Chapter17Evalue.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 17: E-Value : Evidence for Causation in Observational Studies with Unmeasured Confounding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numpy            : 1.24.3\n",
      "pandas           : 2.0.3\n",
      "matplotlib       : 3.7.2\n",
      "seaborn          : 0.13.0\n",
      "scipy            : 1.11.1\n",
      "statsmodels      : 0.14.0\n",
      "graphviz         : 0.20.1\n",
      "matplotlib_inline: 0.1.6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# viz\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
    "plt.rc(\"font\", **font)\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
    "%matplotlib inline\n",
    "\n",
    "from utils import *\n",
    "\n",
    "np.random.seed(42)\n",
    "%load_ext autoreload\n",
    "%autoreload 1\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark --iversions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With observed conditional risk ration $\\text{RR}^{\\text{obs}}_{ZY \\mid X}$, we can calculate the E-value as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evalue(rr):\n",
    "    return rr + np.sqrt(rr * (rr - 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.7297803585806"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Analysis\n",
    "p1 = 397 / (397 + 78557)\n",
    "p0 = 51 / (51 + 108778)\n",
    "\n",
    "## Relative Risk\n",
    "(rr := p1 / p0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Asymptotic Variance of Log of RR\n",
    "logrr = np.log(p1 / p0)\n",
    "se = np.sqrt(1 / 397 + 1 / 51 - 1 / (397 + 78557) - 1 / (51 + 108778))\n",
    "upper = np.exp(logrr + 1.96 * se)\n",
    "lower = np.exp(logrr - 1.96 * se)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.7297803585806\n",
      "20.94733418446287\n"
     ]
    }
   ],
   "source": [
    "## point estimate\n",
    "print(rr)\n",
    "## e-value based on rr\n",
    "print(evalue(rr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.017414334809697\n",
      "15.518182180917343\n"
     ]
    }
   ],
   "source": [
    "## lower CI\n",
    "print(lower)\n",
    "## e-value based on lower CI\n",
    "print(evalue(lower))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_30947/463092966.py:13: RuntimeWarning: divide by zero encountered in divide\n",
      "  y = RR * (RR - 1) / (x - RR) + RR\n",
      "/tmp/ipykernel_30947/463092966.py:14: RuntimeWarning: divide by zero encountered in divide\n",
      "  y_L = RR_L * (RR_L - 1) / (x_L - RR_L) + RR_L\n"
     ]
    },
    {
     "data": {
      "image/png": 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cCSH2g4KGadCzR6yOoWXD1sNGixYtAAC3b9+mxekIMQMKGqZDzyDhFcuyePjwIR4+fGiyKZuGlg1b70bx8vLiFqW7fPmywNUQYvtYluXetyho8IueRcIrjUaDtWvXYu3atdBoNCa5D0PLxvPnz6FUKk1yH5bC0JVy4cIFgSshxPaJRCI4OTlxq4NS0OAPPZPE6ri6uqJRo0Zo27Yt8vPzhS7HpChsEGJehsBBQYNfNECUWB2GYZCYmCh0GWZBYYMQ02FZFiqVCjKZjFs0kpgGRTdCLJghbNy4cQMFBQUCV0OI7dDr9SgoKIBGo4FSqaTDApgYhQ1CLJifnx98fHyg1+tpJVFCeKLX66FUKrlZJ3q9nsKGiVHYIFbpvffeQ7169fDll18KXYpJMQxDXSmE8Khk0KBZJ+ZBzy6xSvn5+UhNTbWLg5RR2CCEHxQ0hEMDRAmvxGIx2rVrx/1uKvaysBdAYYMQPlDQEBaFDcIrsViMXr16mfx+7OX4KMD/wsbVq1e5kfOEkMqjoCE8eqaJVbKX46MAQL169eDh4QGNRkMriRJSDWq1mgsatI6GMOjZJrxiWRZPnz7F06dPTTq6255aNhiGQUxMDADg9OnTAldDiPWRyWQQi8UQiUSQy+UUNARAzzjhlUajwerVq7F69WqTLVcO2M/xUQzatGkDgMIGIdXBMAzkcjkFDQHRmA1ilXx8fBAaGgpfX1+7GMdAYYOQytPr9WAYxmhV0JLniXlR2CBWqVatWrh7967QZZiNoRvlzp07ePz4MTw8PASuiBDLZFgZ1DAIlAKGZaD2JEKsQJ06ddCgQQMAwJkzZwSuhhDLZAgaLMtCr9ejsLBQ6JLI/6OwQYiVoK4UQspXPGgARbNOHB0dBa6KGFDYIFbrnXfeQd26dfHVV18JXYpZUNggpGxlBQ3qQrEsFDaI1crPz0d6ejrS0tKELsUsDGHjzJkzdNAoQv4fBQ3rQANECa9EIhFatWrF/W5Kfn5+AIDs7GyT3o+liIqKgkwmQ25uLu7cucON4SDEXlHQsB7UskF4JZFI8NJLL+Gll16CRGLaLOvr6wsAyMrKMun9WAoHBwe0aNECAHWlEEJBw7pQ2CBWy95aNoD/daWcOnVK4EoIEZZIJOK+0FDQsHwUNgivWJZFfn4+8vPzTT6uwN5aNgCgffv2AIC///5b4EoIEZ6joyMcHBwoaFgBChuEVxqNBitWrMCKFStMulw58L+WjUePHpn8vixFx44dAQBXrlyBQqEQuBpChCeTyShoWAEKG8RqeXp6okGDBmjfvj2eP38udDlm4e/vj9DQUOj1eupKIXZFr9cjPz8fOp1O6FJINVDYIFZLJBLh9u3bOHHiBNzd3YUux2wMrRsnTpwQuBJCzMMwGFSv10OpVHKHiyfWg8IGIVaGwgaxJyVnndAB1awThQ1CrIwhbJw6dQpqtVrgaggxHZreajsobBCr9uGHHyIwMBAff/yx0KWYTaNGjeDh4YHCwkJcuHBB6HIIMQmdTkdBw4ZQ2CBWTaVSISMjw26WLAeKmpE7dOgAgLpSiG3S6XRQKpVc0BCLxRQ0rByFDcIrkUiEqKgoREVFmXy5csA+19oAgE6dOgGgsEFsT1lBQy6XU9CwcnRsFMIriUSCV155xWz3FxAQAADIzMw0231aguKDRFmWpTdiYjN0Oh0FDRtELRvEqgUGBgIA0tPTBa7EvKKjoyGXy/H48WMkJiYKXQ4hvHFwcIBMJqOgYWMobBBesSwLtVoNtVptlsOgG8JGVlYWtFqtye/PUjg4OHBLlx89elTgagjhl4ODAwUNG0Nhg/BKo9Fg+fLlWL58uVmWEPf29oZEIoFer7e7cRvdu3cHAPz1118CV0JI9el0ujK/KFDQsC00ZoNYNZFIhHbt2oFhGBQWFgpdjll169YNABAfHw+9Xm+WAbmE8Kn4YFC5XM4dxZXYHnplidU7duwYANjdAletWrVCrVq1kJubiytXrqB58+ZCl0RIpZWcdaJWqyls2DD6KkSIlZJKpejcuTMA6koh1qXkgl2GwaDEdlHYIDbDHANSLQ2N2yDWxhA0DGjWiX2gsEGs3rZt2xAYGIgxY8YIXYrZGcJGQkKCWQbkElITFDTsF4UNYvUkEgkyMjKQmpoqdClmFxUVBXd3dzx//hznz58XuhxCykVBw75R2CC8EolEiIiIQEREhNlmRxjW2sjIyDDL/VkSkUiErl27AqD1NojlYlkWSqWSO09Bw/5Q2CC8kkgkGDJkCIYMGWK2keXFw4ZerzfLfVoSQ1fKkSNHBK6EkLIxDANHR0cAFDTsFYUNYvV8fX0hEomg1WqNmmntRY8ePQAUHSfFHh8/sQ4SiQROTk4UNOwUhQ1i9aRSKXf017y8PIGrMb9GjRohKCgIKpUKCQkJQpdDCACU2cooFospaNgpiwgbcXFxaNKkCXx8fBAaGoo1a9Zw161YsQLh4eHw9/dHbGwskpOTBayUvIharcbSpUuxdOlSsy6yZehKscewwTAM+vTpAwA4cOCAwNUQUjQYND8/3+4W2iPlEzxs6HQ6XL58Gb///jsePHiAX375BTNmzMCTJ08QHx+Pb775BvHx8cjIyEC/fv0wduxYoUsmFqh169bo1KmT3a5ASGGDWIri3ZkqlYqmZBMAFhA2xGIxli1bhpCQEADAw4cPERoaChcXF/zyyy8YNWoU/P39wTAMZs6ciXPnzuHx48cCV00szZo1a3D48GGEhYUJXYogunfvDrFYjNu3b+PevXtCl0PslFarNZp1IpFI7PYLADEmeNgwGDt2LFxcXDBz5kzs27cPEokEycnJXF88UBRMPD09cefOnXL3o1KpkJeXZ3QixNa5ublxh5w/ePCgwNUQe1RW0HB0dKQxGgSABYWNjRs3QqFQYNmyZejTpw/y8/NRUFBQ6g+VYZgKR9wvX74cbm5u3Klu3bqmLp1YEHuc+mpAXSlEKBQ0yItYTNgAihYoGjRoEFxcXBAfHw8nJ6dSx7tgWRZOTk7l7mPBggVQKBTcKS0tzdRlEwtw8+ZNhIaGYtWqVUKXIhhD2Dhy5AgNzCNmQ0GDVIZFhI1Hjx4ZnReJRNDr9QgJCUF2djZ3uVarRU5ODurXr1/uvmQyGVxdXY1OxPZ5eHggIyMDeXl50Gq1QpcjiObNm8Pb2xvPnz/HyZMnhS6H2AEKGqSyBA8bf/31F2JiYrgWiCNHjiAtLQ3t2rXDoEGDsHnzZmRmZoJlWaxevRqtWrWCp6enwFWT8ohEIjRo0AANGjQw23