{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ordinary Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:32:50.227125Z",
     "iopub.status.busy": "2024-04-19T16:32:50.226868Z",
     "iopub.status.idle": "2024-04-19T16:32:51.761080Z",
     "shell.execute_reply": "2024-04-19T16:32:51.760390Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:32:51.764663Z",
     "iopub.status.busy": "2024-04-19T16:32:51.764118Z",
     "iopub.status.idle": "2024-04-19T16:32:54.388112Z",
     "shell.execute_reply": "2024-04-19T16:32:54.387430Z"
    }
   },
   "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": "2024-04-19T16:32:54.391683Z",
     "iopub.status.busy": "2024-04-19T16:32:54.391108Z",
     "iopub.status.idle": "2024-04-19T16:32:54.402717Z",
     "shell.execute_reply": "2024-04-19T16:32:54.402133Z"
    }
   },
   "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": "2024-04-19T16:32:54.405679Z",
     "iopub.status.busy": "2024-04-19T16:32:54.405240Z",
     "iopub.status.idle": "2024-04-19T16:32:54.414720Z",
     "shell.execute_reply": "2024-04-19T16:32:54.414131Z"
    }
   },
   "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": "2024-04-19T16:32:54.417653Z",
     "iopub.status.busy": "2024-04-19T16:32:54.417086Z",
     "iopub.status.idle": "2024-04-19T16:32:54.448419Z",
     "shell.execute_reply": "2024-04-19T16:32:54.447820Z"
    }
   },
   "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:                Fri, 19 Apr 2024   Prob (F-statistic):          2.83e-239\n",
      "Time:                        16:32:54   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": "2024-04-19T16:32:54.452017Z",
     "iopub.status.busy": "2024-04-19T16:32:54.450960Z",
     "iopub.status.idle": "2024-04-19T16:32:54.462881Z",
     "shell.execute_reply": "2024-04-19T16:32:54.462148Z"
    }
   },
   "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": "2024-04-19T16:32:54.471303Z",
     "iopub.status.busy": "2024-04-19T16:32:54.465877Z",
     "iopub.status.idle": "2024-04-19T16:32:54.476843Z",
     "shell.execute_reply": "2024-04-19T16:32:54.476246Z"
    }
   },
   "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": "2024-04-19T16:32:54.480823Z",
     "iopub.status.busy": "2024-04-19T16:32:54.479795Z",
     "iopub.status.idle": "2024-04-19T16:32:54.517334Z",
     "shell.execute_reply": "2024-04-19T16:32:54.516738Z"
    }
   },
   "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:                Fri, 19 Apr 2024   Prob (F-statistic):           6.30e-27\n",
      "Time:                        16:32:54   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": "2024-04-19T16:32:54.521934Z",
     "iopub.status.busy": "2024-04-19T16:32:54.520283Z",
     "iopub.status.idle": "2024-04-19T16:32:54.537566Z",
     "shell.execute_reply": "2024-04-19T16:32:54.536992Z"
    }
   },
   "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": "2024-04-19T16:32:54.541881Z",
     "iopub.status.busy": "2024-04-19T16:32:54.540851Z",
     "iopub.status.idle": "2024-04-19T16:32:55.239809Z",
     "shell.execute_reply": "2024-04-19T16:32:55.238977Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f886ac24d00>"
      ]
     },
     "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": "2024-04-19T16:32:55.243389Z",
     "iopub.status.busy": "2024-04-19T16:32:55.243144Z",
     "iopub.status.idle": "2024-04-19T16:32:55.266715Z",
     "shell.execute_reply": "2024-04-19T16:32:55.266131Z"
    }
   },
   "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": "2024-04-19T16:32:55.270785Z",
     "iopub.status.busy": "2024-04-19T16:32:55.269716Z",
     "iopub.status.idle": "2024-04-19T16:32:55.276475Z",
     "shell.execute_reply": "2024-04-19T16:32:55.275900Z"
    }
   },
   "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": "2024-04-19T16:32:55.280400Z",
     "iopub.status.busy": "2024-04-19T16:32:55.279378Z",
     "iopub.status.idle": "2024-04-19T16:32:55.322742Z",
     "shell.execute_reply": "2024-04-19T16:32:55.322151Z"
    }
   },
   "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:                Fri, 19 Apr 2024   Prob (F-statistic):           5.69e-38\n",
      "Time:                        16:32:55   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": "2024-04-19T16:32:55.326725Z",
