{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prediction (out of sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:06:15.930159Z",
     "iopub.status.busy": "2022-11-02T17:06:15.928617Z",
     "iopub.status.idle": "2022-11-02T17:06:16.402361Z",
     "shell.execute_reply": "2022-11-02T17:06:16.401659Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-11-02T17:06:16.408334Z",
     "iopub.status.busy": "2022-11-02T17:06:16.407081Z",
     "iopub.status.idle": "2022-11-02T17:06:17.195484Z",
     "shell.execute_reply": "2022-11-02T17:06:17.194803Z"
    }
   },
   "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": "2022-11-02T17:06:17.201025Z",
     "iopub.status.busy": "2022-11-02T17:06:17.199765Z",
     "iopub.status.idle": "2022-11-02T17:06:17.205861Z",
     "shell.execute_reply": "2022-11-02T17:06:17.205334Z"
    }
   },
   "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": "2022-11-02T17:06:17.210347Z",
     "iopub.status.busy": "2022-11-02T17:06:17.209212Z",
     "iopub.status.idle": "2022-11-02T17:06:17.221881Z",
     "shell.execute_reply": "2022-11-02T17:06:17.221324Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.986\n",
      "Model:                            OLS   Adj. R-squared:                  0.985\n",
      "Method:                 Least Squares   F-statistic:                     1064.\n",
      "Date:                Wed, 02 Nov 2022   Prob (F-statistic):           1.74e-42\n",
      "Time:                        17:06:17   Log-Likelihood:                 4.4594\n",
      "No. Observations:                  50   AIC:                           -0.9188\n",
      "Df Residuals:                      46   BIC:                             6.729\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          4.9488      0.079     62.924      0.000       4.791       5.107\n",
      "x1             0.5124      0.012     42.246      0.000       0.488       0.537\n",
      "x2             0.6093      0.048     12.778      0.000       0.513       0.705\n",
      "x3            -0.0216      0.001    -20.250      0.000      -0.024      -0.019\n",
      "==============================================================================\n",
      "Omnibus:                        6.272   Durbin-Watson:                   2.752\n",
      "Prob(Omnibus):                  0.043   Jarque-Bera (JB):                5.171\n",
      "Skew:                           0.723   Prob(JB):                       0.0754\n",
      "Kurtosis:                       3.625   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": "2022-11-02T17:06:17.226300Z",
     "iopub.status.busy": "2022-11-02T17:06:17.225148Z",
     "iopub.status.idle": "2022-11-02T17:06:17.231583Z",
     "shell.execute_reply": "2022-11-02T17:06:17.231036Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.40969647  4.94512482  5.43363276  5.84201378  6.14904543  6.34897612\n",
      "  6.45247004  6.48485512  6.48196167  6.48423561  6.53009328  6.64960978\n",
      "  6.85957769  7.16074809  7.53770719  7.96140876  8.39394633  8.79478112\n",
      "  9.12740246  9.36532639  9.49644688  9.52502482  9.470988    9.36665699\n",
      "  9.25143498  9.16533394  9.14240078  9.20512354  9.36073664  9.60003232\n",
      "  9.89887343 10.22215909 10.52959169 10.78229764 10.94921423 11.01219312\n",
      " 10.96898204 10.83359489 10.63400924 10.40756972 10.19485242 10.03299831\n",
      "  9.94961111  9.95822208 10.05606687 10.22453968 10.43225015 10.64018073\n",
      " 10.80809711 10.90115863]\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": "2022-11-02T17:06:17.235956Z",
     "iopub.status.busy": "2022-11-02T17:06:17.234862Z",
     "iopub.status.idle": "2022-11-02T17:06:17.241695Z",
     "shell.execute_reply": "2022-11-02T17:06:17.241151Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10.87960032 10.69855331 10.38191219  9.98412967  9.57688468  9.23153285\n",
      "  9.00163619  8.90984922  8.94237236  9.05233055]\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": "2022-11-02T17:06:17.246072Z",
     "iopub.status.busy": "2022-11-02T17:06:17.244967Z",
     "iopub.status.idle": "2022-11-02T17:06:17.488468Z",
     "shell.execute_reply": "2022-11-02T17:06:17.487832Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc0436f7010>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "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": "2022-11-02T17:06:17.492256Z",
     "iopub.status.busy": "2022-11-02T17:06:17.492009Z",
     "iopub.status.idle": "2022-11-02T17:06:17.502892Z",
     "shell.execute_reply": "2022-11-02T17:06:17.502349Z"
    }
   },
   "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": "2022-11-02T17:06:17.508050Z",
     "iopub.status.busy": "2022-11-02T17:06:17.506951Z",
     "iopub.status.idle": "2022-11-02T17:06:17.514854Z",
     "shell.execute_reply": "2022-11-02T17:06:17.514318Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept           4.948842\n",
       "x1                  0.512418\n",
       "np.sin(x1)          0.609303\n",
       "I((x1 - 5) ** 2)   -0.021566\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": "2022-11-02T17:06:17.519922Z",
     "iopub.status.busy": "2022-11-02T17:06:17.518814Z",
     "iopub.status.idle": "2022-11-02T17:06:17.527260Z",
     "shell.execute_reply": "2022-11-02T17:06:17.526732Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    10.879600\n",
       "1    10.698553\n",
       "2    10.381912\n",
       "3     9.984130\n",
       "4     9.576885\n",
       "5     9.231533\n",
       "6     9.001636\n",
       "7     8.909849\n",
       "8     8.942372\n",
       "9     9.052331\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.predict(exog=dict(x1=x1n))"
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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