LlAODp6cm1eCkUCrPdryURiUTo1asXAOCPP/4QuBpiD0QiERcsKGiQiggeNrp374758+cjNjYWfn5++M9//oOdO3fC09MT3bp1w8SJE9GlSxcEBARg//792Lhxo9AlkwpIJBKMGDECI0aMMOsodIZhUK9ePQDA06dPzXa/lubll18GAPz2228CV0LsgUgkgpOTE6RSKQUNUiGGLTkowsbk5eXBzc0NCoWCulRsXJ8+fXDw4EH0798fO3fuhIODg9AlmZ1CoYCXlxc0Gg1u3bqF8PBwoUsihFgxvj5DBW/ZIIQvhpYNe+1GAYqmwBqOArt3715hiyE2R6vVorCwUOgyiBWisEF4pVar8dFHH+Gjjz4y+4wI6kYp8q9//QsAhQ3CL8NgUI1GQ4GDVBmFDcI7jUYjyBLFERERqFevnt0PIO7fvz8A4O+//y4104uQ6ig568TGe9+JCVDYIDbDcOyczp07C12KoOrVq4eoqCjo9XqalUJqrKzprXK5XMCKiDWisEGIDRowYAAA6kohNUNBg/CFwgaxOVqt1u6PNGkYt3HgwAHqXyfVQkGD8InCBrEpmzZtwocffoi///5b6FIEFR0dDX9/f+Tn5+PIkSNCl0OsjEajMQoaUqmUggapEQobxKaIxWIAQEpKirCFCIxhGAwcOBAAsHPnToGrIdam+Ewyw4JdhNQEhQ3CK8NKnvXq1RNkNUF3d3cAwL1798x+35ZmyJAhAIA9e/bQgdlIlTg5OUEkElHQILwx33rSxC5IpVKMGTNGsPs3hI3k5GTBarAUHTt2hI+PDx48eIAjR46gb9++QpdErATDMHBycqLlxwlvqGWD2JQ6deoAAO7evStwJcITi8UYPHgwAGDHjh0CV0MsmVarLbV2BgUNwicKG8SmGMLGnTt3aOEh/K8rZffu3dSVQspkGAyqVCrpf4aYDIUNwiu1Wo3PPvsMn332mSAfboZuFIVCgdzcXLPfv6UxdKU8ffqUZqWQUoovPa7T6ex+yjgxHQobhHcFBQUoKCgQ5L4dHBzQsGFDvP7661CpVILUYEnEYjFeffVVANSVQoyVPMaJVCq1yyMlE/OgsEFszvDhw7Fhwwb4+/sLXYpFKD4rhb65EqDsoEGzTogpUdggxMZ16tQJPj4+ePLkCQ4ePCh0OURgFDSIEChsEJukVqvx8OFDocuwCGKxGMOGDQMA/PTTTwJXQ4REQYMIhcIGsTm3bt2Cm5sbt4ImAf79738DAH799Vfk5eUJXA0RglarpaBBBENhg9gcFxcX6PV63LlzR+hSLEZ0dDQaNWqEwsJC7Nq1S+hyiADEYjEkkqJ1HB0cHChoELOisEF4xTAM/P394e/vL9iiQIa1Nh4+fIhnz54JUoOlYRiGa9348ccfBa6GCIFhGDg6OsLR0REymUzocoidobBBeCWVSjFhwgRMmDABUqlUkBocHR3h6ekJgFYSLW7EiBEAgPj4eKSlpQlcDTGHslYFFer/ktg3ChvEJtWvXx8AkJSUJHAlliM4OBidO3cGy7LYunWr0OUQE1Or1cjPz4derxe6FEIobBDbFBYWBoDCRknFu1JoaWrbpVaroVKpwLIsCgoK6LUmgqOwQXil0WiwatUqrFq1StAFpBo2bAgASExMFKwGSzR48GDIZDJcv34d58+fF7ocYgKGoGEglUrpoGpEcBQ2CK9YloVCoYBCoRD021Tbtm0xcuRIdO/eXbAaLFHt2rUxaNAgAMCGDRsErobwrWTQcHBwoMGgxCJQ2CA2qUuXLvjpp58wduxYoUuxOBMmTAAAbNmyBfn5+QJXQ/hCQYNYMgobhNiZLl26oH79+nj27BkdnM1GUNAglo7CBrFZWq0Wd+7cwaNHj4QuxaKIRCKMHz8eAPDdd98JXA2pKQoaxBpQ2CA2a+jQoWjQoAG2b98udCkWZ/To0RCLxTh58iRu3LghdDmkBoqPjaKgQSwVhQ1isxo0aACAZqSUxc/PDy+//DIAGihq7WQyGRwcHChoEItGYYPwimEYeHl5wcvLS/Dpdo0bNwYA3Lx5U9A6LJVhoOgPP/xg1AxPrI9MJqOgQSyaROgCiG2RSqV48803hS4DANCoUSMAFDbK07t3bwQGBiI9PR1xcXHcgl/EsqnVaojFYojFYqFLIaTSqGWD2CxD2MjIyKADspVBIpFg8uTJAIA1a9YIXA2pDJVKBZVKhYKCAuh0OqHLIaTSKGwQm1W7dm34+voCoNaN8kyYMAEODg44c+YMzpw5I3Q5pAIqlQpqtZo7T2GDWBMKG4RXGo0GX3/9Nb7++mtBlys3MLRu0CDRsnl7e2PYsGEAgC+//FLgakh5SgYNw6BQQqwFhQ3CK5ZlkZOTg5ycHIs4+NPIkSOxaNEiREVFCV2KxZo+fToAYPv27Xjw4IHA1ZCSKGgQW0Bhg9i08ePHY+nSpRQ2KtCqVSu0adMGGo0G3377rdDlkGIoaBBbQWGDEMK1bqxbt84iur8IBQ1iWyhsEJuXnp6OP/74g2akVGDIkCHw8fFBZmYmrbhqAXQ6HQUNYlMobBCb16lTJ7z00ku4cOGC0KVYLAcHB8yYMQMA8Nlnn1nEeBt7JhaL4ejoCICCBrENFDaIzWvWrBkA4OrVqwJXYtmmTJkCZ2dnXLlyBYcOHRK6HLsnlUrh7OxMQYPYBAobhFcMw8DNzQ1ubm6CL1duQGGjctzd3bklzD/77DOBq7E/Za2bIRLRWzSxDfSXTHgllUoxa9YszJo1C1KpVOhyAFDYqIrZs2dDLBbjyJEjOH/+vNDl2A3DqqA0OJfYKgobxOYZwsa1a9doLMILBAUFYfjw4QCodcNcis86KSwshF6vF7giQvhHYYPYvPDwcEilUjx79gz3798XuhyLN2/ePADAjh07kJycLHA1tq3k9FZHR0fqOiE2if6qCa80Gg2+++47fPfddxbTJCyVSrnDzVNXyotFRUWhT58+0Ov1WL58udDl2KzCwsJSQcNSuh4J4RuFDcIrlmWRmZmJzMxMi+qyePvtt7F582a0bNlS6FKswnvvvQcA2LRpE1JSUoQtxgYVFhYahXEKGsTWUdggdmH48OH497//DX9/f6FLsQrt27dHbGwstFotPvroI6HLsSkUNIg9spiwcfnyZXTp0gV+fn4IDQ3Fpk2bABRNB5NIJPD19eVOQ4cOFbZYQuzA4sWLAQAbN26ksS48UalUFDSIXbKIsFFYWIh+/fphwYIFyMrKQlxcHCZPnowHDx7gyZMnCAwMRHZ2NneKi4sTumRihY4fP45Vq1bhyZMnQpdiFTp27IgePXpAq9XS2A2eSCQS7ncKGsSeWETYcHR0xOnTp9GnTx8ARUeh9PDwwJ07d5CbmwtPT0+BKyS24I033sDs2bNx9uxZoUuxGobWje+//x6pqakCV2P9xGIxnJycKGgQu2MRYQMAAgMDud/z8vLw9OlThIaGcmFj0qRJ8PPzQ9euXXHt2rVy96NSqZCXl2d0IgQAoqOjAYCOkVIFnTp1Qrdu3aDRaPDhhx8KXY5NEIvFFDSI3bGYsFHc7NmzMW7cOPj5+cHZ2Rm+vr5YuHAh0tLS0KNHDwwbNqzc2y5fvpxbLtvNzQ1169Y1Y+UEAJycnODk5CR0GaUYZqJQ2KiaDz74AEBR68bNmzcFrsa6FBYWQqVSCV0GIYJjWAuan8iyLGbMmIH09HTs2LHDqH/T4Pnz53BxccGjR4/g4eFR6nqVSmX0z52Xl4e6detCoVDA1dXVpPUTYanVam5swYIFC0odwOrw4cPo2bMnQkNDcffuXSFKtFoDBgzA3r17MWjQIOzatUvocqxC8VknDg4OkMlkAldESNXl5eXBzc2txp+hFtOyodPpMG7cOGRmZiIuLs4oaBRf+MZwcK/ymiFlMhlcXV2NToQA/+tGSU5OpkGiVfTRRx9BJBLhl19+wenTp4Uux+KVnN5Kq4ISe2cR/wFarRYjRoyAUqnE9u3bjYLEnj170KdPH+7DYd26dYiJiaEQQaqsTp06CA4OBgBcvHhR2GKsTJMmTTBq1CgAwFtvvWVRC7ZZGlpHg5DSLCJspKenIy4uDkeOHEFgYCC3nsY777yD/v37o1OnToiKioKfnx8OHTqELVu2CF0yKYdGo8GmTZuwadMmi1muvDhD6wYd0bTqli5dCplMhoSEBBw4cEDociwSBQ1CylZ6UIQAgoODK/ymtHTpUixdutSMFZHqYlmWWwDKEr/9vv3225g/fz6aN28udClWJygoCNOmTcPKlSvx1ltvoVevXhCLxUKXZTFKBg25XF7muDNC7JFFtGwQYi6tW7dG27Zt4ejoKHQpVmnBggVwd3fH1atXsX79eqHLsRhKpZKCBiEVoLBBCKk0Dw8PrpVx4cKFNNAWRS14Op2OO09Bg5DSKGwQu7Nv3z68+eab+Ouvv4QuxSpNnjwZERERePz4MXVvomiGnJOTE0QiEQUNQspBYYPYnd9++w1r166lQY7VJJVKsWrVKgDAmjVrcOPGDWELsgAikQhOTk4UNAgpB4UNYnfatm0LADh16pTAlVivnj17YsCAAdDpdJg9e7ZFDgY2JbVaXeoxG9YAIoSURmGD8E4qlVr0dD9D2Dh37pxFTs+1FitWrICDgwMOHTqEPXv2CF2OWbAsC6VSCZVKhcLCQrsLWYRUF4UNwisHBwe88847eOedd0otF24pwsPDUbt2bSiVSly5ckXocqxWWFgY5s2bBwCYPn06nj17JnBFpsWyLAoLC6HVagEULUao1+sFrooQ60Bhg9gdkUhEXSk8effddxEaGoqMjAy89957QpdjMiWDBlA064TWGSGkcihsELtkCBv//POPwJVYN7lcjrVr1wIAvvzyS5tcmbW8oEGDQQmpPAobhFdarRZbt27F1q1bjd6cLU27du0AAFlZWQJXYv169eqFESNGQK/XY+LEiRb9ulcVBQ1C+EFhg/BKr9cjKSkJSUlJFt2f3blzZ2RkZODIkSNCl2ITPv/8c9SuXRsXLlzAmjVrhC6HFxQ0COEPhQ1ilxwdHeHv7y90GTbDx8cHn376KYCilUXv3LkjcEU1p1arKWgQwhMKG8Tu0fRFfowbNw7du3dHQUEBxo4da9EtW5Xh4ODADQCloEFIzVDYIHbr7t276NOnD2JiYoQuxSaIRCJs2LABtWrVwokTJ7B69WqhS6oRhmEgl8tpZVBCeEBhg9itOnXq4NChQzh37hyys7OFLscmBAcHY+XKlQCAd955B7du3RK4ospjWbbMVUFpeishNUdhg9gtd3d3REZGAgCOHTsmcDW2Y8KECejZsycKCwsxZswYoyOiWirDyqAFBQXUrUaICVDYIHatS5cuAICEhASBK7EdDMNgw4YNcHV1xalTp/Dxxx8LXVKFDEFDp9NBr9dDqVQKXRIhNofCBuGVg4MDFi9ejMWLF1vscuXFde7cGQC1bPCtbt26+OKLLwAAixcvttjF04oHDQOZTCZgRYTYJgobxK4Zwsa1a9fw4MEDgauxLaNGjcLw4cOh0+kwYsQIKBQKoUsyUlbQcHJyojEahJgAhQ1i17y8vNC8eXMAoAW+eMYwDNauXYuQkBCkpKRg0qRJFjMegoIGIeZFYYPwSqvVYseOHdixY4fVLFvdv39/9OjRA7Vr1xa6FJvj5uaGrVu3QiwWY/v27di0aZPQJVHQIEQAFDYIr/R6PW7cuIEbN25YzaJO77//Pg4fPox+/foJXYpNatu2LT744AMAwLRp03D9+nXBaqGgQYgwKGwQQkzuP//5D2JjY1FQUIBBgwYhLy9PkDoYhgHDMNx5ChqEmAeFDUL+X3Z2tlUtQmVNxGIxtm7disDAQNy+fRtjx44VbPyGXC6HVCqloEGIGVHYIATAhg0b4Ofnhzlz5ghdis3y8vLCzp07IZVK8csvv2DFihWC1eLo6EhBgxAzorBBCICWLVsCKFrcS61WC1yN7WrTpg23/sbbb7+No0ePmvT+DGM0rGX8ECG2isIGIQAiIyPh7e2N/Px8nDx5UuhybNqkSZMwevRo6PV6DB06FPfu3TPJ/RiChlarRUFBAQUOQgREYYMQFB2xtHfv3gCAffv2CVyNbTOsvxEdHY1Hjx6hf//+vA8YLWvWiaWs8UGIPaKwQXgllUqxYMECLFiwAFKpVOhyquTll18GAPz+++8CV2L75HI59u7dCz8/P1y/fh3Dhg3jbV2WkkHDcKh4GqNBiHAobBBeMQwDBwcHODg4GE0xtAa9e/eGRCLBzZs3cefOHaHLsXkBAQHYu3cvHB0dsX//fsybN6/G+6SgQYhlorBByP9zc3PjjgL722+/CVyNfWjVqhU2b94MAFi9ejXWrVtX7X1R0CDEclHYILzSarXYs2cP9uzZYzXLlRc3d+5c/Pjjjxg1apTQpdiNIUOG4P333wcATJ06tVpBz1aDxtmzZ9G5c2cUFBQIXYrFS0hIQGxsLM0ms1AUNgiv9Ho9Ll++jMuXL1vl6P++ffvi9ddfh4eHh9Cl2JV3333XaIZKVWcEabVamwsaGo0GY8aMwaZNm+Dk5IQnT55gxIgRCAwMREBAAGbMmGE06PXQoUOIjo6Gr68vWrRogYMHD5a77zVr1iAsLAz+/v7o0qWL0RLy33//PZydneHr68uddu3a9cJ6L1++jC5dusDPzw+hoaGljoOzYsUKhIeHw9/fH7GxsUhOTi5zP0qlEm+++SaCgoIQGBiI119/HU+ePOGuHzVqFNzd3Y3qy8rKQpcuXdCpUyd88sknL6yVmB+FDUKI4BiGwXfffYd+/fqhsLAQL7/8MhITEyt9e6lUCplMBoZhbGZl0J9//hkdOnRAaGgoAGDs2LEIDQ1Famoqrly5gt9++w27d+8GACgUCowYMQJr1qxBdnY2vv76a4wcORIKhaLUfo8cOYKVK1ciPj4emZmZmDRpEgYPHsyFtdzcXMyfPx/Z2dnc6dVXX62w1sLCQvTr1w8LFixAVlYW4uLiMHnyZDx48AAAEB8fj2+++Qbx8fHIyMhAv379MHbs2DL39dFHHyE9PR23bt3C/fv34eLigrfeeou7Pjc3F7t37zaqz8/PDwAwb948bNiwAYWFhVV8tompUdggpISMjAx8+umnWLZsmdCl2BWpVIq4uDi0adMGT548Qe/evZGenl7p2zs4OMDZ2RkikW28re3duxfDhg3jzn/33XdYtGgRRCIRPDw80L59ey6QHTlyBFFRUWjfvj0AoF27doiOjsaRI0dK7ffAgQN45ZVXEBgYCAAYMWIEcnJyuEHRubm58PT0rFKtjo6OOH36NPr06QOgaCyOh4cHt89ffvkFo0aNgr+/PxiGwcyZM3Hu3Dk8fvy4zPrGjRvHtU6V7FqrqD5nZ2d06tTJ5IvFkaqzjf9KQnh0//59vPXWW/jkk0+gUqmELseuODs74/fff0fDhg2RlpaG3r17IycnBzqdDvHx8di2bRvi4+Oh1WrLHBNkbTOgKnLhwgVERkZy5728vODg4MCdv3fvHsLCwgAAycnJ8PX1Nbq9n58fkpKSSu1Xo9GU6uJkWRYPHz4EUPRh/uzZM7Rq1QqBgYGYOnVqpf4PDOEFAPLy8vD06VOuVaZkfWKxGJ6enmXO+ipZX/HaDPWdOnUKYWFhCA8Px9dff210+8jISJw7d+6F9RLzqnbYOHv2LJ91EGIx2rZti4CAADx79gyHDh0Suhy74+npiYMHDyIgIAA3btxAmzZtEBQUhG7dumHEiBHo3r07GjdujF27dlnlIOTKys7OLvcb/I8//gi1Wo2BAwcCAAoKCkoFLYZhyhxY2r59e/zyyy+4c+cO9Ho9tmzZgufPn8Pf3x8AEBERAYZh8M8//+DChQs4c+YMvvzyyyrVPnv2bIwbN47r3qhqfd988w0UCgUKCwuxceNGrjYA6NixI7y8vHDnzh3ExcVhwYIFRuHCy8uL674hlqPaYWPixIlYu3Ytn7UQYhFEIhHXR71z506Bq7FP9erVw5EjR1C7dm3cu3cPmZmZAP43+PPBgweYMGECdu3aZXcrg27btg3Lly/H77//zrV0ODk5lXoeWJaFk5NTqdsPGTIE//73vxEbG4tGjRrh5s2bqF+/PurXrw8AmDFjBt5++21IpVJ4e3tj9OjRSEhIqFRtLMti+vTpyM3Nxeeff85dXpX6PvjgA9SuXRuNGjVC586d8fz5c/Tv35+7fv369RgwYAAAoHnz5ujZs2el6yPCqXbYOHHiBE6cOIGRI0fStCxic4YMGQIA+PXXX6krRSBhYWGQyWRGlxU/WivLsvjPf/5jlbOeKsPHxwePHj0yumz9+vX48MMPcfjwYaNuiZCQEGRnZxttm5mZyXWzFMcwDD766COkpKTg9u3bSExMxPz587nrS04dZRimUqsB63Q6jBs3DpmZmYiLi4NEIim3Pq1Wi5ycHC7gFOfh4YGff/4ZWVlZOHr0KP766y/Mnj270vXl5OTAx8fnhfUS86p22HB2dsaWLVvQvn17dOzYEXv37kVKSgqPpRFrJJVKMW/ePMybN8/qlisvrn379vDz84NCoShzkB0xvePHj5dqDler1WBZFnq9HgUFBUhNTcXx48cFqtC0oqOjceXKFe78F198gdWrV+Ovv/4y6lYAgNjYWFy6dImbMmzoAunRowcAYPr06fj4449L3cfHH38MtVqNMWPGcJcNHToUX3zxBViWRV5eHrZu3YqePXtWWKtWq8WIESOgVCqxffv2Uv/7gwYNwubNm5GZmQmWZbF69Wq0atUKnp6eUKlU6NGjR6kuS7VajZEjR2LKlClo0KABgKJpsU2bNsWJEycAAElJSYiPj0f37t252125cgWtWrWqsF5ifjUaIHrixAn8888/ePbsGX788Uf0798fHh4eaNu2LV/1ESvDMAycnZ3h7Oxs1YP1inel7NixQ+Bq7FNWVhaAor8pR0dHAEXfngsKCoyO4mrYztb861//wvbt27nzn3/+OdLS0hAVFcWtL9G1a1cARavfbt26FVOnToWvry+mTJmCLVu2oHbt2gCAu3fvIjU1ldtXYWEhJk2ahJMnT2Lr1q1G/6urVq3CwYMH4evri2bNmqFjx46YOHEiAGDjxo3w9vYuNaU2PT0dcXFxOHLkCAIDA7n63nnnHQBAt27dMHHiRHTp0gUBAQHYv38/Nm7cCKBoQGhiYqJRK056ejp69OiBFi1aYO7cudzlcrkc69atw6xZs+Dn54f+/ftj1apVaNq0KYCisSHHjx9Ht27davr0E54xbDU7PJs0aQJvb29MmzYNr7zyCte0qdVqkZSUhMaNG/NaaHXl5eXBzc0NCoUCrq6uQpdDTEitVmP58uUAgAULFhiN3K+OhIQE9O3bFyNHjsR3333HR4mkCgzfWJ2cnCASibigUdLRo0e5D11botFoEBUVhX379iEkJETocgAAly5dQteuXfHgwYNSXVyWwLAS7aJFiwSuxHbw9RkqefEmZfv555/RrFmz0juUSCwmaBDz02q13MqFhgObWauOHTsiJycHzs7OQpdilzp16oT69etzXSkMw4BhGKOBhv7+/ujUqZNQJZqUVCrFpk2bMGbMGOzfv7/MwZTmtnPnTqxdu9Yig8axY8eQkJCAP/74Q+hSSBmq/UkwZMgQREZGolmzZtyprME+xL7o9XpuGtqL+nktnVgspqAhILFYjOXLl+ONN97gjn1SVkNsZmYm6tatK0CFphcTE2NRMy0+/PBDoUsoV+fOnWl8lQWr9piNQ4cOYcyYMZDJZNi1axcGDx6M4OBgLF261KbnvhP7dP36deTl5Qldht0ZPHgwvv/+e7i7uxvNOvH19YWnpycyMzPRvn17o2N7EEIsT7XDRlBQEPr164f//Oc/+PHHH3Hx4kVcuHABWVlZ+M9//sNnjYQIasSIEWjatCl+/vlnoUuxeWW1XAwePBj37t3D0aNHsXXrVhw9ehTp6ek4f/48GjZsiPT0dHTs2NFmZ6UQYgt4Xa68Tp06+Oqrr7B//34+d0uIoJo3bw4A2Lx5s7CF2DjDdNayDhEuFovRtWtXDB8+HF27doVYLEZQUBD+/vtvtG/fHk+fPkXPnj1pETZCLFS1w8YPP/yA8+fPlzq6nl6vpyPuEZsycuRIMAyDv//+u9zDYpOa0ev1UCqV0Ov1UKlU0Gg0lbqdh4cHDh8+jFdeeQUqlYpbI4IQYlmqHTZOnz6N2bNno27duggPD8err76K2bNno1u3bnj55ZervL/Lly+jS5cu8PPzQ2hoKDZt2sRdt2LFCoSHh8Pf3x+xsbH0hk/MKiAggFsc6ccffxS4GttTPGgARbNOqnKIeLlcjp07d+LNN98Ey7KYOXMmpk2bVunAQggxvWqHja+//hrHjh1DTk4O4uPjMXnyZDRs2BDvvPNOlQ/aU1hYiH79+mHBggXIyspCXFwcJk+ejAcPHiA+Ph7ffPMN4uPjkZGRgX79+mHs2LHVLZuQahk9ejSAokWNdDqdwNXYjrKChmFdjaoQi8VYs2YNPv74YzAMg6+++gp9+/ZFbm6uKcomhFRRtRf14lt6errRIYoDAgIQFxeH7du3w8vLC++99x6AohUEXV1dkZqaCg8Pj1L7UalURseyyMvLQ926dWlRLzNhWZZbXdDNzc2sq4jyvahXcUqlEv7+/nj69Cn++OMP9O3bl7d92yu+gkZJv/76K0aOHIn8/HyEhYXht99+Q6NGjfgomRC7w9eiXlX6r75//z4OHTpU7vLAhiMzVkfxoJGXl4enT58iNDQUycnJRgccEovF8PT0xJ07d8rcz/Lly+Hm5sadbHX+vaViGAa1a9dG7dq1rXq58pLkcjlGjRoFADQrhQeGwaCGoCESiXgJGgAwYMAAnDx5EvXq1cOdO3fQtm1bHDhwoMb7JYRUX6X/s7dt24awsDD06dMH9evX5/qu79+/j48//hgxMTEICgripajZs2dj3Lhx8PPzQ0FBQakPLYZhyj3S7IIFC6BQKLhTWloaLzURMn36dOzatQvr168XuhSrZggahkZVkUgEuVzOS9AwiIyMxJkzZ9CxY0coFAr069cPH3zwgc0eIZYQS1fp/+4PPvgA06dPx9WrV9GzZ09MmTIFCxcuRP369bFp0ya0adMGv/zyS42KYVkW06dPR25uLj7//HMAgJOTU6m59yzLlrt0r0wmg6urq9GJmI9Op8OhQ4dw6NAhmxvbEBYWhkGDBln10WwtQfH/Z1MEDQNvb28cPnwYEydOBMuyWLRoEV566SU8fvyY9/sihFSs0suV3717FzNnzkS9evXw1VdfISgoCP/88w+uXr3Ky7FQdDodJkyYAIVCgbi4OO6YGiEhIcjOzua202q1yMnJoaXRLZROp8M///wDANx6CLZIp9OBYRiTfEjaOrFYDLlcDpVKBUdHR5M+hzKZDN988w3at2+PKVOm4MCBA4iOjsaOHTsQExNjsvslhBir9H+5RqOBXC4HUDS+Qi6XY8WKFbwEDa1WixEjRkCpVGL79u1G3xwHDRqEzZs3IzMzEyzLYvXq1WjVqhU8PT1rfL+EVMeqVasQEhKCffv2CV2K1RKLxbyN0aiM0aNH49SpU2jQoAFSU1PRsWNHrFmzpswVSwkh/KvSf/rWrVtx8+bNohuKRHB3d+eliPT0dMTFxeHIkSMIDAyEr68vfH198c4776Bbt26YOHEiunTpgoCAAOzfvx8bN27k5X4JqY7MzEykpaVh1apVQpdiFQwLdQktMjISZ8+exaBBg6DRaDB9+nQMGDAAOTk5QpdGiM2r9NTXzp074/Lly3j+/Dnc3d2hUCgwdepUtG/fHk2bNkV4eLhFHk6cr2k7pHJMOf3UUu47NTUVoaGh0Ol0uHz5