     "iopub.status.busy": "2024-04-19T16:32:55.325673Z",
     "iopub.status.idle": "2024-04-19T16:32:55.978835Z",
     "shell.execute_reply": "2024-04-19T16:32:55.978144Z"
    }
   },
   "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": "2024-04-19T16:32:55.990289Z",
     "iopub.status.busy": "2024-04-19T16:32:55.986725Z",
     "iopub.status.idle": "2024-04-19T16:32:55.999667Z",
     "shell.execute_reply": "2024-04-19T16:32:55.998978Z"
    }
   },
   "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": "2024-04-19T16:32:56.006267Z",
     "iopub.status.busy": "2024-04-19T16:32:56.002442Z",
     "iopub.status.idle": "2024-04-19T16:32:56.017458Z",
     "shell.execute_reply": "2024-04-19T16:32:56.016880Z"
    }
   },
   "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": "2024-04-19T16:32:56.021422Z",
     "iopub.status.busy": "2024-04-19T16:32:56.020383Z",
     "iopub.status.idle": "2024-04-19T16:32:56.030706Z",
     "shell.execute_reply": "2024-04-19T16:32:56.030131Z"
    }
   },
   "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": "2024-04-19T16:32:56.034628Z",
     "iopub.status.busy": "2024-04-19T16:32:56.033578Z",
     "iopub.status.idle": "2024-04-19T16:32:56.046735Z",
     "shell.execute_reply": "2024-04-19T16:32:56.046137Z"
    }
   },
   "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": "2024-04-19T16:32:56.050647Z",
     "iopub.status.busy": "2024-04-19T16:32:56.049599Z",
     "iopub.status.idle": "2024-04-19T16:32:56.062701Z",
     "shell.execute_reply": "2024-04-19T16:32:56.062131Z"
    }
   },
   "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": "2024-04-19T16:32:56.066629Z",
     "iopub.status.busy": "2024-04-19T16:32:56.065585Z",
     "iopub.status.idle": "2024-04-19T16:32:56.093213Z",
     "shell.execute_reply": "2024-04-19T16:32:56.092639Z"
    }
   },
   "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": "2024-04-19T16:32:56.097185Z",
     "iopub.status.busy": "2024-04-19T16:32:56.096150Z",
     "iopub.status.idle": "2024-04-19T16:32:56.142203Z",
     "shell.execute_reply": "2024-04-19T16:32:56.141603Z"
    }
   },
   "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:                Fri, 19 Apr 2024   Prob (F-statistic):           4.98e-10\n",
      "Time:                        16:32:56   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/3.10.14/x64/lib/python3.10/site-packages/scipy/stats/_axis_nan_policy.py:531: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=16\n",
      "  res = hypotest_fun_out(*samples, **kwds)\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": "2024-04-19T16:32:56.146144Z",
     "iopub.status.busy": "2024-04-19T16:32:56.145093Z",
     "iopub.status.idle": "2024-04-19T16:32:56.159563Z",
     "shell.execute_reply": "2024-04-19T16:32:56.158991Z"
    }
   },
   "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": "2024-04-19T16:32:56.163512Z",
     "iopub.status.busy": "2024-04-19T16:32:56.162478Z",
     "iopub.status.idle": "2024-04-19T16:32:56.174715Z",
     "shell.execute_reply": "2024-04-19T16:32:56.174130Z"
    }
   },
   "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": "2024-04-19T16:32:56.178674Z",
     "iopub.status.busy": "2024-04-19T16:32:56.177623Z",
     "iopub.status.idle": "2024-04-19T16:32:56.191650Z",
     "shell.execute_reply": "2024-04-19T16:32:56.191041Z"
    }
   },
   "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": "2024-04-19T16:32:56.195630Z",
     "iopub.status.busy": "2024-04-19T16:32:56.194606Z",
     "iopub.status.idle": "2024-04-19T16:32:56.206722Z",
     "shell.execute_reply": "2024-04-19T16:32:56.206144Z"
    }
   },
   "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": "2024-04-19T16:32:56.210645Z",
     "iopub.status.busy": "2024-04-19T16:32:56.209598Z",
     "iopub.status.idle": "2024-04-19T16:32:56.230712Z",
     "shell.execute_reply": "2024-04-19T16:32:56.230129Z"
    }
   },
   "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": "2024-04-19T16:32:56.234594Z",
     "iopub.status.busy": "2024-04-19T16:32:56.233542Z",
     "iopub.status.idle": "2024-04-19T16:32:56.282375Z",
     "shell.execute_reply": "2024-04-19T16:32:56.281749Z"
    }
   },
   "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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