{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction (out of sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:39.503194Z",
     "iopub.status.busy": "2024-04-19T16:35:39.502975Z",
     "iopub.status.idle": "2024-04-19T16:35:40.666825Z",
     "shell.execute_reply": "2024-04-19T16:35:40.666147Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:40.671470Z",
     "iopub.status.busy": "2024-04-19T16:35:40.670345Z",
     "iopub.status.idle": "2024-04-19T16:35:43.006959Z",
     "shell.execute_reply": "2024-04-19T16:35:43.006174Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import statsmodels.api as sm\n",
    "\n",
    "plt.rc(\"figure\", figsize=(16, 8))\n",
    "plt.rc(\"font\", size=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Artificial data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:43.011515Z",
     "iopub.status.busy": "2024-04-19T16:35:43.010147Z",
     "iopub.status.idle": "2024-04-19T16:35:43.016862Z",
     "shell.execute_reply": "2024-04-19T16:35:43.016235Z"
    }
   },
   "outputs": [],
   "source": [
    "nsample = 50\n",
    "sig = 0.25\n",
    "x1 = np.linspace(0, 20, nsample)\n",
    "X = np.column_stack((x1, np.sin(x1), (x1 - 5) ** 2))\n",
    "X = sm.add_constant(X)\n",
    "beta = [5.0, 0.5, 0.5, -0.02]\n",
    "y_true = np.dot(X, beta)\n",
    "y = y_true + sig * np.random.normal(size=nsample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:43.021314Z",
     "iopub.status.busy": "2024-04-19T16:35:43.020168Z",
     "iopub.status.idle": "2024-04-19T16:35:43.067968Z",
     "shell.execute_reply": "2024-04-19T16:35:43.067140Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.984\n",
      "Model:                            OLS   Adj. R-squared:                  0.983\n",
      "Method:                 Least Squares   F-statistic:                     962.3\n",
      "Date:                Fri, 19 Apr 2024   Prob (F-statistic):           1.71e-41\n",
      "Time:                        16:35:43   Log-Likelihood:                 1.7606\n",
      "No. Observations:                  50   AIC:                             4.479\n",
      "Df Residuals:                      46   BIC:                             12.13\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          4.9988      0.083     60.220      0.000       4.832       5.166\n",
      "x1             0.5072      0.013     39.617      0.000       0.481       0.533\n",
      "x2             0.5077      0.050     10.088      0.000       0.406       0.609\n",
      "x3            -0.0207      0.001    -18.437      0.000      -0.023      -0.018\n",
      "==============================================================================\n",
      "Omnibus:                        1.782   Durbin-Watson:                   1.918\n",
      "Prob(Omnibus):                  0.410   Jarque-Bera (JB):                1.190\n",
      "Skew:                           0.017   Prob(JB):                        0.551\n",
      "Kurtosis:                       2.245   Cond. No.                         221.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "olsmod = sm.OLS(y, X)\n",
    "olsres = olsmod.fit()\n",
    "print(olsres.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## In-sample prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:43.073768Z",
     "iopub.status.busy": "2024-04-19T16:35:43.072117Z",
     "iopub.status.idle": "2024-04-19T16:35:43.084808Z",
     "shell.execute_reply": "2024-04-19T16:35:43.084233Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.48072132  4.97038253  5.42003057  5.80199702  6.09859888  6.30504376\n",
      "  6.43021733  6.49522338  6.52991656  6.56799731  6.64147501  6.77540891\n",
      "  6.98379097  7.26724702  7.61293392  7.99664971  8.38680984  8.74963648\n",
      "  9.05470813  9.27995772  9.41529825  9.46427999  9.44350722  9.37991018\n",
      "  9.30632049  9.25607706  9.25754854  9.32947246  9.47787672  9.6950892\n",
      "  9.96099828 10.2463571  10.51758879 10.74230298 10.89461751 10.95941077\n",
      " 10.93480614 10.83248029 10.67574478 10.49571602 10.32620291 10.19815215\n",
      " 10.1345638  10.14671241 10.23229466 10.37580777 10.55109659 10.7256508\n",
      " 10.86594626 10.94295293]\n"
     ]
    }
   ],
   "source": [
    "ypred = olsres.predict(X)\n",
    "print(ypred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a new sample of explanatory variables Xnew, predict and plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:43.094404Z",
     "iopub.status.busy": "2024-04-19T16:35:43.088455Z",
     "iopub.status.idle": "2024-04-19T16:35:43.103735Z",
     "shell.execute_reply": "2024-04-19T16:35:43.103093Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.92308446 10.76894881 10.50045546 10.16297567  9.81623394  9.51968542\n",
      "  9.31795918  9.22993149  9.24410422  9.32142002]\n"
     ]
    }
   ],
   "source": [
    "x1n = np.linspace(20.5, 25, 10)\n",
    "Xnew = np.column_stack((x1n, np.sin(x1n), (x1n - 5) ** 2))\n",
    "Xnew = sm.add_constant(Xnew)\n",
    "ynewpred = olsres.predict(Xnew)  # predict out of sample\n",
    "print(ynewpred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:43.114415Z",
     "iopub.status.busy": "2024-04-19T16:35:43.107578Z",
     "iopub.status.idle": "2024-04-19T16:35:43.956450Z",
     "shell.execute_reply": "2024-04-19T16:35:43.955744Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe398203940>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x1, y, \"o\", label=\"Data\")\n",
    "ax.plot(x1, y_true, \"b-\", label=\"True\")\n",
    "ax.plot(np.hstack((x1, x1n)), np.hstack((ypred, ynewpred)), \"r\", label=\"OLS prediction\")\n",
    "ax.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predicting with Formulas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using formulas can make both estimation and prediction a lot easier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:43.966764Z",
     "iopub.status.busy": "2024-04-19T16:35:43.961104Z",
     "iopub.status.idle": "2024-04-19T16:35:43.986809Z",
     "shell.execute_reply": "2024-04-19T16:35:43.986084Z"
    }
   },
   "outputs": [],
   "source": [
    "from statsmodels.formula.api import ols\n",
    "\n",
    "data = {\"x1\": x1, \"y\": y}\n",
    "\n",
    "res = ols(\"y ~ x1 + np.sin(x1) + I((x1-5)**2)\", data=data).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the `I` to indicate use of the Identity transform. Ie., we do not want any expansion magic from using `**2`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:43.996378Z",
     "iopub.status.busy": "2024-04-19T16:35:43.994654Z",
     "iopub.status.idle": "2024-04-19T16:35:44.014237Z",
     "shell.execute_reply": "2024-04-19T16:35:44.013575Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept           4.998829\n",
       "x1                  0.507180\n",
       "np.sin(x1)          0.507685\n",
       "I((x1 - 5) ** 2)   -0.020724\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we only have to pass the single variable and we get the transformed right-hand side variables automatically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-04-19T16:35:44.019541Z",
     "iopub.status.busy": "2024-04-19T16:35:44.017944Z",
     "iopub.status.idle": "2024-04-19T16:35:44.031255Z",
     "shell.execute_reply": "2024-04-19T16:35:44.030632Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    10.923084\n",
       "1    10.768949\n",
       "2    10.500455\n",
       "3    10.162976\n",
       "4     9.816234\n",
       "5     9.519685\n",
       "6     9.317959\n",
       "7     9.229931\n",
       "8     9.244104\n",
       "9     9.321420\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.predict(exog=dict(x1=x1n))"
   ]
  }
 ],
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