MiIjI01yP7ag+GBQqVQKR0dHoUsCy7L48ssvMX/+fKjVavj6+uKHH35Ar169hC6NEItj9qmvx44dg0KhwM2bN7FmzRrMnj0bV69exeTJk9G0aVM4OzvTmy6xC0FBQXj11VcBgFo3KlBy1olOp7OIbguGYTBjxgycPXsWERERyM7ORu/evTFnzhyLaIEhxBZVucO0QYMGGDZsGD799FMcOXIEubm5uHv3Ln766adqLVNOiDWaNWsWAGDLli14+PChsMVYoLKmtzo5OVnU2iuRkZE4d+4cpk6dCgD473//i5iYGFy6dEnYwgixQbws6hUSEoIhQ4Zg2rRpvBZHiKVq27YtYmJioFarsW7dOqHLsSjWEDQM5HI51qxZg99++w2enp64cuUKWrdujcWLF5d59FlCSPXwtqhXmzZteFvUi1gvqVSKKVOmYMqUKTa9HgXDMFzrxldffUUfTP/PmoJGcS+//DKuXbuGQYMGQavV4v3330erVq1w4cIFoUsjxCbwtqhXTExMjRf1ItaPYRh4e3vD29vb4j9gamrw4MF48803cfDgQbMOhLVU1ho0DHx8fLBz505s374dnp6euHr1KmJiYvDuu+/SWA5CaqjSs1FkMhlu376NevXqIT09HUFBQejatSu++uorXtbaMBWajWI/hJwJQ4CCggJu1VhrCxolPXz4ENOmTcOOHTsAAOHh4fj666/Ro0cPgSsjxLzMPhvFlIt6Eduh0+kQHx+P+Ph4m1uu/EU0Go3QJQjKsOy4tQcNoGip87i4OOzYsQO+vr64ffs2YmNj8frrr+PBgwdCl0eI1bGIRb2I7dDpdEhISEBCQoLdhI1Hjx5h4sSJiIqKglarFbocwRgOEW/tQaO4wYMHIzExEVOnTgXDMNiyZQsaNmyIdevW0UHdCKmCSoeNjh07YvHixWjSpAk8PT1RWFiI1atXIy4uDjdu3LDrN1li3+RyOXbv3o3ExES7Ovy8Xq8vtW4GwzA2EzQMateujTVr1uD06dOIjo6GQqHAlClT0LZtW+44QISQitGiXoTUkLOzM+bMmQMAeP/99+2iO8UwGFSpVFrEQl3m0Lp1a5w5cwZffPEFXFxccPbsWbRv3x4jR45EWlqa0OURYtFoUS9CeDBt2jR4eXkhKSkJmzZtErock9LpdNysE51OZ1czNcRiMaZPn47bt2/jjTfeAMMw2Lp1Kxo2bIglS5YgPz9f6BIJsUi8HHLRsKjXRx99xMfuCLE6Li4uWLhwIQBg6dKlUCqVAldkGjqdzqg1QyQSQSaTCVyV+fn6+mLDhg04d+4cOnXqBKVSiaVLl6Jhw4b48ccf7Wa8EiGVZZ7jOxNiByZPnoy6desiIyMDX331ldDl8K5k0DAcJt7WxmhURXR0NBISErBjxw4EBwcjIyMDo0aNQosWLfD777/bTRcTIS9CYYMQnshkMixZsgQAsHbtWpv6dltW0JDL5XYdNAwYhuFmrSxfvhxubm64evUq+vfvj44dO+L48eNCl0iI4ChsEF5JJBKMHz8e48ePh0QiEbocsxs1ahSWL1+OM2fOQCwWC10OLyhoVI6joyPefvttJCcn46233oKjoyNOnjyJzp0746WXXqIDvBG7RmGD8EokEiEgIAABAQEQiezvz0sikeDtt9+Gh4eH0KXwQq/XU9Coojp16uDjjz/G3bt3MXnyZIjFYvzxxx9o0aIFBg4cSMdbIXbJ/j4NCDETlmVx6tQpocuoEYZhuNBIQaNq/P39sXbtWiQmJmLYsGFgGAZ79uxBy5Yt0b9/f5w5c0boEgkxGwobhFc6nQ5///03/v77b5sas1BVOp0Offr0Qbt27RAfHy90OdXGMAzkcjkcHBwoaFRTgwYNsG3bNly/fh0jR46ESCTC77//jjZt2qBv3760MBixCxQ2CK90Oh0OHz6Mw4cP23XYEIvFCAsLAwDMnDnTqp8LhmEgk8koaNRQ48aN8dNPP+HmzZsYM2YMxGIxDhw4gPbt26Nr1674/fffaQl0YrMobBBiIu+//z7c3d1x5coVfP3110KXUyk6nQ75+fn0oWdCDRo0wMaNG3H79m1uIHVCQgL69++Ppk2bYsOGDSgsLBS6TEJ4RWGDEBPx8PDAsmXLAAALFy5ERkaGwBVVzLAyqGEpcgocphUaGorvvvsO9+7dw/z58+Hq6orExESMHz8ewcHB+Oijj5Cbmyt0mYTwgsIGISY0adIktG3bFs+ePcP06dOFLqdchqBhIBKJqNvETAIDA/Hpp58iNTUVK1asQGBgIB48eICFCxeibt26mDJlCq5duyZ0mYTUCIUNQkxIJBLh22+/hUQiwe7du/Hrr78KXVIpJYMGzToRhpubG+bOnYvk5GT8+OOPiIqKQkFBAdatW4dmzZqha9eu2Llzp10c6I/YHgobhJhYs2bNMG/ePDRs2BCenp5Cl2OEgoblkUqleP3113Hx4kX89ddfePXVVyEWi5GQkIAhQ4YgJCQEH3zwAbKzs4UulZBKo7BBiBksXrwYly9fRocOHYQuhUNBw7IxDINu3bph586dSElJwbvvvgtvb29kZGRg0aJFCAoKwtChQ3Ho0CEaX0MsHoUNwiuJRILRo0dj9OjRdrlceXkcHR2Njo4q9GHZKWhYl8DAQHzwwQdITU3Fli1b0K5dO2g0GuzYsQO9e/dGSEgIlixZgvv37wtdKiFlorBBeCUSiRAcHIzg4GC7XK78RXQ6HVauXIlGjRrh8ePHgtWh1Wq53yloWA+ZTIYRI0bg5MmTuHjxIqZNm4batWsjNTUVS5cuRUhICHr37o0dO3YIHmgJKY4+DQgxI7VajfXr1yMlJQVTp04VrA6ZTAapVEpBw4o1b94cX375JTIzM7FlyxZ0794dLMvi0KFDGDp0KPz9/fHmm2/i5MmTdKh7IjgKG4RXOp0OZ86cwZkzZ6x61UxTkcvl+PHHHyEWi7F9+3Zs3bpVsFocHR0paNgAuVyOESNG4MiRI7hz5w4WLlwIf39/5ObmYu3atejQoQPCwsKwaNEi3Lp1S+hyiZ2isEF4pdPpsH//fuzfv5/CRjlatWqF9957D0DROhy3b982+X1qtdoyXw8KGralfv36+PDDD3H//n0cPHgQo0aNgrOzM5KTk/HBBx+gUaNGaN26NVavXo0HDx4IXS6xIxQ2CBHAwoUL0aVLFzx//hxDhw416fLUWq0WSqUSBQUFFADthEQiQa9evfDDDz/gwYMH2Lp1K1566SWIxWKcO3cOs2bNgr+/P7p3746vv/6aptESk6OwQYgAJBIJtm7dCi8vL1y+fBmzZ882yf0YgoaBWq02yf0Qy+Xs7Izhw4fj999/R2ZmJr788ku0adMGer0eR48exdSpU+Hv74+uXbtizZo1yMrKErpkYoMobBAiEH9/f/z0009wcHBAWFgY74P4SgYNiUQCR0dHXu+DWBdvb29MmzYNp06dwr179/DZZ5+hTZs2YFkWCQkJmD59OgICAtCpUyd88cUXSEtLE7pkYiMobBAioF69eiE5ORlz587ldfxEeUGDxmgQg+DgYMybNw+nTp3C/fv38fnnn6Ndu3ZgWRYnTpzAzJkzERQUhBYtWmDx4sU4f/48zWoh1UZhgxCBBQQEcL8/ffoUjx49qtH+KGiQqgoKCsLs2bNx8uRJpKamYtWqVejYsSNEIhEuXbqE999/H61atULdunUxefJk/PHHHyYdZ0RsD4UNQizErVu30KZNGwwePLjaB9uioEFqqm7dupg5cyaOHz+OBw8e4IcffsCrr74KZ2dnZGRk4JtvvsFLL70ET09PDBw4EOvXr6fuFvJCFDYIryQSCYYPH47hw4fTcuVVpNPpkJWVhYSEBMyYMaPKTdZ6vd4mg8bZs2fRuXNno+XVSdkSEhIQGxvL20BgT09PjBo1Cjt37sSjR4+wf/9+TJkyBQEBAcjPz8eePXswYcIEBAUFoUmTJpg7dy4OHTpErR6kFAobhFcikQjh4eEIDw+n5cqrKCIiAlu3bgXDMFi3bh0+//zzKt1eJBJxA0BtJWhoNBqMGTMGmzZtgpOTEwBg3bp1cHd3R2BgYKntO3fuDE9PT/j6+sLX17fMbQyCgoLg4+PDbduuXTvuuvv37+Pll19GQEAA6tati+XLl1e63rFjx8LV1RWvv/660XU6nQ4SiYS7P19fXwwdOrTM/SQnJ0MqlRptO3fuXO76o0ePonXr1vDz80Pjxo3xxx9/AAC6dOmCTp064ZNPPqlUvVXh6OiIPn364Ouvv0ZaWhouXLiApUuXol27dhCJRLhx4wY+//xz9O7dG3Xq1EHfvn2xevVq3Lp1i8Z6EIC1cQqFggXAKhQKoUshJqZSqdglS5awS5YsYVUqldDlVNuKFStYACwAdtu2bVW+vUajMUFVwti8eTM7YcIE7vy8efPY7t27s7t372YDAgJKbd+kSRP23r17ldq3q6srq9PpyrwuKiqK/eabb1iWZdl79+6xrq6u7Pnz5yvcX15eHtutWzd27ty57HvvvceOHDnS6PqcnBy2Xr16lart7NmzbJcuXcq8LjMzk/Xy8uLq2bVrF1u7dm1Wq9WyLMuyz58/Z+vVq8cqlcpK3RcfcnNz2bi4OPaNN95gAwICuL9fwykoKIgdO3Ysu3nzZjY9Pd1sdZGa4+szlL56El7pdDpcunQJly5dogWkqmnOnDmYOXMmAGD06NGIj48vd1u2jG+MttR9tXfvXgwbNow736tXLxw4cAC1a9cuc/vc3Fx4enq+cL8ajQYODg7ltr7t27cPEydOBFA0a6Np06ZITEyscJ9OTk546623sGLFijL3W9naXrStn58fLly4gOjoaABA//798fTpU25hLmdnZ3Tq1AlHjx6t1H3xwd3dHUOGDMGGDRuQlpaGq1ev4rPPPkNsbCwcHByQmpqKjRs3YtSoUQgMDETDhg0xZcoUxMXF4eHDh2arkwiHwgbhlU6nw6+//opff/2VwkY1MQyDzz//HIMHD4Zarca8efPAsix0Oh3i4+Oxbds2xMfHQ6VS4fnz59UeTGoNLly4gMjISO58z549IZVKy91eqVRi27ZtCAoKQtOmTfHLL7+Uud3jx4/h4eGBpUuXIiAgAK1bt8axY8e464vPENLr9UhNTUVYWFiFtYrFYvTu3bvc6w0BYtKkSfDz80PXrl1x7dq1crd1dXXFwIED4efnh5dfftloEGbx7qF79+7B1dUVXl5e3GWRkZE4d+5chfWaCsMwaNq0KebNm4c///wTubm5OHDgAN566y20bt0aIpEIt2/fxrp16/Daa6/Bx8cHzZo1w8yZM7Fnz54az8YilonCBiEWSCQS4ccff8TUqVPxxx9/YPfu3QgODka3bt0wYsQI9OzZE82aNeOmINpqsMvOzq50a4BWq0WPHj3QuHFj3L9/H6tWrcKoUaOQkZFR5vYtWrTAoEGDkJaWhmnTpmHw4MFGA2wNli1bhhYtWqBNmzY1eizOzs7w9fXFwoULkZaWhh49ehi12hTn7e0NmUyGDRs2ICUlBf7+/pgyZUqZj3nGjBlYvHgxHBwcuMu9vLws5tgnzs7O6N27Nz7++GOcOXMGubm52Lt3L2bNmoWoqCgAwLVr1/DFF19g4MCB8PLyQuPGjTFx4kRs3rwZycnJNObDFvDRp2PJaMyGeQk5bsJWxmyUtGvXLpZhGK7/WyKRsC4uLtwpLi5O6BJNxsnJqczLjx49WuaYjZJatmzJ7ty5s1L35eHhwZ47d87osk8//ZRt27Yt++zZs0rtw2Dx4sWlxmyU9OzZMxYA++jRoxfu7+rVq6yLi4vRZSqVih04cCA7bdq0Uttv3LiRnTp1apVqFkpOTg67c+dO9s0332QjIiJKjfcAwPr5+bFDhgxhV69ezV64cIEbn0JMj6/PUNvp3CXEBul0OsycOdPom51