10-1_statsmodels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lecture 10-1\n",
    "\n",
    "# statsmodels\n",
    "\n",
    "## Week 10 Monday\n",
    "\n",
    "## Miles Chen, PhD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# modeling data in python:\n",
    "\n",
    "Most popular package is scikit learn. Scikit-learn is not the best for a 'traditional' stats approach.\n",
    "\n",
    "the statsmodels library is better suited for traditional stats\n",
    "\n",
    "Be sure to visit and read the documentation on the StatsModels website: https://www.statsmodels.org/stable/index.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the statsmodels.api uses numpy array notation\n",
    "# statsmodels.formula.api use formula notation (similar to R's formula notation)\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A minimal OLS example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Four pairs of points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([1,2,3,4])\n",
    "y = np.array([2,6,4,8])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGiCAYAAAA1LsZRAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAX00lEQVR4nO3da4yU9dn48WtYw7JQdlpATmFXtq3Ww4JWIBQ8VKqSUEOkJq211qDti5rigZKmivagFlm1jbUJkRZfKMYqvKigL6qV1Aga9F+gUqlpPVTsbptFXKuznDrGZf4vfNjn2UIryKzXwn4+ySTOb++Z+zKjmW/u+56ZQqVSqQQAQJIB2QMAAP2bGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUh1yjKxbty5mz54dY8eOjUKhEKtXr+7x90qlEjfddFOMHTs26urq4pxzzokXX3yxWvMCAEeZQ46RXbt2xamnnhpLliw54N/vuOOOuPPOO2PJkiWxYcOGGD16dJx//vmxY8eOwx4WADj6FA7nh/IKhUKsWrUq5syZExHvHxUZO3ZszJ8/P6677rqIiCiXyzFq1Ki4/fbb41vf+lZVhgYAjh7HVPPJtm7dGtu2bYuZM2d2r9XW1sbnP//5WL9+/QFjpFwuR7lc7r6/d+/e+Oc//xnDhw+PQqFQzfEAgF5SqVRix44dMXbs2Bgw4NBOvFQ1RrZt2xYREaNGjeqxPmrUqPjb3/52wMe0tLTEzTffXM0xAIAkbW1tMW7cuEN6TFVjZJ9/P6JRqVT+41GOhQsXxoIFC7rvl0qlaGxsjLa2tqivr++N8QCAKuvs7IyGhoYYOnToIT+2qjEyevToiHj/CMmYMWO617dv377f0ZJ9amtro7a2dr/1+vp6MQIAR5gPc4lFVb9npKmpKUaPHh1r1qzpXnv33Xdj7dq1MX369GruCgA4ShzykZGdO3fGq6++2n1/69atsXnz5hg2bFg0NjbG/PnzY/HixXH88cfH8ccfH4sXL47BgwfH1772taoODgAcHQ45RjZu3BgzZszovr/veo+5c+fGfffdF9/73vdiz5498e1vfzvefvvtmDp1ajzxxBMf6hwSAHD0O6zvGekNnZ2dUSwWo1QquWYEAI4Qh/P+7bdpAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUYgQASCVGAIBUVY+R9957L77//e9HU1NT1NXVxSc/+cm45ZZbYu/evdXeFQBwFDim2k94++23xy9+8YtYvnx5nHLKKbFx48a44oorolgsxrXXXlvt3QHQj7WX9sTWjl3RNGJIjCnWZY/Dh1T1GHn22WfjwgsvjAsuuCAiIsaPHx8PPfRQbNy4sdq7AqAfW7mhNRY+vCX2ViIGFCJaLpoQF09pzB6LD6Hqp2nOPPPM+N3vfhcvv/xyRET88Y9/jGeeeSa++MUvHnD7crkcnZ2dPW4A8N+0l/Z0h0hExN5KxA0P/ynaS3tyB+NDqfqRkeuuuy5KpVKceOKJUVNTE11dXXHrrbfGJZdccsDtW1pa4uabb672GAAcxbZ27OoOkX26KpV4vWO30zVHoKofGVm5cmU88MAD8eCDD8Yf/vCHWL58efz0pz+N5cuXH3D7hQsXRqlU6r61tbVVeyQAjjJNI4bEgELPtZpCIcaPGJwzEIelUKlUKh+82cFraGiI66+/PubNm9e9tmjRonjggQfiL3/5ywc+vrOzM4rFYpRKpaivr6/maAAcRVZuaI0bHv5TdFUqUVMoxOKLml0zkuhw3r+rfppm9+7dMWBAzwMuNTU1PtoLQFVdPKUxzj7h2Hi9Y3eMHzHY6ZkjWNVjZPbs2XHrrbdGY2NjnHLKKfH888/HnXfeGd/4xjeqvSsA+rkxxToRchSo+mmaHTt2xA9+8INYtWpVbN++PcaOHRuXXHJJ/PCHP4yBAwd+4OOdpgGAI8/hvH9XPUYOlxgBgCPP4bx/+20aACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACCVGAEAUokRACBVr8TIP/7xj/j6178ew4cPj8GDB8dpp50WmzZt6o1dAQBHuGOq/YRvv/12nHHGGTFjxox47LHHYuTIkfHXv/41Pv7xj1d7V9CvtJf2xNaOXdE0YkiMKdZljwNQNVWPkdtvvz0aGhri3nvv7V4bP358tXcD/crKDa2x8OEtsbcSMaAQ0XLRhLh4SmP2WABVUfXTNI8++mhMnjw5vvzlL8fIkSPjs5/9bNxzzz3/cftyuRydnZ09bsD/ai/t6Q6RiIi9lYgbHv5TtJf25A4GUCVVj5HXXnstli5dGscff3z89re/jSuvvDKuueaauP/++w+4fUtLSxSLxe5bQ0NDtUeCI9rWjl3dIbJPV6USr3fszhkIoMoKlUql8sGbHbyBAwfG5MmTY/369d1r11xzTWzYsCGeffbZ/bYvl8tRLpe773d2dkZDQ0OUSqWor6+v5mhwRGov7YkzbnuyR5DUFArxzPUzXDsC9BmdnZ1RLBY/1Pt31Y+MjBkzJk4++eQeayeddFK0trYecPva2tqor6/vcQP+15hiXbRcNCFqCoWIeD9EFl/ULESAo0bVL2A944wz4qWXXuqx9vLLL8dxxx1X7V1Bv3HxlMY4+4Rj4/WO3TF+xGAhAhxVqh4j3/nOd2L69OmxePHi+MpXvhK///3vY9myZbFs2bJq7wr6lTHFOhECHJWqfppmypQpsWrVqnjooYeiubk5fvzjH8ddd90Vl156abV3BQAcBap+AevhOpwLYACAHH3qAlYAgEMhRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEglRgCAVGIEAEjV6zHS0tIShUIh5s+f39u7AvhItJf2xPq/dkR7aU/2KHBUOKY3n3zDhg2xbNmymDhxYm/uBuAjs3JDayx8eEvsrUQMKES0XDQhLp7SmD0WHNF67cjIzp0749JLL4177rknPvGJT/zH7crlcnR2dva4AfRF7aU93SESEbG3EnHDw39yhAQOU6/FyLx58+KCCy6I8847779u19LSEsVisfvW0NDQWyMBHJatHbu6Q2SfrkolXu/YnTMQHCV6JUZWrFgRmzZtipaWlg/cduHChVEqlbpvbW1tvTESwGFrGjEkBhR6rtUUCjF+xOCcgeAoUfUYaWtri2uvvTZ+9atfxaBBgz5w+9ra2qivr+9xA+iLxhTrouWiCVFTeL9IagqFWHxRc4wp1iVPBke2QqVSqXzwZgdv9erV8aUvfSlqamq617q6uqJQKMSAAQOiXC73+Nu/6+zsjGKxGKVSSZgAfVJ7aU+83rE7xo8YLETgfxzO+3fVP01z7rnnxpYtW3qsXXHFFXHiiSfGdddd919DBOBIMKZYJ0KgiqoeI0OHDo3m5uYea0OGDInhw4fvtw4A4BtYAYBUvfqlZ/s89dRTH8VuAIAjkCMjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAEAqMQIApBIjAECqqsdIS0tLTJkyJYYOHRojR46MOXPmxEsvvVTt3fARaS/tifV/7Yj20p7sUQA4SlU9RtauXRvz5s2L5557LtasWRPvvfdezJw5M3bt2lXtXdHLVm5ojTNuezK+ds//izNuezJWbmjNHgmAo1ChUqlUenMHb775ZowcOTLWrl0bZ5999n5/L5fLUS6Xu+93dnZGQ0NDlEqlqK+v783R+C/aS3vijNuejL3/57+OmkIhnrl+Rowp1uUNBkCf1NnZGcVi8UO9f/f6NSOlUikiIoYNG3bAv7e0tESxWOy+NTQ09PZIHIStHbt6hEhERFelEq937M4ZCICjVq/GSKVSiQULFsSZZ54Zzc3NB9xm4cKFUSqVum9tbW29ORIHqWnEkBhQ6LlWUyjE+BGDcwYC4KjVqzFy1VVXxQsvvBAPPfTQf9ymtrY26uvre9zIN6ZYFy0XTYiawvtFUlMoxOKLmp2iAaDqjumtJ7766qvj0UcfjXXr1sW4ceN6azf0oounNMbZJxwbr3fsjvEjBgsRAHpF1WOkUqnE1VdfHatWrYqnnnoqmpqaqr0LPkJjinUiBIBeVfUYmTdvXjz44IPxyCOPxNChQ2Pbtm0REVEsFqOuzpsaANBT1T/aWygUDrh+7733xuWXX/6Bjz+cjwYBADkO5/27V07TAAAcLL9NAwCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCk6rUYufvuu6OpqSkGDRoUkyZNiqeffrq3dgUAHMF6JUZWrlwZ8+fPjxtvvDGef/75OOuss2LWrFnR2traG7sDAI5ghUqlUqn2k06dOjVOP/30WLp0affaSSedFHPmzImWlpYe25bL5SiXy933S6VSNDY2RltbW9TX11d7NACgF3R2dkZDQ0O88847USwWD+mxx1R7mHfffTc2bdoU119/fY/1mTNnxvr16/fbvqWlJW6++eb91hsaGqo9GgDQy9566638GOno6Iiurq4YNWpUj/VRo0bFtm3b9tt+4cKFsWDBgu7777zzThx33HHR2tp6yP8yVN++0nWkKp/Xou/wWvQdXou+Y9+ZjWHDhh3yY6seI/sUCoUe9yuVyn5rERG1tbVRW1u733qxWPQfVh9SX1/v9egjvBZ9h9ei7/Ba9B0DBhz65ahVv4B1xIgRUVNTs99RkO3bt+93tAQAoOoxMnDgwJg0aVKsWbOmx/qaNWti+vTp1d4dAHCE65XTNAsWLIjLLrssJk+eHNOmTYtly5ZFa2trXHnllR/42Nra2vjRj350wFM3fPS8Hn2H16Lv8Fr0HV6LvuNwXote+WhvxPtfenbHHXdEe3t7NDc3x89+9rM4++yze2NXAMARrNdiBADgYPhtGgAglRgBAFKJEQAglRgBAFL1uRi5++67o6mpKQYNGhSTJk2Kp59+OnukfmndunUxe/bsGDt2bBQKhVi9enX2SP1SS0tLTJkyJYYOHRojR46MOXPmxEsvvZQ9Vr+1dOnSmDhxYve3fU6bNi0ee+yx7LGI9/9fKRQKMX/+/OxR+p2bbropCoVCj9vo0aMP6Tn6VIysXLky5s+fHzfeeGM8//zzcdZZZ8WsWbOitbU1e7R+Z9euXXHqqafGkiVLskfp19auXRvz5s2L5557LtasWRPvvfdezJw5M3bt2pU9Wr80bty4uO2222Ljxo2xcePG+MIXvhAXXnhhvPjii9mj9WsbNmyIZcuWxcSJE7NH6bdOOeWUaG9v775t2bLlkB7fpz7aO3Xq1Dj99NNj6dKl3WsnnXRSzJkzJ1paWhIn698KhUKsWrUq5syZkz1Kv/fmm2/GyJEjY+3atb63p48YNmxY/OQnP4lvfvOb2aP0Szt37ozTTz897r777li0aFGcdtppcdddd2WP1a/cdNNNsXr16ti8efOHfo4+c2Tk3XffjU2bNsXMmTN7rM+cOTPWr1+fNBX0LaVSKSLiQ/0qJtXV1dUVK1asiF27dsW0adOyx+m35s2bFxdccEGcd9552aP0a6+88kqMHTs2mpqa4qtf/Wq89tprh/T4XvvV3kPV0dERXV1d+/2Y3qhRo/b70T3ojyqVSixYsCDOPPPMaG5uzh6n39qyZUtMmzYt/vWvf8XHPvaxWLVqVZx88snZY/VLK1asiE2bNsXGjRuzR+nXpk6dGvfff3+ccMIJ8cYbb8SiRYti+vTp8eKLL8bw4cMP6jn6TIzsUygUetyvVCr7rUF/dNVVV8ULL7wQzzzzTPYo/dpnPvOZ2Lx5c7zzzjvx61//OubOnRtr164VJB+