{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "path_data = '../../../../data/'\n", "\n", "import numpy as np\n", "import pandas as pd\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "plt.style.use('fivethirtyeight')\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "\n", "baby = pd.read_csv(path_data + 'baby.csv')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [ "remove_input" ] }, "outputs": [], "source": [ "\n", "def standard_units(any_numbers):\n", " \"Convert any array of numbers to standard units.\"\n", " return (any_numbers - np.mean(any_numbers))/np.std(any_numbers) \n", "\n", "def correlation(t, x, y):\n", " return np.mean(standard_units(t[x])*standard_units(t[y]))\n", "\n", "def slope(table, x, y):\n", " r = correlation(table, x, y)\n", " return r * np.std(table[y])/np.std(table[x])\n", "\n", "def intercept(table, x, y):\n", " a = slope(table, x, y)\n", " return np.mean(table[y]) - a * np.mean(table[x])\n", "\n", "def fit(table, x, y):\n", " a = slope(table, x, y)\n", " b = intercept(table, x, y)\n", " return a * table[x] + b\n", "\n", "def residual(table, x, y):\n", " return table.column(y) - fit(table, x, y)\n", "\n", "def scatter_fit(table, x, y):\n", " #fig, ax = plt.subplots(figsize=(7,6))\n", " plt.scatter(table[x], table[y], color='blue', s=20)\n", " \n", " plt.plot(table[x], fit(table, x, y), lw=2, color='gold')\n", " plt.xlabel(x)\n", " plt.ylabel(y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Prediction Intervals ###\n", "One of the primary uses of regression is to make predictions for a new individual who was not part of our original sample but is similar to the sampled individuals. In the language of the model, we want to estimate $y$ for a new value of $x$.\n", "\n", "Our estimate is the height of the true line at $x$. Of course, we don't know the true line. What we have as a substitute is the regression line through our sample of points.\n", "\n", "The **fitted value** at a given value of $x$ is the regression estimate of $y$ based on that value of $x$. In other words, the fitted value at a given value of $x$ is the height of the regression line at that $x$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we try to predict a baby's birth weight based on the number of gestational days. As we saw in the previous section, the data fit the regression model fairly well and a 95% confidence interval for the slope of the true line doesn't contain 0. So it seems reasonable to carry out our prediction." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure below shows where the prediction lies on the regression line. The red line is at $x = 300$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [ "remove_input" ] }, "outputs": [ { "data": { "image/png": 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vp04JC51aLcLff8sQF6fCyZO6kaRwYdWICGD9+gy9/myhBVjZSriXroBH2bsmm1R4LUO1NBlgXCAD0EmgjT2eTYcWurFjx3L/79q1K7p3747o6Gjs378fI0eONHkcy7JgGJpHJwhHQ+euf/MmA4WCQevWLORyFpWVQM+eMrRty+LSJf5UY3m5sVi5u7No04bFzZsM9KcrXV1Z9Oih5qYdZ840rkqgz82bwmEF+jF1164xmD69M8rKPK0uN9Ts0SjhUboU7uWfmmxS0eotVHtOBxjHdeJ3XMsECAgIQGBgILLuTpi3a9cOarUaRUVFvHaFhYXc9CZBEA3HXNFRawqS6tbtzp9XIienFOfOKeHhAZw7V+vWX1Nj8nCO2Fg1goM1MFyTE4nAObDorhUUZDo3ZW6uCAMHyozCCvSxxOuyMYqy2q3Qq0YBieJ5rUNJfrCgyJV