{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ordinary Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:45:07.587686Z",
     "iopub.status.busy": "2023-12-14T14:45:07.587449Z",
     "iopub.status.idle": "2023-12-14T14:45:09.145687Z",
     "shell.execute_reply": "2023-12-14T14:45:09.144781Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:45:09.149683Z",
     "iopub.status.busy": "2023-12-14T14:45:09.149293Z",
     "iopub.status.idle": "2023-12-14T14:45:11.803328Z",
     "shell.execute_reply": "2023-12-14T14:45:11.802525Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\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": "2023-12-14T14:45:11.817838Z",
     "iopub.status.busy": "2023-12-14T14:45:11.817055Z",
     "iopub.status.idle": "2023-12-14T14:45:11.822727Z",
     "shell.execute_reply": "2023-12-14T14:45:11.821985Z"
    }
   },
   "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": "2023-12-14T14:45:11.826934Z",
     "iopub.status.busy": "2023-12-14T14:45:11.826428Z",
     "iopub.status.idle": "2023-12-14T14:45:11.835335Z",
     "shell.execute_reply": "2023-12-14T14:45:11.834004Z"
    }
   },
   "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": "2023-12-14T14:45:11.841546Z",
     "iopub.status.busy": "2023-12-14T14:45:11.840481Z",
     "iopub.status.idle": "2023-12-14T14:45:11.882778Z",
     "shell.execute_reply": "2023-12-14T14:45:11.882031Z"
    }
   },
   "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, 14 Dec 2023   Prob (F-statistic):          2.83e-239\n",
      "Time:                        14:45:11   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": "2023-12-14T14:45:11.887305Z",
     "iopub.status.busy": "2023-12-14T14:45:11.886596Z",
     "iopub.status.idle": "2023-12-14T14:45:11.896385Z",
     "shell.execute_reply": "2023-12-14T14:45:11.895094Z"
    }
   },
   "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": "2023-12-14T14:45:11.901744Z",
     "iopub.status.busy": "2023-12-14T14:45:11.901424Z",
     "iopub.status.idle": "2023-12-14T14:45:11.914400Z",
     "shell.execute_reply": "2023-12-14T14:45:11.907770Z"
    }
   },
   "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": "2023-12-14T14:45:11.917801Z",
     "iopub.status.busy": "2023-12-14T14:45:11.917110Z",
     "iopub.status.idle": "2023-12-14T14:45:11.937792Z",
     "shell.execute_reply": "2023-12-14T14:45:11.937068Z"
    }
   },
   "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, 14 Dec 2023   Prob (F-statistic):           6.30e-27\n",
      "Time:                        14:45:11   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": "2023-12-14T14:45:11.941299Z",
     "iopub.status.busy": "2023-12-14T14:45:11.940887Z",
     "iopub.status.idle": "2023-12-14T14:45:11.949168Z",
     "shell.execute_reply": "2023-12-14T14:45:11.948440Z"
    }
   },
   "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": "2023-12-14T14:45:11.952726Z",
     "iopub.status.busy": "2023-12-14T14:45:11.952228Z",
     "iopub.status.idle": "2023-12-14T14:45:12.735918Z",
     "shell.execute_reply": "2023-12-14T14:45:12.735116Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7efe73522110>"
      ]
     },
     "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": "2023-12-14T14:45:12.739980Z",
     "iopub.status.busy": "2023-12-14T14:45:12.739057Z",
     "iopub.status.idle": "2023-12-14T14:45:12.763965Z",
     "shell.execute_reply": "2023-12-14T14:45:12.762979Z"
    }
   },
   "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": "2023-12-14T14:45:12.768723Z",
     "iopub.status.busy": "2023-12-14T14:45:12.768222Z",
     "iopub.status.idle": "2023-12-14T14:45:12.777459Z",
     "shell.execute_reply": "2023-12-14T14:45:12.776295Z"
    }
   },
   "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": "2023-12-14T14:45:12.781122Z",
     "iopub.status.busy": "2023-12-14T14:45:12.780744Z",
     "iopub.status.idle": "2023-12-14T14:45:12.823933Z",
     "shell.execute_reply": "2023-12-14T14:45:12.822351Z"
    }
   },
   "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, 14 Dec 2023   Prob (F-statistic):           5.69e-38\n",
      "Time:                        14:45:12   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": "2023-12-14T14:45:12.827991Z",
     "iopub.status.busy": "2023-12-14T14:45:12.827407Z",
     "iopub.status.idle": "2023-12-14T14:45:13.563634Z",
     "shell.execute_reply": "2023-12-14T14:45:13.562875Z"
    }
   },
   "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": "2023-12-14T14:45:13.570539Z",