xtra2uPbaa+OJJ56IQYMGZY/Tr82aNav7nydMmBDTpk2LT33qU7F8+fJYsGDBQT1Hn4mRESNGRE1NzX5HQbZv377f0RLob66++up49NFHY926dTFu3Ljscfq1gQMHxqc//emIiJg8eXJs2LAhfv7zn8cvf/nL5Mn6l02bNsX27dtj0qRJ3WtdXV2xbt26WLJkSZTL5aipqUmcsP8aMmRITJgwIV555ZWDfkyfuWZk4MCBMWnSpFizZk2P9TVr1sT06dOTpoJclUolrrrqqnj44YfjySefjKampuyR+DeVSiXK5XL2GP3OueeeG1u2bInNmzd33yZPnhyXXnppbN68WYgkKpfL8ec//znGjBlz0I/pM0dGIiIWLFgQl112WUyePDmmTZsWy5Yti9bW1rjyyiuzR+t3du7cGa+++mr3/a1bt8bmzZtj2LBh0djYmDhZ/zJv3rx48MEH45FHHomhQ4d2HzksFotRV1eXPF3/c8MNN8SsWbOioaEhduzYEStWrIinnnoqHn/88ezR+p2hQ4fud+3UkCFDYvjw4a6p+oh997vfjdmzZ0djY2Ns3749Fi1aFJ2dnTF37tyDfo4+FSMXX3xxvPXWW3HLLbdEe3t7NDc3x29+85s47rjjskfrdzZu3BgzZszovr/vvN/cuXPjvvvuS5qq/9n3Mfdzzjmnx/q9994bl19++Uc/UD/3xhtvxGWXXRbt7e1RLBZj4sSJ8fjjj8f555+fPRqk+fvf/x6XXHJJdHR0xLHHHhuf+9zn4rnnnjuk9+4+9T0jAED/02euGQEA+icxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQCoxAgCkEiMAQKr/D3kAwEtJ7B5MAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y, marker = '.')\n",
    "plt.xlim(0,5)\n",
    "plt.ylim(0,10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   x  y\n",
      "0  1  2\n",
      "1  2  6\n",
      "2  3  4\n",
      "3  4  8\n"
     ]
    }
   ],
   "source": [
    "# make a dataframe of our data\n",
    "d = pd.DataFrame({'x':x, 'y':y})\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seaborn lmplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x24b2d093070>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x = 'x', y = 'y', data = d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## formula notation with statsmodels\n",
    "use statsmodels.formula.api (often imported as smf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data is in a dataframe\n",
    "model = smf.ols('y ~ x', data = d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<statsmodels.regression.linear_model.OLS object at 0x0000024B2D1174C0>\n"
     ]
    }
   ],
   "source": [
    "print(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# estimation of coefficients is not done until you call fit() on the model\n",
    "results = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<statsmodels.regression.linear_model.RegressionResultsWrapper object at 0x0000024B26635D90>\n"
     ]
    }
   ],
   "source": [
    "print(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.640\n",
      "Model:                            OLS   Adj. R-squared:                  0.460\n",
      "Method:                 Least Squares   F-statistic:                     3.556\n",
      "Date:                Mon, 28 Nov 2022   Prob (F-statistic):              0.200\n",
      "Time:                        00:07:51   Log-Likelihood:                -6.8513\n",
      "No. Observations:                   4   AIC:                             17.70\n",
      "Df Residuals:                       2   BIC:                             16.48\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      1.0000      2.324      0.430      0.709      -8.998      10.998\n",
      "x              1.6000      0.849      1.886      0.200      -2.051       5.251\n",
      "==============================================================================\n",
      "Omnibus:                          nan   Durbin-Watson:                   3.400\n",
      "Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.308\n",
      "Skew:                          -0.000   Prob(JB):                        0.857\n",