7p6PEvxglAQpUS590aJEDHHxEZ0hRURHy8vI455Tu3bvD1dUVhw4dwmOPPQYAyM3NRUZGBvr27WtPUwmiWWBp9hJzwd/1DQzXYY0XI8OwcHMDqqqAoiLj4zQarcNLYSEDmUx7Hzk5pl/CLMtAqTTvVSn02bDfKiu1Yg1o+2DAABmvyoG5EeC1a9oYPl14Q2SkGps2lTe4X62BURfC4858uFXuFNzPQoxy+XqoPB4FmuFsmV2FTqlUcqMzjUaDnJwcnDt3Dj4+PvDx8cGKFSswcuRI+Pn5ITs7G0uXLoWvry8eeeQRAIC3tzcmTZqE1NRU+Pr6wsfHB6+88gq6du2KwYMH2/HOCKLpEBIrSzH3MtU/b24uXyz0X/6Wut8L2cmyEKgXJ3S8VihYlkFVFXD2rAskEuORWk2N6UKpliIU/2fodTl5sidP2Nzc+McolSIolZYJ1KxZtecCtPemq/qgT33CGsx9kWHUNyEpeRmuVT8IHssyXiiXr4XK42Grr+to2FXo/vzzT4wYMYL7nJaWhrS0NEyYMAHvvPMOLl68iG3btqGkpAR+fn4YNGgQNmzYAC+vWtfU5cuXQywWY9q0aaisrER8fDw++eQTiMVCMTYE4XwIiVV6umXHmnuZmnPj1xcDS93vhewEhNfgjDF+yavVDGJiVMjIEKO6Whc8XrcY1I4Ka9uaqzO3dm05Jk1ioFTWrtHFxfHd481Nt9YlUEL7dcLU0LAGwz5PTcnHjg9mwqX6iGB7jagdyuVroXa/z+prOTJ2FbpBgwZBoVCY3L9r1646z+Hh4YFVq1Zh1apVNrSMIJoPDfnmb+5langed3cWQUEaIzEQqjsnNJIwHLmdOSOGv7+52m46W4Tvh2WBf/4RoarKolvlkZ5ehhdf9ERlJQMPD9aozpyh/UuXXsTgwaa9LV1dtQIq5PRiKFCG59ZNsRoeY4t6foWFDDp3vIwNy6fh3u4ntBsNIiPU4g6okK+B2s15l3sYhUJh0deEGzduoG3btiYzmFRUVKCwsBAhISE2NdDRcVQ37uYI9WX9MAzCjotTIT39jEV9ef06Y/Qy1U1tCZ3X0jUioWP/+kuEigrD0RsLYyET2iZE/dvJZBpeZQPDezO0PyamFEeP1gphfLyUN90YE6OChwd/2lSovp3QuWNjVWBZGK3RNcSzU1TzFzwVT0OsuiC4X+0ShXL5x9C4xtb7GvXFocMLYmNjsWbNGs7pw5AffvgBTz75JG7fvm0z4wiCqBuhb/7VFsYzmyuO2pARhdAoU60WEiVLt+nQH+UZtxOLWbi41I6sPD216b6eeUbKG21Z64BSXOwKoHbouHmzcN+Y+tJg7tylpQxOn1YatbO2zJG4+n+QKGZCrL4quP/8P3Fwbf8h/EPvMXkOZ8VioWMN030boFKpKHaNIOyAkFgdOuSGZ5+VWl0Lrq7zWorQlKhtcq2bf8f06qXmbD52TISkJClmzpQKFF/ln8fLy7wDilzOX4Qz1TeW9FdD1jQNzy+u+gWeipkQaW4JnkPlNgjl3h+AdemAkIA6TWsScnIa/mxai1XBD6aErKSkBD///DPFrhGEg5Ca2tFsbJg5bBG/JZTQuWPHxk60zmLx4gruU1KSFEqlCBpN3U4qht/jU1MrIJNp4OKirXLw7LM5wgdaiH6fVlVppzrrqshuapTpUvkTWt1qD+88OWS3RxiJXI37Q7jT7gJKAhQoa7MHrEuHBtluaxrybNYXsyO6FStWYOXKlQC0Ijdr1izMmjXLZPunnnrKttYRBAHA+mkshcKV99kal39bxG8JjXjc3a06RT1gMHy4DIDWOcSSwHMdly6J0a2bjMvWcvs2w63hKZUMPvooGElJ5hxnzGPowarz8jSH/shvzIM7sf2dJLjkCVearfYYjcpWK8GKHX+wYemzaUvMCl2PHj0wdepUsCyLzz//HPHx8QgPD+e1YRgGnp6e6NGjB0aNGtWYthJEi8Va8ZHLa3Djhgf32ZrpscYqS1Naaul5LHUyEUJ7nDUip23PICdH6wyiNF4uM1qjsxbDPqwzzo5l8fX69Wjv8rTJc1ZLJqKi1RuASF5vu+yBpc+mLTErdA899BAeeughANoCp9OnT0fv3r0b3SiCIPhYKz7Lll3F8uVRdTqSGJ7n9GkxPDzqVzC1LgzXpkwhkbCoqLDlt/yGCKcWT8/aaVdrR9eA+XvnfgesBm7lGyC58zIAwFvg7VzlOROVXqlAE5e5sSWWPpu2xOI1uo8++ohEjiDshLXVuoOCqnlFSkePlgqutxmeR6XSTtnJZBoEB6shk2lw6xZT51qdJet62heaod3G96EVubrbNQzrzlddXXs/kyd78taYJk+ue41Jf81Sv7K5SKTG7CfeuVuotDUncvqsXD8X8U/eQUmAApXeq5q1yAG1z6ZhYd3GxOI4OgBQq9U4ePAgrl27huLiYiNPTIZhMG/ePJsb6chQ7JftoL40jbl4NyF0fVlXLJzuvKdPi6FS1b7M3d2159Z3yTcXR2fuOvojoKwsERo6umo4LNavL7vrjcnwtpuyzc1Ng4KCUgCAn18rXr+4u7PIz79j8dWvX1fh+J4P8dTY10y2eXdLKuatfAU1NW4AgLAwtWAIQnPEoePozp07hyeeeAI5OTkmQw1aotARRFNQX1f/uqY8dec1FCqhDB9CyYx1+SrPnOGn3NPPgmK+Irh9GDtWjTfe0BhUH7ckfq+e6NVyi3EDYsYaN9Gv5fblT1LU1NT2GVU1bxgWP31z5syBUqnE5s2bMWDAAMjl8kY0iyAIW2BpzJZ+cHhurshkKitT+Sr1p/YA80mfHYEuXWRWOMdo03vp6uV16KBGRkbtq7NzZxNhEw2o5WaL9F9ELVaN6FJSUjB8+PDGtIcgHJb6OCHY2wZLX5j6I0bD0Z1+KqvRo6W840yJWEUFg+BgL1RWMgLB2vaGQV6ediTHMOzdGDrhignBwRooFAyUShdkZdVWKpDJNJDLWQQGGvSpRgHJnUVwq9hi8url3h+hRjLBbLmbhgTrC+EIz649sVjo2rVrBxcXx5p+IIimpCnrg9nKhvq8MIXEUfdSNDVCNPQoZFnwckmKROxdwXOs0Z224oEpGAQGaisd6IccVFczqK5mEBWlXYdk1IXwKK6rlttnUEketa3xVuAIz649sdjrctasWdi2bRtqrA1QIQgnobHiyxzFBp3npG7U9s03Zfj0U63oxcTIEBzshRs3GM4jMyZGhaoq7XqcSGR+dCASNUXAeENgIbQOpxN7QwLb5eKNZ0bDO0+OVgWdjESuRNkKI5/ZA68+avyQVWxXkQMc49m1JyaHaN988w3vc2BgIFxcXHDvvffiiSeeQHBwsGDNt9GjR9veSoJwAGxRH8zWNuTmipCQILXJVJSp9Tf9aUzdyCYqSmW0jz9q479I3dxYRERocPas4SuHhUikncVTq2F0XONh6GEpfF2ZjOXq0VWV/osPX52FB+79r2BbjcgP5fJPERD+CG80m5goRU5OqQ1ttx5HeHbtiUmhmz59OhiGEfSwXLJkieAxDMOQ0BFOS0MdBGyxTqKz4exZMaqqGFRVMVy+wIZORVnzrV9oH99Vn4+fnwabNpUjNtYLhqJi7rhaLAn6Nl+/jo9lghpYcRDhl8fi7HZh1/4b+eGoav0JfNv34bZVVvLPbfjZHrR05xaTQrdnz56mtIMgHJ6GOghYuk5iThB1NvTsKeO5xttiKsrS9TcAKChgUFNj+TWvXhXjwQdlAnssPYftxKsuYjqfxaYVkxEbeU5wf+aNbnhs9macvdwdgHF8oYcHyysDZJhpxh7Y2rmluWFS6AYOHNiUdhCE02PpiMlQEOPivIwKeBqKUkEBg+vXGbMjxLpGlELf+m/cYJCUJEVFBQOW1Y7MSksZ3tScZcVTGRQU2H9kY4ogvxyMeXAX3n/lBeOdXe7+GwaoEYaHcYb3JePsWTGv77dvL0NiopRXvZywL1aV6bE1v/76K5KSktClSxfI5XJs3bqV21dTU4PFixejf//+CAwMROfOnfHkk0/ixo0bvHMMHz4ccrmc9zN9+vSmvhWCqBNL03gZCqD+9KSOtWvLeamklEoRb39OjptRSi6dgJoqj6L71q+fmmnhQgmUShHUagYaDQNfX7bOrPsMwzbxKEbYkaQuOgRdxcvT3sJvX96LnMMhRiL33+P3448He9RuyALYtm2Nfm9VVQyvLwcM0CAnpxSFhXeQk1OKAQMcLr6ixWFxvMCIESPM7mcYBh4eHggMDMR9992HESNG1BmOUFZWhqioKEyYMAFPP83P0l1eXo6zZ89izpw5iI6Oxp07d7Bo0SKMGzcOv/76K+/cEydORGpqKvfZw8MDBOFoWLpOYioBsL4AhoZqBUff7V1/f2pqR/z1V8OrEmRkiI0+x8aqefZ5erIoL689V0yMGkVFDHIaVsLNCrTXtiSEIaLD3xj74E6MTdiJ3t3+4LaXV0iw/9dh+PrHsTjy+324WRAEAAjFVVxDGABAFReH8rVrsRbliIvz4gXVtzQvxuaGxUKn0WiQl5eHq1evwtvbG6GhoWBZFtnZ2SgpKUFYWBhatWqF//3vf9i0aROio6Px7bffwsfHx+Q5ExISkJCQAAB45plnePu8vb3x7bff8ratXr0a/fr1Q0ZGBrp27cpt9/T0hJ+fn6W3QhB2wdJ1EkOHEx1CI0JTnnRCNb/q47Fp6IvGsrX23brF4PZtBlIpC5FIg9atWfj7s9z+phM6La6uQJVAJZ0u4Rcx7qEdGJewAzGd/+K2K8uk2HvkEezYPw4//DIMao2nUUaY6+jI/T805zhu9RAWNFt6vxK2x+Kpy9deew3FxcX44IMPcOXKFRw5cgRHjx7FlStX8N5776G4uBhvvfUW/vnnH7z77rs4f/48Xn/9dZsaW1qqddE1TD+2c+dOhIWFoV+/fli0aBHXjiCaIzpBPHWq1KhKtz5CVbx1yOX8eFfdCDIuTsVL2FxXhWcXF9bos84+f38WSqUI+fliKJUi+Puz3JRnamoFLJtOtJ0o1IoUi9jIM1g6+1Vc3NsFF/d2xdLnFyOm818oKW2FzbufwKPPfgvfAf9iwsvbsPPAOICRmE7ldZebN7XVynU/IhFrVV8S9sPi6gUPP/wwevbsieXLlwvuX7hwIU6fPo0ff/wRAPD888/jv//9Ly5evGiRIUFBQVi5ciUmTpwouL+6uhojRoyAj48Ptm3bxm3//PPPERISAn9/f1y+fBlLlixBWFiY0WhQn8zMTItsIojmSm6uG1JTO6K42BVyeQ2WLbsKltVOaV68KIVaXfsdNySkErt2nRc8z4gR3XDrVu1SgL9/Jfbs0bYdM6Ybr4CmTrTc3NRgWQY1NcZxto0Hi97d/odxD+3A2Ad3olPoFW5PkaI1vv3vKOw8MBb/PT4U1TXGkeseHir4+KhRVOSC6mpt3zCMNsZPpb6bLsxAlMViDQIDq3l9EBJSifff/xupqR2hUNT2fVBQtdE1c3LcTLbT3yeRqMAwDMrLxUa/y7qu4eiY6wNrqKsaglW5Lh977DGT+8PCwvD5559zn3v27Int27dbenqzqFQqzJo1CyUlJfjyyy95+6ZOncr9v2vXrujQoQOGDh2KM2fOoHv37oLns2WJCCotYzuoL21JJo4e1aC2KnYoEhKk3LqdPgEBLoL9fu0aA6XSjbetffvatgEBLuD7hmlHVNXVTZMqkGE06Bd7QituCTsRGpjN7Sso8sWun8Zg509jcfjUYKhUrmbOBFRWuiAvj283yzLaEa2JgZ5EYtwHBQXumDSpG+eVeuOGB5YvjxKcsn722drfh2E7/X366NoBMHmso6P/d26uD2yJxU9k69atsX//fsyYMUNw/48//ojWrVtzn4uLi+Ht7d1gA1UqFWbMmIGLFy9i7969vGsI0aNHD4jFYmRlZZkUOoJoiRg6TLi4sOjZU23SKWbWLE9eGIFMpkFqagUSEqQoLGQgk7GIjVXh7FkxmiqjiatrNRbMXIGlzy9Gbn4ggvxucvtuFgRg54Gx2HFgHI79MRAaTWOMKLWjPE9PbdhAcDBrFMBvuM5nylHFnHOQtcH6zdUZpqlSk1ksdFOnTsUbb7yBpKQkzJw5E2FhWk+kK1euYO3atTh48CAWLlzItd+/fz+io6MbZFxNTQ2mT5+OS5cuYe/evRY5nFy4cAFqtZqcUwjCAENnlJ491Wa/PRu+dNq1Y7F0qcSowCrDGDut2BIP9wq89txrmP/kSt72IL+buH6zvVbc9o/DibP97iZptjTTij7Cx6hUtf+XyTTYvr3MKFxAKIBfH1NhJOaciUx53uq3c4aUXk2VmsyqenTl5eX48MMPceDAAd4+sViMF154AXPmzAEAVFZWYsqUKTzPSCGUSiWy7t6lRqNBTk4Ozp07Bx8fHwQEBGDKlCn4888/8eWXX4JhGOTn5wMAWrVqBYlEgqtXr+Krr75CQkICWrdujYyMDCxatAgxMTHo16+fVR1BEM5OXeENhgHlMpmxl6fQN/B77uHXZ7MFUk8l0v4vBc8/8aHJNqOf34Vvfx6F+o8mhY/z9NRArdaOzNTq2jZKpQgLF0pw5IjxlwPDF7ZMpkG7dqzZMBJzvw/9fTIZC4YBSkv57ZwhpVdTpSaz2BlFR2FhIQ4fPswFboeEhGDw4MFo27at1Rf/5ZdfBOPzJkyYgAULFiA2NlbwuPT0dEycOBE5OTmYNWsWLl26hLKyMgQFBSEhIQELFiwwG9ZgS2hdyXZQX9qO+vSlYR262FgV3N3BewnNnOlpNKLTf1ldvSqqo/SNaby9FHh7/suYMfYzk22mLPgcm76bjMaYKtWfyh09WsqN0Ni712Kg9bLMz79jdOz164zJ0kYEH3v8nVv9Naxt27YYN26cTS4+aNAgKBQKk/vN7QOA4OBg7Nu3zya2EERLx3C0VlzMwN+f/7LWZvL35ALJdXFruinQ+Hgpzp0z9VoxThXW1udffLDoeST9R9hxrabGBRPmfKkNAag3LNzdIVg1XZ+oKK3XyejRUqvTlbX0XJKODlVSJYgWxrVrDCZPrhWrzp3VWL68wujlfvs2g+xsbRv9JNRVVbWicfasC8aM8USbNlqhZFnWTIYS7efAdrn4eHEyRt4vnDi+pLQVHp/7BfYdGV6PuzMUUxZ+fizKyswLnaenBlVVMBBpFi4uAPTW6Qxj7exdudvU9e1tl6NhUuh8fHwgEomQl5cHNzc3+Pj4gDFT+h3QpgErKiqyuZGOAD04hLMwebIn74V+7pwLkpKkRh6WcrlwirG//+Y7XVy5IsaVK+bfDR2CrmLdsicx9N6DgvtvFgRg4tytOHxqiLW3Y4CxuObn1waSG7fRjvYiIjS4dMnQmURbRRx3ixgIBe3bu3K3qevb2y5Hw6TQzZs3DwzDcDkldZ9bKvTgEM6CYf5KAKio4P9tt27NQi5neWm8bt1icOyYyGIPy84dL+PztKnoF3tScP8/18PxxPwtOHm2qRzHhN5fDKqqtCNThjG+Mf1yO6mpFRgwQMarSmA43Xv2rBg9e8qs+jIsNMLevNmyY02557f0iuKGmBS6lJQUs59bGvTgEM2JnBw3PPus1OIZCEPxun2bgVzO31heLsL48VKYcwSJjTyDTSsm83JK6nP2cgympGzkark5Eq6uQLVBUg59z1P9Ua9SySAxUYqoKA3P27KqikFWlhhZWdqRs6Ezj9DvYNYs4xG2pV+kTbnnt/SK4obYtUxPc8LSEisE0RRcu8YYleHRJzW1o8mSPIbrTBKJBr6+/Niw6mptwmZD9KsU6OgbexKZP3YCe4nBmW96GInc8TP9EPmfS2C6sOg++mwji1z9SvYAQGSkGh4e/H6o0UsZqj+6A7SVw3X5QwMC1EbXvXxZbLYsko6GBICbyndqLg9qS8QqocvOzsbs2bPRvXt3hISE4NixYwCAoqIivPzyyzhz5kxj2OgQ0INDOBJ11ZYTql6gY/Nm/rN84oTSaKRRXc1AoTD9sh0cdwg3jwaAvcTgxLZ7ebklAeDn40PR8YEsMF1Y9J9wHBlXI2HLBM5ahM5nacC4FldXluuHzZvLjUIj+EHg/H0eHrUJrktL676uKfES+tJs6RdpoRqC5ra3VCwWuoyMDNx333347rvvEB4ejrKyMqjV2m+Gbdq0we+//45169Y1mqH2hh4cwpEwNZWuG+nl5/OFTldG5vp1RnCNbe3aci4Tv47WrVm4utZuGxa/D4pTcrCXGBzaeD8CfG/x2u8+OAJB9+WA6cLiwek/4VpuhwbcYdMgEsHstKJQ2R+A5bKk6KisNK6wbjhyNiVea9eW341Z1MbpxcTQF2lbY3F4weLFi+Hl5YWff/4ZYrEYnTp14u1PSEgwWzGAIAjbYWoNRt9pCtBm4GdZxqiMjJBjVWysmnesv78Gj4/4GsuefgIuLsKZjbftS8TsN97Hv7fb8bZr04IJhxdYiru75m5IQEPXw43j94T65cCBMnTurDYIMTC+dlycceo0NzcWKlVtW09PFps3W5b1IzSUFcy2QtgOi4Xut99+w5w5c9CuXTvcvn3baH9ISAjy8vJsahzRNFDoRPPDVOokw5GeWMzP13j2rBhqA83SHaM9pwTxsVuw6qXpJq9dLXkCFa1eR8/ewSbzO9oi92VdAd6W5rRs317DxQNyWw3s0/WBTpxOnxbzhIu7IiMsWP7+GmRliXifbR1ETn+n9cfiqUuVSgWpVGpyf3FxMcTipqw/RdiKutZ7CPtj6HwCQHAq3XB6zMOD/7mqijF6gfv6quFWtg4xbt44udFNUOQ+2PIcZL1K0XdKDS4p0pHwcBByc829Pmzhldzw0ZxMxhp5j9aeu5Zr10T49VcRJ049e5ouwjp6tNTIASg3l//uM/xsC+jvtP5YLHRRUVH45ZdfBPexLIs9e/ZQWZxmCoVOOD6WvuR0TlMhIZWIi1Nh+/YyzvFEfw1OJFLj5WmrtM4kn7tDcmeO0bkqpS8ianQpmC4sZr/xAcrKZSgsZDhbdCMuofgz+6HNzCIS1a6jCa+z8dFotOECOnT96ObGvzeWZXi/A90XEEuu0VDo77T+WDx1mZycjCeffBIrV67EmDFjAGgrDvz9999IS0vDn3/+abNCq0TTQjE3js+tW4zZzzp0IxL9xLm66bP/DHPFAz1WYcnzr5m8TqUsBVWy/wMYbcFVr1YevP1CFQyCgjTIyRGhqWrS1WK89ubuDi7p8rFjIiQmSo3CAkyh71Ci68fr1xkgVnduljedevq0GAMHyngZZXRERpoeEdYX+jutPxYL3dixY3Hjxg288cYbWLFiBbcN0Jbpef311/Hggw82jpVEo9JUpTKI+mMY0yYU4yYIWwGP0hVwL3sPv5ooCvDym2/hk69m4+ZN49+70LMxc6Yn74UbGMjPoFI/hNJz1Y1EokFFRa3Q6Hs6GqY1qwvDaV4AvDUwQ2cdlYoxEtG6itk2BPo7rT9WJXV+8cUXMXbsWOzZswdZWVnQaDTo2LEjRo4cidDQ0MaykWhkKPO642OYd1J43ekuGiXau62Ed97XJps8/0Y60rc+DZbVCoFhaIEOw2fj2jVtyixd+86dtS/1Pn28jLKK1I22zhrDAL6+GpSWMoIB6aZwdWVx4oTS6OWvc9qwZCTHMCzEYnApvcyRmlpxVzxNrx3WVcy2IQ4l9Hdaf8wK3aBBg9C/f3/069cP9957L/z9/RESEoJnnnmmqewjiGaNrTzlDEdNgYEG59AoILnzCtwqtmo/uxmfI