     "iopub.status.busy": "2023-12-14T14:45:13.568552Z",
     "iopub.status.idle": "2023-12-14T14:45:13.582155Z",
     "shell.execute_reply": "2023-12-14T14:45:13.581285Z"
    }
   },
   "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": "2023-12-14T14:45:13.589280Z",
     "iopub.status.busy": "2023-12-14T14:45:13.587289Z",
     "iopub.status.idle": "2023-12-14T14:45:13.601098Z",
     "shell.execute_reply": "2023-12-14T14:45:13.600295Z"
    }
   },
   "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": "2023-12-14T14:45:13.607674Z",
     "iopub.status.busy": "2023-12-14T14:45:13.605776Z",
     "iopub.status.idle": "2023-12-14T14:45:13.616340Z",
     "shell.execute_reply": "2023-12-14T14:45:13.615535Z"
    }
   },
   "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": "2023-12-14T14:45:13.623762Z",
     "iopub.status.busy": "2023-12-14T14:45:13.621539Z",
     "iopub.status.idle": "2023-12-14T14:45:13.633469Z",
     "shell.execute_reply": "2023-12-14T14:45:13.632740Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.224911192540883, p=0.30318644106312964, df_denom=46, df_num=2>\n"
     ]
    }
   ],
   "source": [
    "print(res3.f_test(R))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-14T14:45:13.640248Z",
     "iopub.status.busy": "2023-12-14T14:45:13.638180Z",
     "iopub.status.idle": "2023-12-14T14:45:13.651539Z",
     "shell.execute_reply": "2023-12-14T14:45:13.650823Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<F test: F=1.2249111925408838, p=0.30318644106312964, 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": "2023-12-14T14:45:13.658079Z",
     "iopub.status.busy": "2023-12-14T14:45:13.656008Z",
     "iopub.status.idle": "2023-12-14T14:45:13.698812Z",
     "shell.execute_reply": "2023-12-14T14:45:13.696948Z"
    }
   },
   "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": "2023-12-14T14:45:13.703345Z",
     "iopub.status.busy": "2023-12-14T14:45:13.702985Z",
     "iopub.status.idle": "2023-12-14T14:45:13.753182Z",
     "shell.execute_reply": "2023-12-14T14:45:13.751312Z"
    }
   },
   "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, 14 Dec 2023   Prob (F-statistic):           4.98e-10\n",
      "Time:                        14:45:13   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"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/scipy/stats/_stats_py.py:1806: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=16\n",
      "  warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\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": "2023-12-14T14:45:13.757765Z",
     "iopub.status.busy": "2023-12-14T14:45:13.757095Z",
     "iopub.status.idle": "2023-12-14T14:45:13.773832Z",
     "shell.execute_reply": "2023-12-14T14:45:13.772698Z"
    }
   },
   "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": "2023-12-14T14:45:13.778507Z",
     "iopub.status.busy": "2023-12-14T14:45:13.777765Z",
     "iopub.status.idle": "2023-12-14T14:45:13.787824Z",
     "shell.execute_reply": "2023-12-14T14:45:13.786507Z"
    }
   },
   "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": "2023-12-14T14:45:13.792550Z",
     "iopub.status.busy": "2023-12-14T14:45:13.791380Z",
     "iopub.status.idle": "2023-12-14T14:45:13.810615Z",
     "shell.execute_reply": "2023-12-14T14:45:13.809290Z"
    }
   },
   "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(\n",
    "        [\n",
    "            i\n",
    "            for i in (ols_results2.params - ols_results.params)\n",
    "            / ols_results.params\n",
    "            * 100\n",
    "        ]\n",
    "    )\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": "2023-12-14T14:45:13.815622Z",
     "iopub.status.busy": "2023-12-14T14:45:13.815211Z",
     "iopub.status.idle": "2023-12-14T14:45:13.824302Z",
     "shell.execute_reply": "2023-12-14T14:45:13.823460Z"
    }
   },
   "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": "2023-12-14T14:45:13.828510Z",
     "iopub.status.busy": "2023-12-14T14:45:13.827476Z",
     "iopub.status.idle": "2023-12-14T14:45:13.837616Z",
     "shell.execute_reply": "2023-12-14T14:45:13.836694Z"
    }
   },
   "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": "2023-12-14T14:45:13.841857Z",
     "iopub.status.busy": "2023-12-14T14:45:13.840639Z",
     "iopub.status.idle": "2023-12-14T14:45:13.890243Z",
     "shell.execute_reply": "2023-12-14T14:45:13.889282Z"
    }
   },
   "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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