      "Kurtosis:                       1.640   Cond. No.                         7.47\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\miles\\anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 4 samples were given.\n",
      "  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"
     ]
    }
   ],
   "source": [
    "print(results.summary())\n",
    "# the intercept here is artificially too big because boys are 1, and girls are 2\n",
    "# so a baby boy will subtract 1 times 0.7327, and a girl will subtract 2 times 0.7327\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the abline_plot function for plotting the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.graphics.abline_plot(model_results = results)\n",
    "plt.scatter(d.x, d.y)\n",
    "\n",
    "plt.xlim(0,5)\n",
    "plt.ylim(0,10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generating an anova table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           df  sum_sq  mean_sq         F  PR(>F)\n",
      "x         1.0    12.8     12.8  3.555556     0.2\n",
      "Residual  2.0     7.2      3.6       NaN     NaN\n"
     ]
    }
   ],
   "source": [
    "print(sm.stats.anova_lm(results))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Making predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    4.2\n",
       "dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.predict({'x' : 2})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## numpy array notation\n",
    "similar to sklearn's notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = sm.add_constant(x)  # need to add a constant for the intercept term.\n",
    "# because we are using the numpy notation, we use sm rather than smf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1.]\n",
      " [1. 2.]\n",
      " [1. 3.]\n",
      " [1. 4.]]\n"
     ]
    }
   ],
   "source": [
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$y_i = \\beta_0 + \\beta_1 x_i + \\epsilon_i$$\n",
    "\n",
    "$$\\mathbf{\\hat{Y}} = \\boldsymbol{\\beta} \\mathbf{X}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2 = sm.OLS(y, X)  # OLS is capitalized in the numpy notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "results2 = model2.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.640\n",
      "Model:                            OLS   Adj. R-squared:                  0.460\n",
      "Method:                 Least Squares   F-statistic:                     3.556\n",
      "Date:                Mon, 28 Nov 2022   Prob (F-statistic):              0.200\n",
      "Time:                        00:07:52   Log-Likelihood:                -6.8513\n",
      "No. Observations:                   4   AIC:                             17.70\n",
      "Df Residuals:                       2   BIC:                             16.48\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const          1.0000      2.324      0.430      0.709      -8.998      10.998\n",
      "x1             1.6000      0.849      1.886      0.200      -2.051       5.251\n",
      "==============================================================================\n",
      "Omnibus:                          nan   Durbin-Watson:                   3.400\n",
      "Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.308\n",
      "Skew:                          -0.000   Prob(JB):                        0.857\n",