MJuN+12q1mDt3LgYNGgSxWCxEiSbl4+ODR48eVbp1Q61WG33DZxim3G6XF227ePFiHDlyBAcPHkStWrWq+QjKv0/DTKHy6tNoNNx1DMMYjcVRKpUYOHAgGjZsiNWrV5e6bU5ODnx8fHip2dQ8PT3x6quv4tVXXwVQ1MV18uRJnDhxAidOnMDZs2eRlZWFHTt2YMeOHQAAFxcXtG3bFm3atOFOxbuRiOWhbhRCLNjx48eRnp5udFlBQQH0ej00Gg2USiXS0tJw/PhxgSo0rejoaFy5cqVS22ZlZaFJkya4ceMGAODUqVO4e/cu2rZtCwCYPn06Pv74YwDA+fPnERMTwz23u3btglwuR8OGDQEUDdJNSEjAgQMH4Orqystj2bNnD/r06YMnT54AKJrCGxMTA1dXV6hUKvTo0QOHDh0CAKxatQpjxozhXutvv/0WPXv2BAA8f/4cffr0QbNmzcoMGgBw5coVtGrVipe6zc3DwwP9+/fHJ598gr///hsKhQIJCQlYtmwZ+vbtC1dXVzx79gx//vknPvzwQ/Tv3x/e3t4IDQ3F8OHDsWrVKvzzzz+01oeFoZYNQiyY4QicEokEMpkMBQUFYFkW+fn5ZW5na/71r39h+/bt6N69OwDgjTfewN69e6HRaPD8+XOuxePq1avw8/PDhx9+iCFDhiA3Nxc+Pj74+eef4e3tDQC4e/cuN7alZcuWGD9+PLp27Yr8/HyEhITgl19+4VqN/vvf/6JOnTpGg0J79uyJH3/8ERs3bsRbb72FpKQkuLm5GdXbsGFDPH78mAsJBw4cQGhoKM6cOYP+/fvj4sWLiIqKgkajQWRkJLZs2QKgqBUjMTGRGxw5adIk3LlzBw0aNAAAtG/fHl999RUA4Ny5czh27Bhu3bqFH3/8kbvvxYsXY8qUKSgoKMDx48fx3Xff8ftiCEQul6Nz587o3LkzgKLWvmvXruGff/7B6dOncfr0aSQmJuLevXu4d+8efv75ZwBFLUZRUVFcy0erVq0QHh5uky2A1oBhWdseeZOXlwc3NzcoFArevqGQ8qnVam4BpAULFhg1U9vyfZtKfHw8evbsCblcDqBoZoQhcBR39OhRdO3aVYAKTUuj0SAqKgr79u1DSEiI0OUAAC5duoSuXbviwYMHRl1aluL9998HACxatEjgSsxHoVDg7NmzXPg4ffp0mVNqnZyc0Lx5c0RHR6Nly5aIjo5G48aNK5zhZO/4+gyllg3CK4lEgsGDB3O/k5rp1KkT/P39uaZ3nU5XKmj4+PigU6dOQpRnclKpFJs2bcKYMWOwf/9+bhVRIe3cuRNr1661yKBx7NgxJCQkcCuK2gs3NzfExsYiNjYWQNH6M/fv3+eCx5kzZ3Dp0iXk5+fj5MmTOHnyJHdbmUyGyMhILnxER0ejadOmFvn6WjOLadnQaDSYOHEidu3ahX/961/46aefABS9ucpkMqMBYp07d0ZcXFyl9kstG/bDFls2AOCXX37Ba6+9BolEUmY/9L///W9s3rxZgMoIsR46nQ5JSUk4f/48Lly4wJ3y8vJKbSuVShEREYHIyEg0a9YMkZGRiIyMhK+vr9UfAqCqbKpl49mzZxgwYACio6Mxa9YsJCcnc9c9efIEgYGBSElJEa5AQgQ0aNAgbN++HTNnzjQaLBoQEIDevXtj/fr1AlZHiHUQi8Vo1KgRGjVqhJEjRwIo6pZMTk7mgochiOTm5uLy5cu4fPmy0T48PT2NwkdkZCQiIiIsosXN0llE2DAs89u7d28sWbLE6LqqLPELACqVCiqVijtfVmolpqPX67llnRs3bkwHY6sGjUYDvV5v1Iw7aNAgDBgwAMePH0dWVhb8/PzQqVMno8Fuz58/xw8//IA333zT7r59EVIdIpEIYWFhCAsL4w6KZ+iCuXLlCq5cuYKrV6/iypUruH37Nh49eoSjR48aLQXPMAwaNGiAyMhING3aFBEREYiIiECDBg1spnWVDxYRNipa5rf4Er979+5Fw4YNsWbNGjRt2rTM7ZcvX46lS5easlxSAa1Wi507dwKwra4Mc9FoNEZdJcUDh1gsLncQKMuyGDZsGPbt24eTJ09i/fr13KBSQkjlMQyD4OBgBAcH41//+hd3uVKpxI0bN7jwYTjl5OTg9u3buH37NvfeBxT9v4aFhSEiIgKNGzfmQkjDhg3tsiXEIsJGRYov8fvVV19h+fLlGDZsWLnHFFiwYAHmzJnDnc/Ly0PdunXNVS4h1VYyaFRlOBXDMBg4cCAOHDiArVu34ubNm9i9ezeCgoJMUSohdkcul6Nly5Zo2bKl0eUPHjzAlStXcPnyZdy4cYM7PXv2DLdu3cKtW7ewe/dubntDmCkeQBo1aoTw8HB4eHiY+2GZjcWHjWbNmmHTpk3c+dmzZ2PRokXcgZRKkslkNIqYWJ2SQUMqlcLR0bFK+xg3bhxCQ0MxZMgQXLhwAa1atUJcXJxNToklxFL4+PigZ8+e3KJrQNEXhczMTNy4cQOJiYlGIeTx48fcmiAlZw3VqVMH4eHhCA8PR4MGDYx+d3Z2NvdD45XFhw2gakv8EmJt+AgaBt26dcP58+cxcOBAXLx4EbGxsVi5ciVmzJhB4zgIMROGYRAQEICAgACjEAIULSVfMoDcunUL6enpyM3NxalTp3Dq1KlS+/T39+fCR/EwEhoaahXd1RYfNvbs2YMvvvgCu3btgru7u9ESv4RYOz6DhkG9evVw4sQJTJw4EVu2bMHKlSsxduxY+p8hxAJ4eXnBy8uLWxHVoKCgAHfu3OHGf9y+fRtJSUncwNTMzExkZmYiPj7e6HYikQh169ZFaGgoQkNDUb9+fe730NBQ1KlTxyK+aFhM2Chvmd9//vmn3CV+CbFmJYOGg4MDb12ATk5O+PHHH9G6dWu0bNmSggYhFs7JyYmbTltSbm4ukpKSuPBRPIw8f/4c9+/fx/37941myRi4ubkZhY/iYSQoKMhsvQQWs6iXqdCiXuZFy5VXjuH4JoZ/Pz6DRkU2bdqEzMxMvPXWW3SMCEKsHMuyePDgAZKTk5GcnIy7d+9yvycnJyMzM7PC24vFYtStWxchISGoV68eNwvH8HtgYCAKCgpsZ1EvYjvEYjEGDBjA/U7KxjAMnJycUFBQAKlUapagkZ6ejjfffBNKpRIHDhzAxo0bUb9+fZPfLyHENBiGga+vL3x9fdG+fftS1xcUFCAlJaXcMFJYWIiUlJRyF80Ui8Xw9/fnpVYKG4RXYrEYzZs3F7oMqyASieDs7Gy2/tSAgAB89dVXmDFjBo4fP47IyEh8+umnmDJlCi2+RogNcnJy4qbXlqTX65GdnY3k5GTcv3+fCx0pKSlct4xarUZaWhovtVA3CrEZlt6NotVqIRaLBR+slZKSgrFjx3IDzbp3744NGzYgODhY0LoIIZbDEEauX7+OXr161fgzlL7OEF7p9Xpu8JJerxe6HIuhVquhVCpRWFhYpcW6TCE4OBhHjhzBF198Ablcjr/++gvR0dG0tD8hhCMSieDv7482bdrwsz9e9kLI/9Nqtdi2bRu2bdsGrVYrdDkWQa1Wc8fr0Wq1FvG8iEQiTJ8+HVeuXEHHjh0xadIkavkjhJgMjdkgxISKBw2gaNaJJS1IFxYWhoSEBKMAdOnSJXz77bdYtmwZ3N3dBayOEGIrqGWDEBMpK2hY4lL6IpGIG9/CsiwmT56MtWvXIjw8HF9//bVFtMQQQqwbhQ1CTMBagkZJDMPg448/RuPGjfHo0SNMnToVUVFROHjwoNClEUKsGIUNQnhmrUHDoGvXrrh8+TLWrFkDDw8P3LhxA3369EG/fv2QmJgodHmEECtEYYMQHmk0GqsOGgZSqRRTp05FUlIS5syZA6lUiv379+P06dNCl0YIsUIUNgjhkUQi4VZOtdagUZy7uztWrlyJ69evY/r06Xj99de5606cOIH09HQBqyOEWAsKG4RXYrEYffv2Rd++fe1yuXKGYSCXy+Ho6Gj1QaO4Bg0a4IsvvoBEUjSBTaVSYcSIEQgLC8Ps2bNfeAwGQoh9o7BBeCUWixETE4OYmBi7CRslF+liGMaipreawsOHDxEcHAyVSoVVq1YhJCQEkyZNwt27d4UujRBigShsEFIDKpUKBQUFgq8Kam5169ZFQkICDh48iE6dOkGtVuPbb79FeHg4RowYgaSkJKFLJIRYEAobhFd6vZ47mI+tL1euUqmgVquh1+vtMnAwDINevXrh2LFjOH78OPr16we9Xo9t27bh6dOnQpdHCLEgtIIo4ZVWq8UPP/wAwDIPhsYXQ9AwkEqlgh9gTUgdO3bEvn37cOnSJezbtw+tW7fmrvvggw/g6emJUaNGwdnZWcAqCSFCoZYNQqqoZNCQyWQ2G6qqqnnz5li4cCF3PicnB8uWLcObb76JwMBAzJ8/HykpKcIVSAgRBIUNQqqAgkbVyOVyfPLJJwgNDcXTp0+xYsUKhIaGom/fvvjll1+g0WiELpEQYgYUNgipJAoaVVerVi3MnDkTt2/fxt69exEbGwuWZXHgwAG8+uqr+PLLL4UukRBiBhQ2CKkECho1IxaL0b9/f/z5559ISkrC22+/jcDAQIwYMYLb5ujRo/jhhx/w7NkzASslhJgChQ1CKqH4zBoKGjUTFhaG5cuX4/79+/D19eUu//DDDzFmzBj4+Phg+PDh2LdvH3WzEGIjKGwQUglyuRwSiYSCBo9Eov+9/bAsi+7duyM8PBxKpRI///wzXn75Zfj7+2P69Ok4c+aMgJUSQmqKwgbhlVgsRmxsLGJjY21uBVG5XE5Bw0QYhsHChQtx8+ZNnDlzBjNmzICXlxcePXqENWvW4N133zXa3t7WNCHE2lHYILwSi8Xo0KEDOnToYNVhQ6VS2fyiZJaIYRi0bt0aq1evRkZGBv744w8MHz7c6ABwGRkZCAoKwvTp05GQkACdTidgxYSQyqBFvQgpwTAYVKPRwMnJyai5n5iPVCrlDupX3K+//or09HSsWbMGa9asgbe3N15++WW8/PLLiI2NhYuLi0AVE0LKQ++ihFd6vR4ZGRnIyMiwypaBwsJCbtYJy7L0rdkCjRs3Dr///jvGjh0Ld3d3PHz4EN9//z0GDRoET09PHD16VOgSCSElUNggvNJqtVi/fj3Wr18PrVYrdDlVUlhYaDT7wdHR0eaP3mqNZDIZXnrpJXz//fd48OAB/vzzT8yaNQv169eHTqdDixYtuG03bNiA//znPzh8+DAKCwsFrJoQ+0ZhgxBQ0LBWUqkUsbGx+O9//4ukpCQkJyejdu3a3PXr16/HZ599hp49e8Ld3R29evXCZ599hkuXLlllyxsh1orGbBC7R0HDNjAMg6CgIKPLZs+ejX379uHPP/9EVlYW/vzzT/z5558AgPDwcNy8edOuD6BHiLlQ2CB2jYKGbRs6dCiGDh0KlmVx48YNLmwkJCSgadOmXNBgWRYdOnRA/fr10blzZ3Tu3Bnh4eEURAjhCYUNYre0Wi0FDTvBMAyaNGmCJk2aYNasWVCr1cjNzeWuv3fvHv755x/8888/+OmnnwAAPj4+XPDo2bMnGjZsKFT5hFg9GrNB7JZEIuEW6aKgYV8cHByMlkr39/fHn3/+iffeew9dunSBTCbDgwcPsGPHDkyfPh3r1q3jts3Pz8cff/yBx48fC1E6IVaJWjaIXZPJZJBKpbSWhp1zdHTkVr4FitZaOXPmDI4dO4Zjx46hZ8+e3LanT5/GSy+9BABo0KAB2rZti3bt2qFt27Zo1qwZJBJ6WyWkJPqvILwSi8Xo0qUL97ul0el0peqioEFKkslk6NSpEzp16oSFCxcaXZefn4+GDRvi1q1bSEpKQlJSEn788UcARUva//TTTxg0aBAAQKlUQiKRUKsZsXsUNgivxGIxunbtKnQZZTIMBjUcVI2Q6ujfvz/69++P