{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction (out of sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "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)\n",
    "np.random.seed(1234) # for reproducibility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Artificial data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
 
 
 
 
    }
   },
   "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": {
 
 
 
 
    }
   },
   "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:                     956.6\n",
      "Date:                Fri, 20 Mar 2026   Prob (F-statistic):           1.96e-41\n",
      "Time:                        11:18:46   Log-Likelihood:                 1.2217\n",
      "No. Observations:                  50   AIC:                             5.557\n",
      "Df Residuals:                      46   BIC:                             13.20\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          4.9654      0.084     59.175      0.000       4.796       5.134\n",
      "x1             0.5088      0.013     39.314      0.000       0.483       0.535\n",
      "x2             0.5651      0.051     11.109      0.000       0.463       0.668\n",
      "x3            -0.0206      0.001    -18.144      0.000      -0.023      -0.018\n",
      "==============================================================================\n",
      "Omnibus:                        0.840   Durbin-Watson:                   2.269\n",
      "Prob(Omnibus):                  0.657   Jarque-Bera (JB):                0.577\n",
      "Skew:                          -0.263   Prob(JB):                        0.749\n",
      "Kurtosis:                       2.972   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": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.44997408  4.96265684  5.43161584  5.82605136  6.12627912  6.32696437\n",
      "  6.4379984   6.4828734   6.49482276  6.51136093  6.56811991  6.69299498\n",
      "  6.90156162  7.1945165   7.55756297  7.96376004  8.37794864  8.76252818\n",
      "  9.08363424  9.31670235  9.45050393  9.48899104  9.45064714  9.36545023\n",
      "  9.26994764  9.20125134  9.19094055  9.25987342  9.41476003  9.64705998\n",
      "  9.93438555 10.24417991 10.53906618 10.78298825 10.9471348  11.01467283\n",
      " 10.98351335 10.86665452 10.69004615 10.4883262  10.29912985 10.15690615\n",
      " 10.08725815 10.10273638 10.20077685 10.36412228 10.56365745 10.76319271\n",
      " 10.92540989 11.01799353]\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": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[11.00539682 10.84456472 10.55765996 10.1951886   9.82363439  9.50918122\n",
      "  9.30150901  9.2216303   9.25674569  9.36337756]\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": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xadde5de1e8ed>"
      ]
     },
     "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": {
 
 
 
 
    }
   },
   "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": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept           4.965353\n",
       "x1                  0.508755\n",
       "np.sin(x1)          0.565142\n",
       "I((x1 - 5) ** 2)   -0.020615\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": {
 
 
 
 
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    11.005397\n",
       "1    10.844565\n",
       "2    10.557660\n",
       "3    10.195189\n",
       "4     9.823634\n",
       "5     9.509181\n",
       "6     9.301509\n",
       "7     9.221630\n",
       "8     9.256746\n",
       "9     9.363378\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": "3.14.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