      "Kurtosis:                       1.640   Cond. No.                         7.47\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\miles\\anaconda3\\lib\\site-packages\\statsmodels\\stats\\stattools.py:74: ValueWarning: omni_normtest is not valid with less than 8 observations; 4 samples were given.\n",
      "  warn(\"omni_normtest is not valid with less than 8 observations; %i \"\n"
     ]
    }
   ],
   "source": [
    "print(results2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OLS solution:\n",
    "\n",
    "$$(X^TX)^{-1}X^TY$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1.],\n",
       "       [1., 2.],\n",
       "       [1., 3.],\n",
       "       [1., 4.]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1. , 1.6])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.inv(X.T @ X) @ (X.T @ y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example\n",
    "\n",
    "Taken directly from https://www.statsmodels.org/stable/examples/notebooks/generated/ols.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(9876789)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "generate artificial data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsample = 101\n",
    "x = np.linspace(0, 10, nsample)\n",
    "X = np.column_stack((x, x ** 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.  , 0.  ],\n",
       "       [0.1 , 0.01],\n",
       "       [0.2 , 0.04],\n",
       "       [0.3 , 0.09],\n",
       "       [0.4 , 0.16],\n",
       "       [0.5 , 0.25]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:6,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  9.5 ,  90.25],\n",
       "       [  9.6 ,  92.16],\n",
       "       [  9.7 ,  94.09],\n",
       "       [  9.8 ,  96.04],\n",
       "       [  9.9 ,  98.01],\n",
       "       [ 10.  , 100.  ]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[95:,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "X has two columns. First column goes from 0 to 10. Values are spaced out by 0.1.\n",
    " The second column is the first column squared. Values go from 0 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = np.array([10, 5, 2])\n",
    "e = np.random.normal(size=nsample, scale = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = sm.add_constant(X)\n",
    "y_true = np.dot(X, beta)\n",
    "y = y_true + e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note we added a column of 1s to the matrix X.\n",
    "\n",
    "The true values of beta are 1 for the intercept, 0.1 for the linear component, and 10 for the quadratic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.  , 0.  , 0.  ],\n",
       "       [1.  , 0.1 , 0.01],\n",
       "       [1.  , 0.2 , 0.04],\n",
       "       [1.  , 0.3 , 0.09],\n",
       "       [1.  , 0.4 , 0.16],\n",
       "       [1.  , 0.5 , 0.25]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:6,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use array notation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.924\n",
      "Model:                            OLS   Adj. R-squared:                  0.922\n",
      "Method:                 Least Squares   F-statistic:                     596.2\n",
      "Date:                Mon, 28 Nov 2022   Prob (F-statistic):           1.40e-55\n",
      "Time:                        00:07:52   Log-Likelihood:                -450.04\n",
      "No. Observations:                 101   AIC:                             906.1\n",