3NxcnDlzBv/88w9OnTqF06dPQ6FQGM2I2bx5M2bOnInIyEi0bNkS0dHRaNmyJZo2bUrH2SF2hd5xiV0oPutEqVSiVq1aNNOA1EidOnXQp08f9OnTB0DR6rlJSUkICQnhtrl69SpUKhXOnj2Ls2fPcpdLpVJERERg+/bt3MBTlUoFBwcH+rskNonCBuEVy7LIyckBAHh5eVnEG2dZ01stoS5iW0QiUakZK1988QVmzZqFCxcu4Pz589zPJ0+e4PLly/D29ua2XbBgATZt2oTIyEg0a9YMzZo1Q2RkJJo2bYpatWqZ++EQwisKG4RXGo0Ga9euBVD05il0U3HJoEFdKMScRCIRwsLCEBYWhqFDhwIoCuT3799HYmIi3N3duW2vXbuGJ0+eICEhAQkJCUb7CQ4OxuXLl+Hq6goASElJQa1ateDp6Wm+B0NIDdC7LrFZSqXS6PgsFDSIJWAYBsHBwQgODja6fO/evUhMTMTVq1dx5coVXL16FVevXkVWVhby8vKMjmY7ffp0/P777/D09ESjRo3QuHFjo5/BwcHUekcsCr3zEpukVCqNZplQ0CCWztHRES1atDA6kBwAPHr0COnp6Ubh4dmzZ9x1J06cwIkTJ7jrXFxcoFAouPMbN26EWq1GgwYNEBYWhsDAQJqBRczObt591Wo1d+hwYjrFn2NzP9/F76+wsJCbbujo6Ai9Xk+vP7FKrq6uiIiIMPr7PXToEPLz83H79m3cunULN2/e5H66u7sbdR1++umnuHnzJndeJpMhNDQU9evXR2RkJBYvXsxdx7IstYgQI3y9bzIsy7K87MlC5eXlwc3NDW+//TYcHR2FLocQQkyqZGA4dOgQcnJykJubiydPnhgd7dbX1xeTJ0/mzq9duxYqlQq1a9c2Orm7u8Pd3Z0bM0LsR2FhIT7++GMoFIoavf5207JBCCH2oGTLRK9evbjfdTod8vLy8PjxY+Tm5hotNsayLB4/fgytVounT5+W2m/JYHLkyBFIJBIukLi6usLV1dUiF/MjwrOblo2cnBxK5WagVquxcuVKAMDcuXPNOhtFyPsmxNqxLIuMjAzcv3/f6JSSkoKUlBRER0dj69at3LZ16tRBQUGB0T4YhoGPjw9iY2OxYcMG7vI//vgDtWvXRmBgIPz8/GhFVSuSl5cHLy8vatmoLAcHB/rwMQOxWIx27doBKBqUaepvOSzLorCwEGKx2Oj1pdebkKoLDQ1FaGhomdcV757RaDR46623uCCSkpKCjIwMqNVqZGdn49mzZ9z/H8uyGDlyJBdMRCIRfH19ERgYiLp166J9+/aYM2cOdz93796Fp6cnXF1dafyIBeDrfdRuwgYxD7FYbNRsa0qGoKHVaqHVaumNiRATKv7/JZVKsWjRIqPr9Xo9Hj16hLS0NKOWC6VSiZYtWyI9PR3p6enQaDTIzMxEZmYmzpw5A41Gw4UNlmXRtGlTFBYWQi6Xw9/fH35+ftypVatW+Pe//83t++nTp3Bzc6P/fStAYYNYpeJBw4Cm8xEiHJFIBG9vb6NVUQHAyckJx44dA1AUSHJycpCWloa0tDSkp6ejbt263LbPnz+HTCZDYWEhlEol7t69i7t373LXv/LKK1zYYFkWvr6+3E9/f3/4+PhwNbRo0QKvvvoqd9vc3FzUrl2b3icEYjFhQ6PRYOLEidi1axf+9a9/4aeffuKuW7FiBb799ls8f/4cERER+Pbbb8tt6iPCYlmWm+Nvqm8cZQUNuVxuNMqeEGJ5RCIRfHx84OPjg1atWpW63sXFBU+fPkVBQQGysrKMTpmZmWjcuDG3rUKhgEqlAgCkpqYiNTXVaF8DBw7kwoYhkOh0Onh5eXGBxNvbGz4+PmjZsiVef/117rZpaWlwd3eHs7MztZrwxCLCxrNnzzBgwABER0dj1qxZSE5O5q6Lj4/HN998g4SEBPj5+eG///0vxo4dW2o5X2IZNBoNVq9eDcA0y5WXFzQkEgmto0GIjXByckL9+vVRv379crepXbs2CgsLkZ2dzQWShw8f4uHDh3jw4AGioqK4bfPy8ri1Rx48eIAHDx4Y7WvQoEFc2GBZFqGhodBqtXBwcICnpyc8PDy4n+3bt8fs2bO52x4+fBiurq7cNjTWpGwWETacnJzw1ltvoXfv3liyZInRdb/88gtGjRoFf39/AMDMmTPx3nvv4fHjx/Dw8BCgWiKUioIGIcT+yGQy1KtXD/Xq1atwOzc3N6jVajx69IgLJIZQ8vDhQzRp0oTbNi8vDxKJBFqtFmq1mhtfYsCyLBc2WJZFnz59oNPpuOslEgnq1KkDT09PxMbGcl++AODLL7+EXC7n1i0pfnJxcbHpLh6LeJcWi8Xo3bt3mdclJyejWbNmRtt6enrizp07ZYYNlUrFNa0BRX84xPpR0CCE1IRUKuUGmlbEzc0NBQUFKCgowOPHj/Ho0SOjn8WDjVKpRGRkJHd9QUEBtFotF2YiIiK4bVmWxaxZs8rt7u3RowcOHz7MnX/11VchkUiMAolhgbV69eohJibGaN+W3ppi8e/UBQUFpZ5EhmFKze82WL58OZYuXWqO0ogZsSxr9O2BggYhxFQYhoGzszOcnZ0RFBRU7nZOTk64cOECd16pVOLx48fcyc3NjbtOo9Fg5MiRePLkSalTYWEhateuzW2r1+uxZ8+eSgcTHx8faDQauLm5lTpFRkbiP//5D7ftr7/+ColEAldXV6PtXF1dTdqyYvHv1k5OTii57hjLsnBycipz+wULFhjN2c7LyzMa7Uysk0gkglwuh1KphKOjIwUNQojFkcvlCAwMRGBgYKnrHBwcsHnz5jJvV1hYaDTmjGVZbNq0qcxg8uTJE0RGRnLb6vV6PH78GHq9vsyVX7OysozCxhtvvIHc3Nwy6+jUqRM3c8iwLV+TMSz+HTskJATZ2dncea1Wi5ycnHIHDslkMshkMnOVR8xILBbT6HBCiM1xdHQ0OnaXWCw2Wk+kIgzDICMjA0+ePEFeXh4UCgV3ysvL48Y7GrRu3RqPHj0y2s4QdEp+ifv1118RGxtbw0dXxOLDxqBBgzBx4kSMGzcOfn5+WL16NVq1agVPT0+hSyMmxLIsNBpNqdksFDQIIeR/GIaBr68vfH19K7X9gQMHSl2mUqmgUCiMuqoB4L///S/q1KmDuLi4GtdpMWGjYcOGePz4MQoKCqDX63HgwAGEhobizJkzmDhxIrp06YL8/HxERERg48aNQpdLyiESibj589Xt/2NZFkqlEjqdDnq9no7WSwghJiSTyUotxgYAo0aN4m2ShcWEjVu3bpV73fz58zF//nwzVkOqSyKR4KWXXqr27YsHDQBc64YtTwkjhBBbR+/gxGKUDBpA0QBhChqEEGLdLKZlg9gGlmW5aclOTk6VHmNRXtAw9VFjCSGEmB59ZSS80mg0WLFiBVasWMEtD/wiFDQIIcS2UdgggqKgQQghto+6UYigVCoVFzQYhoFcLqegQQghNoZaNoigDDNNKGgQQojtopYNIijDMuQsy1LQIIQQG0Vhg5iV4Tg3xWep0NRWQgixbfQuT8zGMBhUqVSWOrgeIYQQ20UtG4RXIpEIUVFR3O8GJWedFBYWQi6XC1IjIYQQ86KwQXglkUjwyiuvGF1WMmgwDFPqAGuEEEJsF3WjEJMqK2jQrBNCCLEv1LJBeGU4NDxQ1MqhVCqh1+sBUNAghBB7RWGD8Eqj0WD58uUAgBkzZkAiKfoTo6BBCCH2i8IGMZni01zp6K2EEGK/7CZsqNVqqNXqUpeLRCLu27dhu/IwDAOpVFqtbTUaTbnTPU21LQCjgZhV2Var1XLdH1XZtvhzotFowDAMXF1duaDxov1KpVJuDY6qbKvT6Yzuu+RrU3Lb4sdiKUkikXD1WsK2er0eWq223G3FYjHXYmQJ2xbvSqvptsX/P021LVDx/zK9R5S9bXXfI8pS3f/7qr5HVPQ/R+8RZW9b0d9wVdhN2Fi5ciUcHR1LXd6gQQOMGDGCO1/R0Urr1auHMWPGcOdXr17NHU69JH9/f0yYMIE7/9VXX0GhUJS5rZeXF958803u/HfffYecnJwyt3Vzc8OsWbO485s2bUJmZmaZ2zo5OWH+/Pnc+S1btuD+/ftlbiuVSvHOO+9w5+Pi4pCUlFTmtgCwePFi7vfdu3fjxo0bpbZZt24dAGDBggXcH+/vv/+Oy5cvl7vfefPmwdnZGQBw8OBBnDt3rtxtZ86cidq1awMAjhw5gn/++Ye7buXKlUbbTpkyBd7e3gCA48ePIyEhodz9jh8/HgEBAQCAU6dO4fDhw+VuO3r0aAQHBwMAzp8/j/3795e77fDhwxEeHg4AuHr1Kn799ddytx08eDCaNGkCAEhMTMTOnTvL3XbAgAFo3rw5AODOnTvYtm1budv27dsXMTExAIDU1FT88MMP5W4bGxuLDh06AACysrKwfv36crft0qULunbtCgDIycnB2rVry922Xbt26NWrFwBAoVBg9erV5W7bqlUrvPTSSwCAgoICrFixotxto6KiuJlQxbvzyhIREYEhQ4Zw5yvalt4jipjiPcJgwYIFXDgx13tESfQeUaTke8Q333xT7rZVQe3ahBBCCDEphrXxpRzz8vLg5uaGnJwcuLq6lrqemkjL3rYqTaQajQYFBQWQyWTQarVcq8LcuXPh4OBgtiZSpVJZ6r7L21boZk9LaSKlbpQi1I1S9W2pG8U+3iNyc3Ph5eUFhUJR5mdoZdlNN4qDg0OlFpKqymJTVdm2+D+/NWxb/M21IizLQq1WQyQSQafTGd2urOe8svut6rZisdjovip6vYv/M1Vmv0JvKxKJKv23ZgnbVmXRNkvYFjDd/z29R1jOtpbwv2zL7xEvYjdhg/CPZVkUFBRw3yxYloVIJEJERAQAOsAaIYSQIhQ2SLWUDBrFp7cWH3hHCCGE0FdPUmUVBQ1CCCGkJPp0IFVCQYMQQkhVUTcKqbTKBA21Ws2tWVB87jwhhBD7RV9HSaVpNBpq0SCEEFJl9ElBKq34mhkUNAghhFQWdaOQKnF0dATLstziN4QQQsiL0FdTUi69Xl/mCnYUNAghhFQFhQ1SJr1eD6VSCaVSWeGSuYQQQsiLUNggpRiChl6vB8uyKCwsFLokQgghVozGbBAjxYMGUNRlIpfLK317kUiEBg0acL8TQgghFDYIR6/Xo6CggDvqo0gkglwur1JokEgkGDFihKlKJIQQYoXoqycBwE/QIIQQQspCnySEggYhhBCTom4UO2dYgpyvoKFWq7FixQoAwLx582i5ckIIIdSyYe8YhuECAV8tGhqNBhqNho/yCCGE2ABq2SBwcHAAwzAQi8XUdUIIIYR3FDbsUFnLjUulUoGqIYQQYuvoa6yd0ev1yM/Pp24OQgghZkNhw44Un3VSWFgIrVYrdEmEEELsAIUNO1HW9FaxWCxwVYQQQuwBjdmwA2UFDScnJ5McvZVhGNSrV4/7nRBCCKGwYePMGTSAooGmY8aMMcm+CSGEWCfqRrFh5g4ahBBCSFkobNgoChqEEEIsBXWj2Ci9Xi9I0FCr1Vi9ejUAYObMmbRcOSGEEAobtkoikUAul0OtVkMul5u1RaOgoMBs90UIIcTyWUU3yqJFi+Dq6gpfX1/udObMGaHLsngSiYS6TgghhAjOKlo2cnNz8cUXX9AshwrodDrodDrqtjATlmWh1Wqh0+mELoUQQqpNLBZDIpGY/Eup1YQNT09PocuwWDqdDkqlEizLgmVZyGQyoUuyaWq1GllZWdRdRAixCU5OTvDz8zPpl1WrCRvJyclo0qQJ8vPzMWrUKLz//vtlbqtSqaBSqbjzeXl55ipTEMWDhuF8WQdaI/zQ6/W4d+8exGIx/P39uSPmEkKItWFZFmq1Gjk5Obh37x4aNGhgsiN/W0XYaNmyJZycnHD16lXcv38f3bp