{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Prediction (out of sample)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2026-07-29T11:38:25.249192Z", "iopub.status.busy": "2026-07-29T11:38:25.249004Z", "iopub.status.idle": "2026-07-29T11:38:26.394954Z", "shell.execute_reply": "2026-07-29T11:38:26.393402Z" } }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2026-07-29T11:38:26.397307Z", "iopub.status.busy": "2026-07-29T11:38:26.396985Z", "iopub.status.idle": "2026-07-29T11:38:28.228183Z", "shell.execute_reply": "2026-07-29T11:38:28.226396Z" } }, "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": "2026-07-29T11:38:28.231324Z", "iopub.status.busy": "2026-07-29T11:38:28.230842Z", "iopub.status.idle": "2026-07-29T11:38:28.238414Z", "shell.execute_reply": "2026-07-29T11:38:28.236980Z" } }, "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": "2026-07-29T11:38:28.241022Z", "iopub.status.busy": "2026-07-29T11:38:28.240775Z", "iopub.status.idle": "2026-07-29T11:38:28.259719Z", "shell.execute_reply": "2026-07-29T11:38:28.258279Z" } }, "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: 953.0\n", "Date: Wed, 29 Jul 2026 Prob (F-statistic): 2.13e-41\n", "Time: 11:38:28 Log-Likelihood: 1.0576\n", "No. Observations: 50 AIC: 5.885\n", "Df Residuals: 46 BIC: 13.53\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const 4.9740 0.084 59.084 0.000 4.805 5.143\n", "x1 0.5192 0.013 39.991 0.000 0.493 0.545\n", "x2 0.4925 0.051 9.650 0.000 0.390 0.595\n", "x3 -0.0218 0.001 -19.138 0.000 -0.024 -0.020\n", "==============================================================================\n", "Omnibus: 1.389 Durbin-Watson: 2.284\n", "Prob(Omnibus): 0.499 Jarque-Bera (JB): 0.810\n", "Skew: -0.298 Prob(JB): 0.667\n", "Kurtosis: 3.182 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": "2026-07-29T11:38:28.262000Z", "iopub.status.busy": "2026-07-29T11:38:28.261752Z", "iopub.status.idle": "2026-07-29T11:38:28.269037Z", "shell.execute_reply": "2026-07-29T11:38:28.267609Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.42861647 4.92145133 5.3748977 5.76211334 6.06594325 6.28173818\n", " 6.41811844 6.49555767 6.54301904 6.59319668 6.67714416 6.81917245\n", " 7.03285571 7.31880107 7.66454891 8.04661992 8.4343727 8.79503805\n", " 9.09910284 9.32515896 9.46342059 9.51733199 9.50300165 9.44655563\n", " 9.37984522 9.33521379 9.34018289 9.41293056 9.55930469 9.77186225\n", " 10.03109216 10.30862091 10.57187421 10.7894289 10.93617569 10.99744447\n", " 10.97141467 10.86941431 10.71405884 10.53553551 10.36664369 10.237406\n", " 10.1701357 10.17577068 10.2520764 10.384013 10.54620633 10.70711684\n", " 10.83422143 10.89935693]\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": "2026-07-29T11:38:28.271251Z", "iopub.status.busy": "2026-07-29T11:38:28.271013Z", "iopub.status.idle": "2026-07-29T11:38:28.278531Z", "shell.execute_reply": "2026-07-29T11:38:28.277806Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[10.86757938 10.70468834 10.42999881 10.08752723 9.7352147 9.43074102\n", " 9.21740262 9.11351211 9.10791472 9.16271933]\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": "2026-07-29T11:38:28.283031Z", "iopub.status.busy": "2026-07-29T11:38:28.282786Z", "iopub.status.idle": "2026-07-29T11:38:28.842282Z", "shell.execute_reply": "2026-07-29T11:38:28.838687Z" } }, "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": "2026-07-29T11:38:28.846581Z", "iopub.status.busy": "2026-07-29T11:38:28.846321Z", "iopub.status.idle": "2026-07-29T11:38:28.868519Z", "shell.execute_reply": "2026-07-29T11:38:28.867744Z" } }, "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": "2026-07-29T11:38:28.874916Z", "iopub.status.busy": "2026-07-29T11:38:28.871556Z", "iopub.status.idle": "2026-07-29T11:38:28.888972Z", "shell.execute_reply": "2026-07-29T11:38:28.885521Z" } }, "outputs": [ { "data": { "text/plain": [ "Intercept 4.974031\n", "x1 0.519221\n", "np.sin(x1) 0.492526\n", "I((x1 - 5) ** 2) -0.021817\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": "2026-07-29T11:38:28.891260Z", "iopub.status.busy": "2026-07-29T11:38:28.891011Z", "iopub.status.idle": "2026-07-29T11:38:28.908216Z", "shell.execute_reply": "2026-07-29T11:38:28.906742Z" } }, "outputs": [ { "data": { "text/plain": [ "0 10.867579\n", "1 10.704688\n", "2 10.429999\n", "3 10.087527\n", "4 9.735215\n", "5 9.430741\n", "6 9.217403\n", "7 9.113512\n", "8 9.107915\n", "9 9.162719\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 }