopub.status.busy": "2026-08-27T07:06:00.836371Z",
     "iopub.status.idle": "2026-08-27T07:06:00.855356Z",
     "shell.execute_reply": "2026-08-27T07:06:00.854909Z"
    }
   },
   "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": "2026-08-27T07:06:00.858153Z",
     "iopub.status.busy": "2026-08-27T07:06:00.857435Z",
     "iopub.status.idle": "2026-08-27T07:06:00.881795Z",
     "shell.execute_reply": "2026-08-27T07:06:00.881254Z"
    }
   },
   "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:                Thu, 27 Aug 2026   Prob (F-statistic):           4.98e-10\n",
      "Time:                        07:06:00   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": "2026-08-27T07:06:00.884019Z",
     "iopub.status.busy": "2026-08-27T07:06:00.883730Z",
     "iopub.status.idle": "2026-08-27T07:06:00.892414Z",
     "shell.execute_reply": "2026-08-27T07:06:00.891394Z"
    }
   },
   "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": "2026-08-27T07:06:00.894742Z",
     "iopub.status.busy": "2026-08-27T07:06:00.894569Z",
     "iopub.status.idle": "2026-08-27T07:06:00.901422Z",
     "shell.execute_reply": "2026-08-27T07:06:00.900967Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "56240.87037739987\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": "2026-08-27T07:06:00.904185Z",
     "iopub.status.busy": "2026-08-27T07:06:00.903435Z",
     "iopub.status.idle": "2026-08-27T07:06:00.914412Z",
     "shell.execute_reply": "2026-08-27T07:06:00.913583Z"
    }
   },
   "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": "2026-08-27T07:06:00.923221Z",
     "iopub.status.busy": "2026-08-27T07:06:00.922496Z",
     "iopub.status.idle": "2026-08-27T07:06:00.929902Z",
     "shell.execute_reply": "2026-08-27T07:06:00.928899Z"
    }
   },
   "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": "2026-08-27T07:06:00.932171Z",
     "iopub.status.busy": "2026-08-27T07:06:00.931444Z",
     "iopub.status.idle": "2026-08-27T07:06:00.942264Z",
     "shell.execute_reply": "2026-08-27T07:06:00.939170Z"
    }
   },
   "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": "2026-08-27T07:06:00.944545Z",
     "iopub.status.busy": "2026-08-27T07:06:00.944358Z",
     "iopub.status.idle": "2026-08-27T07:06:00.974538Z",
     "shell.execute_reply": "2026-08-27T07:06:00.971393Z"
    }
   },
   "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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