1Q2RkJAYPHlxq2+XLl2Pp0qUCVGl+JYOGWCw2+2BQe6NWq6HX61G3bl04OTkJXQ4hhNSIXC6HVCrF/fv3oVar4ejoaJL7sYoBosuWLcP48eMhEokQEhKCwYMHIyEhocxtFyxYAIVCwZ3S0tLMXK15WGrQYBgG/v7+8Pf3F7wWUzJV+ieEEHMzx/uZVbRsqNVqo74khmEglUrL3FYmk9n8mAVLDRpA0XLlEyZMELoMQgghFsTiv56xLIsOHTpg165dAIAHDx5gz5496Nmzp8CVCcOSgwYhhBBSFosPGwzD4LvvvsPq1avh6+uL9u3bY8qUKejbt6/QpQmisLCQggYhhBCrYhXdKM2bN8exY8eELsMiyOVyFBQUQCQSWWTQ0Gg0+OqrrwAAU6dOLbe7ixBr9/jxYzRu3BhnzpxBcHCw0OWQahg8eDDat2+POXPmCF2KzbP4lg1izHCcE0sMGkBRt5dhcK6hBYZYjs6dO4NhGDAMAwcHBzRu3Bhbt26t8jZ86tq1a41rrsp21TVmzBi8/fbb3Pnly5ejf//+RkHDUmrlgyX+rVTVsWPH0L9/f27A+p49e4yuX7RoEZYtW2aSJRJedN8GX3/9NUJCQuDo6IiWLVvi+PHj5e4zODiYe76Ln6ZOncpts3btWkRGRsLV1RWurq5o164d9u/fz/fDqzIKGxau+AHVDEQikUUGDWLZWJbFpUuXsGLFCmRlZeHWrVvo06cPRo0ahXv37lV6Gz78/fffOHz4sNFlhw8fxt9//13lms1Rt16vx759+zBgwAAAgFKpxIYNGzB+/HiLq7U8Xbt2xaZNmyq1rSX9rdREfn4+oqKisGbNmjKvj4yMRHBwMLZs2WL2+waA7du3Y9asWVi4cCEuXryITp06oW/fvkhNTS1z+7NnzyIrK4s7/fnnnwCAIUOGcNsEBgbi448/xrlz53Du3Dl0794dAwYMwPXr1/l9gFXF2jiFQsECYBUKhdClVJlWq2Xz8vLYgoICoUupNJVKxS5ZsoRdsmQJq1KpbO6+lUole+PGDVapVJpk/6Z069YtFgB77do17rKrV6+yANj9+/dXehs+pKamsoMHD2anTJnCRkdHs1OmTGFfe+01Nj09vco1m6PuY8eOsd7e3qxOp2NZlmV37drFenp6WmSt5enSpQu7cePGSm1rSX8rfAHA7t69u9TlS5YsYTt16iTIfcfExLCTJ082uqxRo0bs22+/Xan9zpw5k61fvz6r1+sr3M7d3Z1dv359uddX9L7G12cotWxYKJ1Oxy2HrdVqoVarBa6IWLvz58/D3d0dERERAID09HQsXLgQMpkMzZo1q/Q2fKhbty527NgBNzc3XLhwAbVr18bPP/+MgICAKtdsjrr37t2L/v37c+sRHDt2DK1atbLIWvlgSX8rphYTE4MzZ84YrTxt8NFHH6FWrVoVnirq9qiIWq3G+fPn0atXL6PLe/XqhZMnT1bq9j/99BPeeOONclu6dTodfv75Z+Tn56Ndu3bVqpMvVjFA1N4UDxpA0awTGmhp2dRqdaUCoWEGUXFKpbJSB3RzcHCo0bELLly4AIVCARcXF+j1eiiVSsjlcqxbt477kK/MNgAwfPhwJCYmcufv37+P5s2bo1GjRoiJicHYsWO5y3v16oVbt24Z1ZKRkYG5c+fC3d0d0dHRePLkCYYNG4aVK1ca3U9l66nsdlOmTCmzvh07dmDYsGG4ceMGgKIm8A4dOuCbb75BmzZtsHfvXqxYsYLbT0pKCvz9/av8/FZ2u/Ke36NHj5b7GEo+xzXB599KdZ9zcwkICIBKpUJ2djbq1atndN3kyZMxdOjQF96+Oh49egSdTgcfHx+jy318fJCdnf3C2+/ZswdPnz4t8wClV69eRbt27VBYWIhatWph9+7dXCgUCrVsWJiygoalDgYl/8P+/0HwKnPi87ZVcf78eUydOhWXLl3CsWPH0KVLF8ycOdPozaoy2wDAtm3bcOnSJVy6dAnffvstHB0d8cUXX+DatWto2rQpt921a9fK/JabkpKC8ePHY+3atXBxccHatWsxfvx4pKSkVLnmqmxXXn2RkZHw8vLiZr1NmDAB48ePR5s2bZCYmIj09HTExsZyt1MqlaWWdeaz1vKe34oeQ0klv5UfP34ckydPrtS3cj7/VqrznBe3ZMmSMgdFFj+dO3euzMdRGYbwX9aBFevUqYOwsLAKTyW/PFRVyfd2tpLHttqwYQP69u1bKvQCQMOGDXHp0iWcOnUKU6ZMwejRo7lQJ5gadcJYAWsas2EYo2E45efnv7AvztKo1Wr2q6++Yr/66itWrVab9b6FHLOhUqnYZ8+evfBU1vibgoKCSt22po+pdu3a7LZt27jz169fZ0UiEZucnFylbYpLTk5mAwIC2IMHD7Isy7IeHh5sfn4+d/3HH3/MLlmypMK6unTpUqOaq7JdRfXt2LGDHTFiBPvll1+yw4YNM9pmwIABRvsZMWIEO3z4cJPWyrKln98XPYbiHj9+zCYlJXGnmJgY9pNPPjG6rLzxYHz+rVTnOS8uJyeHTUxMrPBUmTFUKGfcxKlTp1gAbE5OTqnrli1bxjo7O1d4OnbsWLXuW6VSsWKxmP3ll1+MLp8xYwbbuXPnCveXkpLCikQids+ePS+8b5Zl2R49erATJ04s93pzjNmgsGEhbCFoCI0GiJbv7t27LAD26tWrRpeHh4ezy5Ytq/Q2xeXm5rKNGzdmv/vuO5ZlWTY9PZ2tX7++0TYjR45kd+3aZbKaq7Ldi+rTaDRs/fr12aioKPbZs2fcNu3atWM3bNhgdLvPPvuMjYqKMlmtLFv6+a3MY6hIZQeI8vm3Ut3n3BTKCxvr169nAwMDy7xNycBW1qkyA/jLu++YmBh2ypQpRpc1btz4hQNEFy9ezPr6+rIajeaF982yLNu9e3d29OjR5V5PA0TtBHWdEFM7f/48JBIJwsPDjS7v2bMndu/eXeltDNRqNQYOHIhXXnmFm/55/fr1Us355TXx81VzVbZ7UX0SiQTNmzfHkiVLUKtWLQDAw4cPcfbsWbz88stGt+vduzeuX7+OJ0+emKTWsp7fyjwGPvD5t1Kd55xPz58/57qjAODevXu4dOmS0dTS48ePlxqkaVCTbpTK3PecOXOwfv16fP/990hMTMTs2bORmpqKyZMnAwDWrFmDHj16GO1Xr9dj48aNGD16NCSS0sMu33nnHRw/fhwpKSm4evUqFi5ciPj4eIwcObLSz5spUNiwACKRiBvlTkGDmMKFCxcQHh5eaoBpz549cf78eaSnp1dqG4Nx48bB19cXy5Yt4y67e/cugoKCuPO5ubnIzc1FgwYNTFZzVbarTH03b95EZGQkd/63335DmzZt4O3tbbTvZs2aoVWrVoiLizNJrWU9v5V9DDXF599KdZ5zPp07dw4tWrRAixYtABR9uLdo0QKLFi0CUHT4h927d5vk4JEvum8AeO2117Bq1Sq8//773ErZf/zxBzdQ9dGjR7h7967Rfg8fPozU1FS88cYbZd7vgwcP8O9//xsNGzZEjx49cPr0aRw4cED444nVqF3EClhLN4per2cLCwutvuvEXsds2JN3332X7dChA1tYWGh0+e+//862a9eOValUrFarZSdOnMguWrRIoCpLe1F9arWadXd3N/of7N+/P/vJJ5+Uub99+/axjRs35tbe4Et5z29lHoOlqc5zbk5r1qxhe/bsKch9WxLqRrEjDMNAJpNZfYsGy7LIyclBTk4OLVdug1JSUvDhhx8iKysLbdq0QfPmzdG8eXO888476NevH6KjoxEeHo6IiAjI5XIsXLhQ6JI5L6ovKSkJYWFhRv+DHTt2xPDhw8vd36RJk5CRkcFbjRU9v5V5DJamOs+5OUmlUnz55ZeC3Le9YVgb/0TIy8uDm5sbFAoFXF1dhS4HwP8W6bLF7hK1Wo3ly5cDABYsWFCjdSEs8b4LCwtx79497lgGhBBi7Sp6X+PrM5RaNsxMq9VyizgVFBTQt39CCCE2j8KGGRmChoFhUCghhBBiy+jTzkxKBg2JRAJHR0eb60YhhBBCSqKwYQYUNAghhNgzOhCbidlb0GAYBm5ubtzvhBBCCIUNE7K3oAEUTSWbNWuW0GUQQgixINSNYkIajYb73R6CBiGEEFIWatkwIUdHRxQWFgJAjQ9DTAghhFgrChsmxDCM3bVmaDQabNq0CQAwZswYSKVSYQsihBAiOAobPNJqtUYHVQPsb5Aky7LIzMzkfieEEEJozAZPDINBCwoKoNfrhS6HEGJijx8/hre3N1JSUoQuhVTT4MGD8fnnnwtdhl2gsMGD4rNOWJY1GhhKiCXp3LkzGIYBwzBwcHBA48aNsXXr1ipvw6euXbvWuOaqbFddY8aMwdtvv82dX758Ofr374/g4GCLq5UPlvi3UlXHjh1D//794e/vD4ZhsGfPHqPrFy1ahGXLliEvL4/3+9ZqtXj33XcREhICuVyO0NBQvP/++y/8Mvr1119zxyhp2bIljh8/bnT98uXL0bp1a7i4uMDb2xuvvPIKbt26xXv9fKOwUUMajcZoeqtUKoVMJhOwIkLKxrIsLl26hBUrViArKwu3bt1Cnz59MGrUKNy7d6/S2/Dh77//xuHDh40uO3z4MP7+++8q12yOuvV6Pfbt24cBAwYAAJRKJTZs2IDx48dbXK3l6dq1Kzee6kUs6W+lJvLz8xEVFYU1a9aUeX1kZCSCg4OxZcsW3u/7k08+wbp167BmzRokJibi008/xWeffVbhUWa3b9+OWbNmYeHChbh48SI6deqEvn37IjU1ldsmISEBU6dOxalTp/Dnn39Cq9WiV69eyM/P5/0x8KpGB6i3AgqFggXAKhQK3vetVqvZvLw87qRUKnm/D2ujUqnYJUuWsEuWLGFVKpXN3bdSqWRv3Lhhla/1rVu3WADstWvXuMuuXr3KAmD3799f6W34kJqayg4ePJidMmUKGx0dzU6ZMoV97bXX2PT09CrXbI66jx07xnp7e7M6nY5lWZbdtWsX6+npaZG1lqdLly7sxo0bK7WtJf2t8AUAu3v37lKXL1myhO3UqRPv9/fSSy+xb7zxhtFlgwYNYl9//fVybxMTE8NOnjzZ6LJGjRqxb7/9drm3efjwIQuATUhIqHatFb2v8fUZSi0b1aTRaLhprUBRiwYdcpxYsvPnz8Pd3R0REREAgPT0dCxcuBAymQzNmjWr9DZ8qFu3Lnbs2AE3NzdcuHABtWvXxs8//4yAgIAq12yOuvfu3Yv+/ftzg7+PHTuGVq1aWWStfLCkvxVTi4mJwZkzZ6BSqUpd99FHH6FWrVoVnkp2cxh07NgRR44cwe3btwEAly9fxokTJ9CvX78yt1er1Th//jx69epldHmvXr1w8uTJcutXKBQAgDp16lTq8QqFZqNUAwWNijk5OQldgtmwAo7RkUqlVZrtdOHCBSgUCri4uECv10OpVEIul2PdunXch3xltgGA4cOHIzExkTt///59NG/eHI0aNUJMTAzGjh3LXd6rV69SfcoZGRmYO3cu3N3dER0djSdPnmDYsGFYuXKl0f1Utp7KbjdlypQy69uxYweGDRuGGzduAChqfu/QoQO++eYbtGnTBnv37sWKFSu4/aSkpMDf37/Kz29ltyvv+T169Gi5j4HPfns+/1aq+5ybS0BAAFQqFbKzs1GvXj2j6yZPnoyhQ4e+8PZleeutt6BQKNCoUSOIxWLodDosW7YMw4cPL3P7R48eQafTwcfHx+hyHx8fZGdnl3kblmUxZ84cdOzYEU2bNq2wTqFR2KginU5HQaMCDg4OmD9/vtBlmI1Go8Hy5csFue8FCxbAwcGh0tufP38eU6dOxYwZM/D06VPMmzcP7dq1w5gxY6q0DQBs27aN+/3MmTMYMGAAvvjiC7z55pt44403uOuuXbtW5rfclJQUjB8/HrGxsejatSvWrl2Lw4cPIyUlxejNu7L1VHa7a9eulVlfZGQkvLy8cOzYMXTu3BkTJkzA+PHj0aZNGyQmJiI9PR2xsbHc7ZRKZan/ez5rLe/5regxlPTRRx/ho48+Mqr51KlTmDZtGnfZ/v370alTp1K35fNvpTrPeXFLlizB0qVLS9VY3NmzZ0u1NFWWYcHFgoKCUtfVqVOn2i0G27dvx08//YStW7eiSZMmuHTpEmbNmgV/f3+MHj263NuV/ALBsmy5XyqmTZuGK1eu4MSJE9Wq0ZwobFSRWCyGg4MD1Go1BQ1iVS5evIiJEyciLCwMQNGo92bNmmHixIkICQmp9DbF3bt3D4MGDcIPP/yAZs2aITExEU2aNOGuL++DsEOHDqUuK/5hXpWaq7JdRfVNnz4d33zzDa5cuQKWZbkP5b1796Jnz55GqwB7enriyZMnJq21rOf3RY+huJLfykeOHIlXX30VgwYN4i4r71s5n38r1XnOi5s2bRqGDRtWZp0GxWcEVVVubi4AwMvLq9R1JQNbWcoLbPPnz8fbb7/N1d6sWTPcv38fy5cvLzNseHp6QiwWl2rFePjwYanWDqDoudu7dy+OHTuGwMDACmu0CDUa8WEFTDVAVKPR8Lo/UnNCDBDV6/WsSqUS5KTX6ytd9927d1kA7NWrV40uDw8PZ5ctW1bpbYrLzc1lGzduzH733Xcsy7Jseno6W79+faNtRo4cye7atavSdVa15qps96L6NBoNW79+fTYqKop99uwZt027du3YDRs2GN3us88+Y6OiokxWK8uWfn4r8xgqUtkBonz+rVT3OTcFlDNAdP369WxgYGCZt3n8+DGblJRU4amgoKDM29apU4f9+uuvjS776KOP2AYNGpRbY0xMDDtlyhSjyxo3bmw0QFSv17NTp05l/f392du3b5e7r6qgAaIWgi1jJUyJhBqFymJYrnzTpk12sd6IYX0BIU5VGa9x/vx5SCQShIeHG13es2dP7N69u9LbGKjVagwcOBCvvPIKN/3z+vXrpb5hl/etm6+aq7Ldi+qTSCRo3rw5lixZglq1agEo+lZ59uxZvPzyy0a36927N65fv861bvBda1nPb2UeAx/4/Fu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      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Figure 17.1\n",
    "# bias factor and hyperbola\n",
    "RR = rr\n",
    "RR_L = lower\n",
    "xmax = 40\n",
    "x = np.arange(0, xmax, 0.01)\n",
    "f, ax = plt.subplots(1, 1, figsize=(6, 6))\n",
    "ax.plot(x, x, linestyle=\"--\", color=\"grey\", alpha=0.1, linewidth=2)\n",
    "ax.set_xlabel(r\"$RR_{ZU}$\")\n",
    "ax.set_ylabel(r\"$RR_{UY}$\")\n",
    "x = np.arange(RR, xmax, 0.01)\n",
    "x_L = np.arange(RR_L, xmax, 0.01)\n",
    "y = RR * (RR - 1) / (x - RR) + RR\n",
    "y_L = RR_L * (RR_L - 1) / (x_L - RR_L) + RR_L\n",
    "ax.axhline(y=RR, linestyle=\"-\", color=\"grey\")\n",
    "ax.axhline(y=RR_L, linestyle=\"--\", color=\"grey\")\n",
    "ax.axvline(x=RR, linestyle=\"-\", color=\"grey\")\n",
    "ax.axvline(x=RR_L, linestyle=\"--\", color=\"grey\")\n",
    "ax.plot(x, y, linestyle=\"-\", color=\"black\")\n",
    "ax.plot(x_L, y_L, linestyle=\"--\", color=\"black\")\n",
    "high = RR + np.sqrt(RR * (RR - 1))\n",
    "high_L = RR_L + np.sqrt(RR_L * (RR_L - 1))\n",
    "ax.scatter(high, high, marker=\"o\", color=\"black\")\n",
    "ax.scatter(high_L, high_L, marker=\"o\", color=\"black\")\n",
    "ax.text(high_L + 5, high_L, \"(15.52, 15.52)\")\n",
    "ax.text(high + 5, high, \"(20.95, 20.95)\")\n",
    "ax.set_xlim(0, 40)\n",
    "ax.set_ylim(0, 40)\n",
    "ax.legend(\n",
    "    [\n",
    "        r\"$RR_{ZU} * RR_{UY} / (RR_{ZU} + RR_{UY} - 1) = 10.73$\",\n",
    "        r\"$RR_{ZU} * RR_{UY} / (RR_{ZU} + RR_{UY} - 1) = 8.02$\",\n",
    "    ],\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## application"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
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       "   mar  MINDEXSUM  PTbirth  smoking  drinking  hispanic  black  \\\n",
       "0    1          4        0        1         0         0      0   \n",
       "1    1          1        0        1         0         0      0   \n",
       "2    2          0        0        0         0         0      0   \n",
       "3    2          0        0        1         0         0      0   \n",
       "4    1          0        0        0         0         0      0   \n",
       "\n",
       "   nativeamerican  asian  agebelow20  ageabove35  somecollege  preeclampsia  \n",
       "0               0      0         0.0         0.0          1.0           0.0  \n",
       "1               0      0         0.0         0.0          0.0           0.0  \n",
       "2               0      0         1.0         0.0          0.0           NaN  \n",
       "3               1      0         0.0         0.0          0.0           0.0  \n",
       "4               0      0         0.0         0.0          1.0           0.0  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NCHS2003 = pd.read_table(\"NCHS2003.txt\", sep=\"\\s+\")\n",
    "NCHS2003.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.378674\n",
      "         Iterations 6\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.2676077954509872, 0.004423678272658207)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_logit = smf.logit(\n",
    "    \"\"\" PTbirth ~ ageabove35 +\n",
    "        mar + smoking + drinking + somecollege +\n",
    "        hispanic + black + nativeamerican + asian\n",
    "    \"\"\",\n",
    "    data=NCHS2003,\n",
    ").fit()\n",
    "est, se = y_logit.params[1], y_logit.bse[1]\n",
    "est, se"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.306834493057289\n",
      "1.9400658087603366\n"
     ]
    }
   ],
   "source": [
    "est, lower_ci = np.exp(est), np.exp(est - 1.96 * se)\n",
    "print(est)\n",
    "print(evalue(est))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.295552682600102\n",
      "1.9143451120885522\n"
     ]
    }
   ],
   "source": [
    "print(lower_ci)\n",
    "print(evalue(lower_ci))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ],
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(1, 3, figsize=(10, 4))\n",
    "RR1 = np.arange(1, 1.5, 0.01)\n",
    "ax[0].plot(RR1, evalue(RR1), linestyle=\"-\", color=\"black\")\n",
    "ax[0].set_xlabel(r\"$RR$\")\n",
    "ax[0].set_ylabel(r\"E-Value\")\n",
    "ax[0].set_xlim(1, 1.5)\n",
    "\n",
    "RR2 = np.arange(1, 3, 0.01)\n",
    "ax[1].plot(RR2, evalue(RR2), linestyle=\"-\", color=\"black\")\n",
    "ax[1].set_xlabel(r\"$RR$\")\n",
    "ax[1].set_ylabel(r\"$RR$\")\n",
    "ax[1].set_xlim(1, 3)\n",
    "\n",
    "RR3 = np.arange(1, 10, 0.01)\n",
    "ax[2].plot(RR3, evalue(RR3), linestyle=\"-\", color=\"black\")\n",
    "ax[2].set_xlabel(r\"$RR$\")\n",
    "ax[2].set_ylabel(r\"$RR$\")\n",
    "ax[2].set_xlim(1, 10)\n",
    "plt.show()"
   ]
  }
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