{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction (out of sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-30T06:42:31.832581Z",
     "iopub.status.busy": "2026-07-30T06:42:31.832310Z",
     "iopub.status.idle": "2026-07-30T06:42:32.511369Z",
     "shell.execute_reply": "2026-07-30T06:42:32.509839Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-30T06:42:32.513764Z",
     "iopub.status.busy": "2026-07-30T06:42:32.513410Z",
     "iopub.status.idle": "2026-07-30T06:42:34.513914Z",
     "shell.execute_reply": "2026-07-30T06:42:34.512966Z"
    }
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\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": "2026-07-30T06:42:34.518461Z",
     "iopub.status.busy": "2026-07-30T06:42:34.517232Z",
     "iopub.status.idle": "2026-07-30T06:42:34.525950Z",
     "shell.execute_reply": "2026-07-30T06:42:34.524084Z"
    }
   },
   "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": "2026-07-30T06:42:34.529787Z",
     "iopub.status.busy": "2026-07-30T06:42:34.528619Z",
     "iopub.status.idle": "2026-07-30T06:42:34.550007Z",
     "shell.execute_reply": "2026-07-30T06:42:34.548196Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.981\n",
      "Model:                            OLS   Adj. R-squared:                  0.980\n",
      "Method:                 Least Squares   F-statistic:                     789.4\n",
      "Date:                Thu, 30 Jul 2026   Prob (F-statistic):           1.50e-39\n",
      "Time:                        06:42:34   Log-Likelihood:                -2.5586\n",
      "No. Observations:                  50   AIC:                             13.12\n",
      "Df Residuals:                      46   BIC:                             20.77\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          4.9861      0.090     55.095      0.000       4.804       5.168\n",
      "x1             0.4970      0.014     35.610      0.000       0.469       0.525\n",
      "x2             0.4856      0.055      8.851      0.000       0.375       0.596\n",
      "x3            -0.0200      0.001    -16.322      0.000      -0.022      -0.018\n",
      "==============================================================================\n",
      "Omnibus:                        0.352   Durbin-Watson:                   2.042\n",
      "Prob(Omnibus):                  0.839   Jarque-Bera (JB):                0.361\n",
      "Skew:                          -0.184   Prob(JB):                        0.835\n",
      "Kurtosis:                       2.805   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": "2026-07-30T06:42:34.552899Z",
     "iopub.status.busy": "2026-07-30T06:42:34.552616Z",
     "iopub.status.idle": "2026-07-30T06:42:34.560634Z",
     "shell.execute_reply": "2026-07-30T06:42:34.559082Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.48605912  4.95999909  5.39560386  5.76640624  6.05549094  6.25827363\n",
      "  6.38325421  6.45062024  6.48893022  6.5304215   6.60571376  6.73877829\n",
      "  6.9429996   7.21897634  7.55442296  7.92618823  8.30405885  8.65572346\n",
      "  8.95208131  9.17202339  9.3059006   9.3571091   9.34153229  9.28493121\n",
      "  9.21871212  9.17476649  9.18023134  9.25303074  9.39893086  9.61059266\n",
      "  9.86877769 10.14550884 10.40866697 10.62726797 10.77655335 10.84205799\n",
      " 10.82198675 10.72750936 10.58092532 10.41200009 10.25307476 10.13375248\n",
      " 10.07603476 10.09070666 10.17556485 10.31577963 10.48633136 10.65612116\n",
      " 10.79308034 10.86943923]\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": "2026-07-30T06:42:34.563176Z",
     "iopub.status.busy": "2026-07-30T06:42:34.562893Z",
     "iopub.status.idle": "2026-07-30T06:42:34.572218Z",
     "shell.execute_reply": "2026-07-30T06:42:34.570626Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.85365462 10.70934319 10.45555009 10.13567675  9.80685472  9.52595791\n",
      "  9.33567781  9.25407117  9.27013906  9.34651979]\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": "2026-07-30T06:42:34.575263Z",
     "iopub.status.busy": "2026-07-30T06:42:34.574997Z",
     "iopub.status.idle": "2026-07-30T06:42:34.860758Z",
     "shell.execute_reply": "2026-07-30T06:42:34.858928Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f28e966aba0>"
      ]
     },
     "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": "2026-07-30T06:42:34.863402Z",
     "iopub.status.busy": "2026-07-30T06:42:34.863126Z",
     "iopub.status.idle": "2026-07-30T06:42:34.875339Z",
     "shell.execute_reply": "2026-07-30T06:42:34.874021Z"
    }
   },
   "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": "2026-07-30T06:42:34.878253Z",
     "iopub.status.busy": "2026-07-30T06:42:34.877973Z",
     "iopub.status.idle": "2026-07-30T06:42:34.890851Z",
     "shell.execute_reply": "2026-07-30T06:42:34.888010Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept           4.986115\n",
       "x1                  0.497023\n",
       "np.sin(x1)          0.485644\n",
       "I((x1 - 5) ** 2)   -0.020002\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": "2026-07-30T06:42:34.893878Z",
     "iopub.status.busy": "2026-07-30T06:42:34.893600Z",
     "iopub.status.idle": "2026-07-30T06:42:34.905466Z",
     "shell.execute_reply": "2026-07-30T06:42:34.903871Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    10.853655\n",
       "1    10.709343\n",
       "2    10.455550\n",
       "3    10.135677\n",
       "4     9.806855\n",
       "5     9.525958\n",
       "6     9.335678\n",
       "7     9.254071\n",
       "8     9.270139\n",
       "9     9.346520\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.predict(exog=dict(x1=x1n))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.14.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}