      "Df Residuals:                      98   BIC:                             913.9\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         16.8504      6.193      2.721      0.008       4.561      29.140\n",
      "x1             2.1636      2.862      0.756      0.452      -3.516       7.843\n",
      "x2             2.2096      0.277      7.978      0.000       1.660       2.759\n",
      "==============================================================================\n",
      "Omnibus:                        1.903   Durbin-Watson:                   2.305\n",
      "Prob(Omnibus):                  0.386   Jarque-Bera (JB):                1.803\n",
      "Skew:                           0.235   Prob(JB):                        0.406\n",
      "Kurtosis:                       2.544   Cond. No.                         144.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = sm.OLS(y, X)\n",
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quantities of interest can be extracted directly from the fitted model. Type `dir(results)` for a full list. Here are some examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters:  [16.85044423  2.16361558  2.20962084]\n",
      "R2:  0.9240498683747473\n"
     ]
    }
   ],
   "source": [
    "print(\"Parameters: \", results.params)\n",
    "print(\"R2: \", results.rsquared)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can use the `get_prediction()` method which produces a prediction results object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred_ols = results.get_prediction()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<statsmodels.regression._prediction.PredictionResults at 0x24b2d146c10>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_ols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prediction results object has another method `summary_frame()` which produces a data frame of predictions for each observation. The columns are as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>mean_se</th>\n",
       "      <th>mean_ci_lower</th>\n",
       "      <th>mean_ci_upper</th>\n",
       "      <th>obs_ci_lower</th>\n",
       "      <th>obs_ci_upper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16.850444</td>\n",
       "      <td>6.192862</td>\n",
       "      <td>4.560911</td>\n",
       "      <td>29.139977</td>\n",
       "      <td>-26.898503</td>\n",
       "      <td>60.599391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>17.088902</td>\n",
       "      <td>5.950169</td>\n",
       "      <td>5.280985</td>\n",
       "      <td>28.896819</td>\n",
       "      <td>-26.527203</td>\n",
       "      <td>60.705007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>17.371552</td>\n",
       "      <td>5.715143</td>\n",
       "      <td>6.030038</td>\n",
       "      <td>28.713067</td>\n",
       "      <td>-26.120604</td>\n",
       "      <td>60.863709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>17.698395</td>\n",
       "      <td>5.487954</td>\n",
       "      <td>6.807729</td>\n",
       "      <td>28.589061</td>\n",
       "      <td>-25.678377</td>\n",
       "      <td>61.075167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18.069430</td>\n",
       "      <td>5.268787</td>\n",
       "      <td>7.613694</td>\n",
       "      <td>28.525166</td>\n",
       "      <td>-25.200192</td>\n",
       "      <td>61.339051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>241.259810</td>\n",
       "      <td>5.268787</td>\n",
