{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Prediction (out of sample)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2026-08-27T06:56:12.237885Z", "iopub.status.busy": "2026-08-27T06:56:12.237668Z", "iopub.status.idle": "2026-08-27T06:56:13.044644Z", "shell.execute_reply": "2026-08-27T06:56:13.043982Z" } }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2026-08-27T06:56:13.046746Z", "iopub.status.busy": "2026-08-27T06:56:13.046186Z", "iopub.status.idle": "2026-08-27T06:56:14.998639Z", "shell.execute_reply": "2026-08-27T06:56:14.998117Z" } }, "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": "2026-08-27T06:56:15.005750Z", "iopub.status.busy": "2026-08-27T06:56:15.003763Z", "iopub.status.idle": "2026-08-27T06:56:15.012489Z", "shell.execute_reply": "2026-08-27T06:56:15.011173Z" } }, "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": "2026-08-27T06:56:15.014641Z", "iopub.status.busy": "2026-08-27T06:56:15.014428Z", "iopub.status.idle": "2026-08-27T06:56:15.040155Z", "shell.execute_reply": "2026-08-27T06:56:15.038752Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.983\n", "Model: OLS Adj. R-squared: 0.982\n", "Method: Least Squares F-statistic: 891.5\n", "Date: Thu, 27 Aug 2026 Prob (F-statistic): 9.63e-41\n", "Time: 06:56:15 Log-Likelihood: 0.60925\n", "No. Observations: 50 AIC: 6.781\n", "Df Residuals: 46 BIC: 14.43\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const 5.0275 0.085 59.186 0.000 4.856 5.198\n", "x1 0.4763 0.013 36.356 0.000 0.450 0.503\n", "x2 0.4568 0.051 8.869 0.000 0.353 0.560\n", "x3 -0.0176 0.001 -15.319 0.000 -0.020 -0.015\n", "==============================================================================\n", "Omnibus: 0.591 Durbin-Watson: 2.149\n", "Prob(Omnibus): 0.744 Jarque-Bera (JB): 0.217\n", "Skew: 0.152 Prob(JB): 0.897\n", "Kurtosis: 3.109 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": "2026-08-27T06:56:15.042446Z", "iopub.status.busy": "2026-08-27T06:56:15.042242Z", "iopub.status.idle": "2026-08-27T06:56:15.051478Z", "shell.execute_reply": "2026-08-27T06:56:15.048126Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.58696428 5.031648 5.44067341 5.78914709 6.06115952 6.25239896\n", " 6.3708599 6.43552955 6.47326831 6.51439667 6.58771367 6.71576526\n", " 6.91114008 7.1744012 7.49399358 7.84814256 8.20843133 8.54446979\n", " 8.82888751 9.04183065 9.17422384 9.22926131 9.22188201 9.17631524\n", " 9.12209981 9.08923094 9.10323206 9.18096145 9.32784244 9.53697237\n", " 9.79025671 10.06138189 10.32013858 10.537385 10.68983479 10.76388295\n", " 10.75784108 10.68221476 10.55797752 10.41312499 10.27807523 10.18067119\n", " 10.14160614 10.17102388 10.26685208 10.41514281 10.59236412 10.76926627\n", " 10.91568741 11.00550904]\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": "2026-08-27T06:56:15.053653Z", "iopub.status.busy": "2026-08-27T06:56:15.053455Z", "iopub.status.idle": "2026-08-27T06:56:15.064764Z", "shell.execute_reply": "2026-08-27T06:56:15.063889Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[11.01325842 10.9007197 10.68580557 10.40933682 10.12504794 9.88643107\n", " 9.73363928 9.68365563 9.72613521 9.82593786]\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": "2026-08-27T06:56:15.067346Z", "iopub.status.busy": "2026-08-27T06:56:15.067092Z", "iopub.status.idle": "2026-08-27T06:56:15.495019Z", "shell.execute_reply": "2026-08-27T06:56:15.493694Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "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": "2026-08-27T06:56:15.498250Z", "iopub.status.busy": "2026-08-27T06:56:15.497353Z", "iopub.status.idle": "2026-08-27T06:56:15.510796Z", "shell.execute_reply": "2026-08-27T06:56:15.510181Z" } }, "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": "2026-08-27T06:56:15.513690Z", "iopub.status.busy": "2026-08-27T06:56:15.513457Z", "iopub.status.idle": "2026-08-27T06:56:15.526661Z", "shell.execute_reply": "2026-08-27T06:56:15.526029Z" } }, "outputs": [ { "data": { "text/plain": [ "Intercept 5.027464\n", "x1 0.476277\n", "np.sin(x1) 0.456768\n", "I((x1 - 5) ** 2) -0.017620\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": "2026-08-27T06:56:15.533211Z", "iopub.status.busy": "2026-08-27T06:56:15.532265Z", "iopub.status.idle": "2026-08-27T06:56:15.549147Z", "shell.execute_reply": "2026-08-27T06:56:15.548671Z" } }, "outputs": [ { "data": { "text/plain": [ "0 11.013258\n", "1 10.900720\n", "2 10.685806\n", "3 10.409337\n", "4 10.125048\n", "5 9.886431\n", "6 9.733639\n", "7 9.683656\n", "8 9.726135\n", "9 9.825938\n", "dtype: float64" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.predict(exog=dict(x1=x1n))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.14.7" } }, "nbformat": 4, "nbformat_minor": 4 }