       "      <td>230.804074</td>\n",
       "      <td>251.715546</td>\n",
       "      <td>197.990188</td>\n",
       "      <td>284.529432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>245.740740</td>\n",
       "      <td>5.487954</td>\n",
       "      <td>234.850074</td>\n",
       "      <td>256.631406</td>\n",
       "      <td>202.363968</td>\n",
       "      <td>289.117512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>250.265862</td>\n",
       "      <td>5.715143</td>\n",
       "      <td>238.924348</td>\n",
       "      <td>261.607376</td>\n",
       "      <td>206.773705</td>\n",
       "      <td>293.758019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>254.835177</td>\n",
       "      <td>5.950169</td>\n",
       "      <td>243.027260</td>\n",
       "      <td>266.643094</td>\n",
       "      <td>211.219071</td>\n",
       "      <td>298.451282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>259.448684</td>\n",
       "      <td>6.192862</td>\n",
       "      <td>247.159151</td>\n",
       "      <td>271.738217</td>\n",
       "      <td>215.699737</td>\n",
       "      <td>303.197631</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>101 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean   mean_se  mean_ci_lower  mean_ci_upper  obs_ci_lower  \\\n",
       "0     16.850444  6.192862       4.560911      29.139977    -26.898503   \n",
       "1     17.088902  5.950169       5.280985      28.896819    -26.527203   \n",
       "2     17.371552  5.715143       6.030038      28.713067    -26.120604   \n",
       "3     17.698395  5.487954       6.807729      28.589061    -25.678377   \n",
       "4     18.069430  5.268787       7.613694      28.525166    -25.200192   \n",
       "..          ...       ...            ...            ...           ...   \n",
       "96   241.259810  5.268787     230.804074     251.715546    197.990188   \n",
       "97   245.740740  5.487954     234.850074     256.631406    202.363968   \n",
       "98   250.265862  5.715143     238.924348     261.607376    206.773705   \n",
       "99   254.835177  5.950169     243.027260     266.643094    211.219071   \n",
       "100  259.448684  6.192862     247.159151     271.738217    215.699737   \n",
       "\n",
       "     obs_ci_upper  \n",
       "0       60.599391  \n",
       "1       60.705007  \n",
       "2       60.863709  \n",
       "3       61.075167  \n",
       "4       61.339051  \n",
       "..            ...  \n",
       "96     284.529432  \n",
       "97     289.117512  \n",
       "98     293.758019  \n",
       "99     298.451282  \n",
       "100    303.197631  \n",
       "\n",
       "[101 rows x 6 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred_ols.summary_frame()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the summary frame, we can produce a prediction interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "iv_l = pred_ols.summary_frame()[\"obs_ci_lower\"]\n",
    "iv_u = pred_ols.summary_frame()[\"obs_ci_upper\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x24b2eb72dc0>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(x, y, \"o\", label=\"data\")\n",
    "plt.plot(x, y_true, \"b\", label=\"True\")\n",
    "plt.plot(x, results.fittedvalues, \"r--\", label=\"OLS\")\n",
    "plt.plot(x, iv_u, \"r:\")\n",
    "plt.plot(x, iv_l, \"r:\")\n",
    "plt.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}