7vmEzz25HQUFoqQm8twIgcAHTrUjoTM2WyYEPqff7TnCAtT4/JlfuZ/LXUke+6gxtWrLsjPr8t5w/h8nToJezYa1tXTwTAspFKWN8qTSlmuQGpwsPnfy9KlEsERoiVFVnXo958uTVhThBa0dI9Ns4VXY2NjkZ2drW3IMAgNDUW/fv048aMimVQs1JY4Y18avnTj4lT1+lYuVNizQ3ABPO7Mg1vlN4LHsHBBuXw9VJJHBW3RJzZWxb1wDWvK6e/z82tl5PYfE6PCP/+IUF5e1zSh8Zqa8DbLCAtT4/RpJW/btWsM4uK8UF3Nr1Agk2lHbMHBLNePt24xPJv171Mfb7kcABAepuKFU+hPU1paGsew/0wVcrU1tnoObYHDFV49e/Ys8vPzcfz4cZw4cQInTpzA119/jW3btoFhGLRp0wb9+vXjxC82NhYiEaXPJAgd1nrKmXpZ6kYujDoXkpKX4Fq1HygwPl7NtsLc1Zux48cEBAS48F625q6tTWGlxbC6wdmzYiQkSE2OVi5fFhsIS9Mg5Iwxa5ankS2enizCwjQYM0YGQOso8s03ZYiL8+K1u3RJe5+mhMrQGcRwmtKRK5y0dI/NOtfo/Pz8MGrUKIwaNQoAUFZWhlOnTnHCd/jwYXz//fcAAKlUihs3bjSqwQTRnLDWU07oZfnTvgvwLHkeLtXC4T0akT/K5Z/iSt59PC/AGzf4L1tDW/TJyREhONgLcjkrsNamzR4yYIAMHTsaTlEaZ/xvGliMHl2F+Hgpr7zNv/8av8BrahjeCPXsWRdMmuRpZHdNjXDGGB11OYNYIiaGmVcM04Q1FvXx2HSm6U6rh19SqRRDhgxBSkoKPv30U7z77ruIi4sDy7IoK7Pu28uvv/6KpKQkdOnSBXK5HFu3buXtZ1kWaWlpiIyMhL+/P4YPH45Lly7x2lRVVWHu3LkICwtDYGAgkpKSkJuba+1tEUSjYG0ycN3LsXPHyzi+rR9ObnRFq3+7G4nctdxOmLH0F5yrLkGp32Wo3ePvOmCIBM9naEtMjIrLrwhokzgrlSLk5IgFUndpUSpFcHPTTlW6u7Nwc2Ph6akRbGs59R1ZMHjlFe16V1WVNpXXuXMuyM+37JWWkWF8n4b5LgyFqq58t5ZUODFMqL15c9N4TtYnKb0zBahb5XX5999/48SJE9xU5vXr1+Hi4oJu3brh6aefRr9+1hVQLCsrQ1RUFCZMmICnn37aaP97772H9PR0pKenIyIiAitXrsTo0aPx+++/w8tLO+2QkpKCffv2Yf369fDx8cErr7yCxMREHDlyhDK1EHbHGk85Uc057P8kGZ1CLgjuV7t0xZSUz7F1R29u2/krtWstQiMI/ZetkC09e8oE03jpBNBwPU6pZLh1MXNrfjqPytpUW7bIWclHI6CxQtv0S+2YwzBfpbVxapa4/9vLc7I+13Wm6U6zQve///0Px48fx/Hjx3Hq1CkUFRXB29sbffr0wcSJE9G3b1/07t0bEomkXhdPSEhAQkICABh5crIsi48//hgvvvgiHn1Uu5j+8ccfIyIiAjt27MC0adNQUlKCzZs3Iz09HUOGDAEArFmzBtHR0Th8+DCGDh1aL7sIoqkQV/8OiWImxOprAACvEP7+Mk0cbqjSMWVmdxQWMkZpt/RfPvpFQgHA01OD1NQKq9addMTGap0sBgzgB0S7urIIDPSqMwygTRsNwsO1weU5OSILpjetj6PjC6lpRCKgWzcVN8WpC+Y+e5b/+vPyYtGtm6recWrO5v7vTAHqZoXuwQcfhKurKx555BG8+uqriIuLQ5cuXZrEsOvXryM/Px/3338/t00ikaB///44efIkpk2bhjNnzqCmpobXJjg4GJ07d8bJkydJ6AiHRFx1FJ6KJyHSCHiTAFC53Ydy7/fAunQAAEwxM3LSld9Zu7bcKA2VWg3MmSPh1tSE3Nl1o5BbtxiuqnhgYK0gbttWhqQkKSorGXh4sLh+XYTKyrqnB0tLGZw6Zc2MiqUCp33Zeniw8PXV4MYNfr8YZi8BtM4oR4/yBej6dQY9enhBo6ltW1bG4MABvhdnY9Bc1r6cKUDdrNC1b98e2dnZ2LdvH27evImrV6+iX79+iIuLQ+vWrRvVsPz8fACAr68vb7uvry9XJaGgoABisRht2rQxalNQIPwSAbTurbbE1udryThrX3qLjyHMYxHEjPA3/mJVPLKr5qOGvVvu5nYNAG1f5OV1g/6fqpubBgCL6moxV2Zm0iQGV6/yX/BVVSJcvszfdumSiNfHOTluqKjoCJZ1RceONVi27CqCgqpRXQ1kZgIvvRTJjei0gdJCL2TjEIGGeWEaXqP2XGIxi/DwcjAMg4wMwzUjFt7eNSgocOdte+utDBw6VIPU1I5QKFwhl2vv08+vM/Lyatt6edUIPn+6iWJbPZvTp3fGX3/VfvmYNInB+vV/89rk5LgZ2RsU1PReP+nptf/XPRO2wNZ/53WFK1gVXnD48GF8+OGH0Gg06NSpE/r27cuFF4SHh9vUcB0Mw/+DYVnWaJshdbWxZQyHM8Z+2Qun6kuWhUvld/BUzAADYc+6ao+xqGz1JlhxW4gAdDBxqoAAF+g7M3fvrsGtWwzuhrgCABQKTzBM3SMthmHg6noPN6IoKGD0vDQ9sHx5FJcBpLKS4ZX4aTpM/+2q1SL8/bfM5HHl5fyCs3FxaiQlBSIhQcqJi+4+Q0IA/cpiISFis8+frZ7NsjK+QCuVnkbnfvZZY3udZVrU4eLoAPPhBSdPnsS3336LsrIytGnTBn379sWWLVtsYpifnx8A7agtODiY215YWMiN8tq1awe1Wo2ioiK0bduW16Z///42sYMgLIZl4VrxBTxLnjXZZN2OGZiz8i107iIz+eIynNpavLgCS5ZIeFNIAwbwX/a3bzOIjFQbrTtJJCwqKmqFo3NntVFxVn0KC5k6ckQKiZCl2xqCZYHlcjmLqCjjdTYhx4pvvimzy9ScJWtfzuQI4ghY5XUJ1IYXDBkyBPn5+Th27BjWrl2LkydPYt++fTYzLDQ0FH5+fjh06BB69uwJAKisrMTx48exdOlSAED37t3h6uqKQ4cO4bHHHgMA5ObmIiMjA3379rWZLQRhElYDt/L1kNyZa7JJlecs9B62EucvenPbCgtNx08ZxtItWSIxEkWh3JebNpVj8mRPXL4sBstqEBnJIi3NWCRHjzZdV7JtWxbZ2fVN+mCpQ0n9EjhbQuvWwg4hQuJiL+cRS9a+nMkRxBFocHgBoJ0qDAsLw7333mvVxZVKJbLu/jY1Gg1ycnJw7tw5+Pj4ICQkBMnJyXj77bcRERGBTp064a233oJUKsW4ceMAAN7e3pg0aRJSU1Ph6+vLhRd07doVgwcPtsoWgrAYVgW3so8gKU012aRS+iKqvOYDjNYj2VPGFxdzLy5Lvs0L5b4MDWU5RxOhMj3619Z/iRrmatR6WtZeUyRi4epqScVv7VShuZAD/TADmUyDigoGarX1gufmpgts5x9rasXCkRwrLBFYR7LXGbAqvOD27dtgWZaLnXv44Ydx77334t577zVyGrGEP//8EyNGjOA+p6WlIS0tDRMmTMDHH3+MF154ARUVFZg7dy4UCgV69eqFXbt2cTF0ALB8+XKIxWJMmzYNlZWViI+PxyeffEIxdIRtYavhrnwbHso3TTaplC1ElexFrpabPta8uCz5Nt+QF6HQsfpef9u3lyExsdbTUj9H5M2bjNnac3/+KYanpwZVVcYC5ubGz6KiFVeNGWGsRSTix8hphc7YBv1UZvo0N9f/5mavo2M2qbOPjw8AwNPTE7179+aqGPTp0wdSqenpj5aEUzlQ2BmH60u2Ah6laXAve99kkwqvZaiWPgMwtvtiJZTAWSdEuvU7oXAAlgW3tieVlmPLFtbmbuvGQeKmpiGN19QMa8fpMnTo7tXNTRu+oF1T5I8o164tw5o1HkYONIY0RrJiXVLnEoXCpuc1R3MJQagP9vg7Nyt06enpuPfeexEbG0sjJBM43Mu5GeMQfakphUfpUriXrzXZJEf1DryCpwIWeDnaGlPZSOLitO6RlmSob8hL1DCTSliYGrm5IoumNV1dWfTooTZ5XcN7c3dnucB1/XaGNri7swgK0jSaINhD6Byp2oCtcTivy2efNe09RhBOg0YByZ2FcKv4wmSTyQs2YvN3kwAwJl/ATYEp77uzZ8VQqy1ra1gTbdIkT15AtTkhNMy+cusWYxSobgqRyHi90Jy9hvejw3BqNzbWfLFTADh2TMQLfN++vQwDBjQ0T2fjQV6XtoVq6hAtEkb9LyTFU+GdJ4d3fgcjkWPhijL5RpQEKBA+XIXN302GbjpNF6RtjyS3ppxYqqoYXp5Gc20Ny/AYfrYmma+2nptlL+G6MvUb2qtSCfezYXLqykrtKC8hQYrr12ttuXaNQUKCFD17yjBypDaVmUqlnfZMTHTspRdLEkQTlkNCR7QYGHUuPG8nwjtPjlYFEXCr/Ja3n2VaocznK5QEKHAn4F+uYKmpl4wtvmXrv4wNX9RC6F7y7durIZNpEBys5hIw63BxYREdXVpvTz1zowl9b0xjWMTGqhATo4JxdhOWl6lf6L519+biwj/WXBUBDw/g3DlhUdYXbP1UXwBQWenYI6T6VBsgTGN1HB1BNCcY1TWLarmp3eNNnkPnMHH2rJi3FmWLb9nWFusU8sYzXM/p2VON9PQMhIYKr4MYBpbrkhzrMOf1aa6mHQCTVcpjYtS8aV5T933gQJnR/dQ3FMPcFxEPD8ceIZHXpW2hER3hdIhqMiAtHKoduQnUclOLw6Bs8zNKAhRcLTdz6F46p06V2vxbti3WYsx9+xcaOW3axG+/aVO5yfPFxKhQVVU7Nbh4cQW3z3DUJpHUfhaqu3btGoP4eCn8/FoZJXw+fVpsNLKzpJ/NTfEZ7hOJWLi4sJDJNNi+nUSkJUEjOsIpENWchaciGWLVRcH9apduKJd/DI1rdL2vYepbdkO8GBuSAUMo1MAQoZHTp5+aF2j9+9QfXRlmafn1V5FRvJ3QOXQkJPBHefro1uMGDJDh11+VRsea6mNz8YR1xQsSLQez4QWmKCsrQ3FxMViBYlAhISECRzgvDuES7yRY25fi6lPwVMyESH1dcL/KNQ4V8g+hcbnHViYK0hBXcEti5kztGzhQJhhPFhenQnr6GURERAiGA7Rty1psr9DxusKr1mKqyKuQ/XVNzxpmc2lMAbNHeIEz43DhBfpUV1dj5cqV2LhxI4qKiky2u337tk0MIwghxFVHtOJmopZbjdtgVHi/y9VyawosmX40JVrm1mLMrd/NmuVpMmha//pCI8abN/n23bzJmLSvviNOofMZhiaYQjeNqS9ghn2qVIqgVFq2rkkQFgvdvHnzsGnTJgwbNgwDBgyA/O63HIJobFwq92vL3bDCI4ka92Go8H4brDiwiS3TYokYWOt0AtTf0UL/+kLTd4aVDxQKxsi+Hj28IBJpU2117qxCTY3pVGNComZ4vgEDZBYFlQO105hxcV5cvKI5JxiKMSPqwmKh+/bbb/H444/jww8/bEx7CEJb7qbyW0gUM8BAOKi32mMcKlutACtuK7i/KbEk72R9nE6s8X4UiVgEBmq4dGC6nJKhoSw+/bScE6KZMz3RqhV4lQ9at2aN7NFoGGg0WtHJzQVyckpN2ikk4kIjMGFMl9/Rj1fU72PDFGAUY0bUhcVCp9Fo0Lt377obEkR9YFm0cdkD77ylJptUSyahotUyQCRvOrsswBJX8PpMATbE0UK/gLOhEMlk/C8P/v4st0+IumLOhES8rjAEHTExanh4wGwOy8JChtfHQuuaBGEOi4Vu6NChOHHiBKZOndqI5hAtCoNabt4exk2qPJ9CpdergMhUVenmQX2qDZgTUGvirAyFyFRxUp19166JeAHWdcWcCYm4fpVyjQYGAdva83l6auvl6VJx6QSsrnhFijEjrMXiOLqVK1fi/PnzWL58OfLz8xvTJsKZYVVwU76vTb11q7VgwdJK6f+hxD8PJQEKVHq/2exFDuBn8zhwoKxJ3dwNheLff0WorNTmrdRNZwLg7NuzRwmZTGNxzJlQ3NvSpRIu5ZZGw0Am0yAsTH13NKmtTlBeLsKSJRLuPNbGK1qbVYZouZgML/D39wdjUMVQrVZDpdJmSXd1dYVIxNdJhmFw8+bNRjLVMaHwAguwqJbbK7hw6xF0iujShIY5L/rPpamRkj71qXRgbp+psARbhis0VYZ/Ci+wLQ4VXjB69GgjoSMIi2Er4FG6HO5lH5hsUuH1OqqlyVwtN/ZWpsm2RP3RjZTMxbGZco6pK8TB0LNSF9vm5SWcsaQhAfJ12Uzel4QpTArdxx9/3JR2EM6AphQepUvgXr7OZJOKVu+g2nOqXWq5ORpNXVzTnIOIqyuLhASpkS3WhDjox7bFxKgQF2e8DtiQyuh13Q95XxKmsNgZ5c0338SIESMQFRUluP/SpUvYvXs35s+fbzPjiGaARgHJnRS4VXxpskm59yeokSQCNEPAQyh2bc8eZaPVSdMXmVu3mLsldrTcuCFCRoaIs0U3cqtvgmelksHRo8ZTkrZ0JLGlaBLOjcVfq1esWIELFy6Y3H/p0iW8+abpNZj6EB0dDblcbvQzfvx4AEBycrLRvgceeMCmNhDGGNdy44ucfi23kgAFajyTSOQEEIpda8w6afoOMbqQAh3V1cIjN3MJlvX3GYYsNMXoyp4OPkTzwmZJnZVKJVxdXW11OgDAoUOHoNYrM3zr1i0MHjwYo0aN4rYNHjwYa9as4T67ubnZ1AZCC6POhaTkJbhW7RfczzLeKJevg8rjwSa2rPkiNCJqqjpphtf28GB5teZ0QmVpiAPFthGOjFmhO3/+PP766y/u8/HjxzmvS30UCgU+++wzdOrUyabGtW3Lz3qxefNmeHl58YTO3d0dfn5+Nr0uoUVby+05uFQfE9yvEQXcreU2qIktc3wsWX9bu7YcPXp48WLM1GoY5XlsyDVMYTjtt3hxBZYskVgkVEJVE3QZWWhURTgiZqsXrFixgpuOZBhGsFqBDi8vL6xduxYPPfSQ7a0EwLIsunfvjoSEBKxatQqAdury+++/h5ubG7y9vTFgwAC8+uqr8PX1bRQbhHC28AJRzWVISp6BS81pwf1qcTgq5GugdrN9lhxn6ktLXd91pW60oymmzvaWXqMx+9LwukLXdyYovMC22OPv3KzQ3bx5Ezdv3gTLskhISMCCBQswdOhQ/gkYBp6enggPD2/UacODBw9izJgxOHr0KGJiYgAAO3fuhEQiQWhoKLKzs/H6669Do9Hg8OHDcHd3N3muzExyY9dHIspAmHsqJGJhz4JydQSuVr2GCk3jlrtxJsaM6YYbN2pTvYSEVGLXrvM2a1/fY2yB4XUbev2cHDekpnaEQuEKubwGy5ZdRVBQtS1MtQm9+/QBAPzv99/tbAlhirqE06J6dBqNBtu2bUNCQoLRdGJTMWXKFNy4cQMHDx402SYvLw/R0dH47LPPMHLkyCaxq7mOQhyllps+zbUvhbA2mLk+wc+ONqKLjVXhyJFamy2dWm2qwO/6QiM622KPv3OLvC7VajVmz56Nbdu2NbY9gvz777/Yt28fpkyZYrZdQEAAAgMDkWVJNtkWiLjqCLzyI+CdJ4esKMFI5GrcBuOO7xmUBChQ1vZAk4qcs2HorZiaWmE2XZU570ZLr1HXMbZKmaW7rpsbX7QMVzZ04RNZWWKuCoEQt24xJj9Tmi/CFljkdenq6iqYEqyp+OKLL+Du7o4xY8aYbVdUVIS8vDxyTtHDpfJHeCqeNFPL7T93a7kFNLFlzo2ht6L+qEWoHl194susPaY+NfHMXdcw04q+1yZgeeaS27cZk59tZTPRsrE4jm7y5Mn44osvUFlZ2Zj2GMGyLDZt2oQxY8bAy8uL265UKrFo0SKcOnUK169fxy+//IKkpCT4+vrikUceaVIbHQqWhWvFN2iV5wPvPDmkxUlGIlftMQ532v2DkgAFylt/QSLXBDhCuipb22AYK2ftZx1yOWvysyP0G9H8sTiOrmPHjmBZFn369MGECRPQoUMHSCQSo3ajR4+2qYG//PILrly5gk8//ZS3XSwW4+LFi9i2bRtKSkrg5+eHQYMGYcOGDTxBbBGwLFwrtsKz5DmTTaolk1HRaqnD1XJzVgzXp2Qyy176jYmtU2bVlZnE0swlgYEscnL4nxvLZqJlYpEzCgD4+PjUfTKGwe3btxtsVHPCbg4UrAZu5esguTPPZJPmVsvN0ZxRGhKnZuhgERurgrs7miyvpVBfCgV1O0Lcmzm7HMFmckaxLQ5VvcCQPXv2NKYdhCWwKriVpUNSuthkk0rpS6jymgcwAlVMCatoyPqQ4RRbaSmDI0fqV47GVjhqwVJbFZglCFNYLHQDBw5sTDsIU1hYy61K9iLA2DYFW0unIetDNOVGEI4D1UpxRNhyeNx59W4V7naCIlfh9QZK/ItQEqBAlddcErlGwFJnCiFSUyt4VboXL64wakOu8wTRNJgc0T377LNgGAbvvfcexGIxnn322TpPxjAMPvzwQ5sa2GKwqJbbalR7TqFabk1EQ8rALF0qgVKp/T0plQyWLJEYTcGR6zxBNA0mhe7o0aMQiUTQaDQQi8U4evRonXF0VJHcOhhNMTzuLKyjltsa1EjGU5kbO9CQ9SFLpj3JdZ4gmgaTQqdftUDoM1E/GHUBJHfmwrXyO8H9LNxQLl8LleTRJraMsCXm1uh03py5uSKjYwiCsD02q0dHmIZR59yt5XZAcD/Vcmu+mApBMDftqT9lCQDu7ixiY9VUw40gGol6C51KpcKVK1dQVlaGe+65BzJZ84jVaipEqquQlDwHl+pfBfdrRIF3a7mRN2tzxtQ6m7lpT8MpyqAgDa3NEUQjUqfQ7dq1Czt27ICrqysmTJiAhx9+GHv27MG8efOQn58PQFvV+7nnnsOiRYsa3WBHxp613Aj7UJ91Ngo9IIimxazQ7d69GzNmzICnpyc8PT2xd+9erF69Gi+99BKioqIwevRo1NTU4NChQ3jnnXcQEhJSZ4UBZ0MiyoDs38kQqy4J7le7RKNc/hE0rtFNbBnRFNRHtBrizUkQhPWYTQE2bNgwlJWVYd++fZDJZJg3bx42btyIwYMHY9u2bZyXpUqlQkJCAtRqNY4cOdJkxtsLcfXJu7XcsgX3q1z73q3l5jjprJoDjpYCzBIcIUWVEM2xLx0VSgFmWxyuHl1mZiYSExO59bcZM2aguroajz32GC+UwMXFBWPHjnX6yt2imgt3a7k9ZCRyNW5DcMf37N1abvtJ5FoIurW406eV3NpcY0JB5gRhPWanLouKiuDr68t91v1ff5v+vqYu4dPUuFT9xPtc4/4fXLz9HDp06m8ni4iWBgWZE4T11OmMQkHgtVRLk6FxiYLatSdYcVsAQE2Rc49iCceCgswJwnrqFLpr167hjz/+AADcuXMHgHZK0zCc4OrVq41gnoPBuEPlkWBvK1oUDSmV44yQxyZBWI9ZZxQfHx+jER3LsoKjPN12qkdH1BehvjSs6xYXp2rRU3WWOr/Qc2k7yBnFtjhcPbr09PSmsoMgBKGpOj5Un40grMes0D3++ONNZQdBCEJTdQRBNBSHrveSlpYGuVzO+7nnnnu4/SzLIi0tDZGRkfD398fw4cNx6ZJw4DbRPFm7thxxcSqEhakRF6ei4GqCIKzG4ZM6R0REYO/evdxnsVjM/f+9995Deno60tPTERERgZUrV2L06NH4/fff4eXlZQ9zCRtDU3UEQTQUhx7RAdpgdD8/P+6nbVutWz/Lsvj444/x4osv4tFHH0VUVBQ+/vhjKJVK7Nixw85WEwRBEI6CwwvdtWvX0KVLF8TExGD69Om4du0aAOD69evIz8/H/fffz7WVSCTo378/Tp48aSdrCYIgCEfDoacue/fujY8++ggREREoLCzEqlWrkJCQgBMnTnCVEwyztPj6+iIvL8/seW2dqszZU581JdSXtoP60jboao1Qf9oOW/dlXeEKDi10Dz7IL0Tau3dvdO/eHV988QX69OkDwDhzi6k4P31sGcNB8Uq2g/rSdlBf2h7qT9vgcEmdHQ2ZTIbIyEhkZWXBz88PAFBQUMBrU1hYKJiLkyAIgmiZNCuhq6ysRGZmJvz8/BAaGgo/Pz8cOnSIt//48ePo27evHa0kCIIgHAmHnrpctGgRHn74YQQHB3NrdOXl5ZgwYQIYhkFycjLefvttREREoFOnTnjrrbcglUoxbtw4e5tOEARBOAgOLXQ3b97Ek08+iaKiIrRt2xa9e/fGTz/9hPbt2wMAXnjhBVRUVGDu3LlQKBTo1asXdu3aRTF0BEEQBIdDC91nn31mdj/DMEhJSUFKSkoTWUQQBEE0N5rVGh1BEARBWAsJHUEQBOHUkNARBEEQTg0JHUEQBOHUkNARBEEQTg0JHUEQBOHUkNARBEEQTg0JHUEQBOHUkNARBEEQTg0JHUEQBOHUkNARBEEQTg0JHUEQBOHUkNARBEEQTg0JHUEQBOHUkNARBEEQTg0JHUEQBOHUkNARBEEQTg0JHUEQBOHUOLTQvfPOOxgyZAhCQkIQHh6OxMREXLx4kdcmOTkZcrmc9/PAAw/YyWKCIAjC0XCxtwHmOHbsGGbMmIGePXuCZVksX74co0aNwsmTJ+Hj48O1Gzx4MNasWcN9dnNzs4e5BEEQhAPi0EK3a9cu3uc1a9agffv2OHHiBIYNG8Ztd3d3h5+fX1ObRxAEQTQDHHrq0hClUgmNRgO5XM7bfvz4cXTq1Am9evXC7Nmz8e+//9rHQIIgCMLhYBQKBWtvIyxl6tSpuHLlCg4fPgyxWAwA2LlzJyQSCUJDQ5GdnY3XX38dGo0Ghw8fhru7u+B5MjMzm9JsgiCaMb379AEA/O/33+1sCWGKiIgIs/ubjdAtXLgQu3btwo8//ogOHTqYbJeXl4fo6Gh89tlnGDlyZKPblZmZWWcnE5ZBfWk7qC9th/fdGaQShcKudjgL9ng2HXqNTkdKSgp27dqFPXv2mBU5AAgICEBgYCCysrKaxjiCIAjCoXF4oZs/fz527dqFvXv34p577qmzfVFREfLy8sg5hSAIggDg4EI3Z84cbN++HVu2bIFcLkd+fj4AQCqVQiaTQalUYsWKFRg5ciT8/PyQnZ2NpUuXwtfXF4888oidrScIgiAcAYcWunXr1gEAHn30Ud72+fPnIyUlBWKxGBcvXsS2bdtQUlICPz8/DBo0CBs2bICXl5c9TCYIgiAcDIcWOkUdi78SicQo1o4gCIIg9GlWcXQEQRAEYS0kdARBEIRTQ0JHEARBODUkdARBEIRTQ0JHEARBODUkdARBEIRTQ0JHEARBODUkdARBEIRTQ0JHEARBODUkdARBEIRTQ0JHEARBODUkdARBEIRTQ0JHEARBODUkdARBEIRTQ0JHEARBODUkdARBEIRTQ0JHEARBODUkdARBEIRT4zRCt27dOsTExMDPzw/33XcffvvtN3ubRBAEQTgATiF0u3btwoIFC/Dyyy/j6NGjiIuLw2OPPYYbN27Y2zSCIAjCzjiF0KWnp+Pxxx/HlClT0LlzZ6xatQp+fn747LPP7G0aQRAEYWeavdBVV1fjzJkzuP/++3nb77//fpw8ebLRrx8REdHo12gpUF/aDupL21GiUKBEobC3GU6DPZ7NZi90RUVFUKvV8PX15W339fVFQUGBnawiCIIgHIVmL3Q6GIbhfWZZ1mgbQRAE0fJo9kLXpk0biMVio9FbYWGh0SiPIAiCaHk0e6Fzc3ND9+7dcejQId72Q4cOoW/fvnayiiAIgnAUXOxtgC149tln8dRTT6FXr17o27cvPvvsM9y6dQvTpk2zt2kEQRCEnWn2IzoAGDNmDNLS0rBq1SoMGjQIJ06cwFdffYX27dtbfa5ff/0VSUlJ6NKlC+RyObZu3crbn5ycDLlczvt54IEHeG2qqqowd+5chIWFITAwEElJScjNzW3QPTZH3nnnHQwZMgQhISEIDw9HYmIiLl68yGvDsizS0tIQGRkJf39/DB8+HJcuXeK1of60rC/p2bSMtWvXon///ggJCUFISAgefPBB7N+/n9tPz6R11NWfjvBcOoXQAcCTTz6Jv/76CwUFBThy5AgGDBhQr/OUlZUhKioKK1asgEQiEWwzePBgZGRkcD9ff/01b39KSgr27NmD9evXY9++fSgtLUViYiLUanW9bGquHDt2DDNmzMD+/fuxe/duuLi4YNSoUSguLubavPfee0hPT8ebb76JgwcPwtfXF6NHj0ZpaSnXhvrTsr4E6Nm0hMDAQCxZsgRHjhzBoUOHEB8fj4kTJ+L8+fMA6Jm0lrr6E7D/c8koFArWJmdyQoKCgrBy5UpMnDiR25acnIzbt29j+/btgseUlJSgU6dOSE9Px/jx4wEAOTk5iI6Oxo4dOzB06NAmsd0RUSqVaN++PbZu3Yphw4aBZVlERkZi5syZmDNnDgCgoqICERERWLZsGaZNm0b9aQLDvgTo2WwIHTp0wOLFizF16lR6Jm2Arj+nTZvmEM+l04zompLjx4+jU6dO6NWrF2bPno1///2X23fmzBnU1NTwAtiDg4PRuXPnJglgd2SUSiU0Gg3kcjkA4Pr168jPz+f1lUQiQf/+/bm+ov4UxrAvddCzaR1qtRo7d+5EWVkZ4uLi6JlsIIb9qcPez6VTOKM0JQ888ABGjBiB0NBQZGdn4/XXX8fIkSNx+PBhuLu7o6CgAGKxGG3atOEdRwHswIIFCxAdHc39AeTn5wOAYLB/Xl4eAFB/msCwLwF6Nq3hwoULSEhIQGVlJaRSKbZs2YKuXbtyL1Z6Jq3DVH8CjvFcktBZydixY7n/d+3aFd27d0d0dDT279+PkSNHmjyupQewL1y4ECdOnMCPP/4IsVjM21efYP+W3J+m+pKeTcuJiIjAL7/8gpKSEuzevRvJycnYu3cvt5+eSesw1Z9RUVEO8VzS1GUDCQgIQGBgILKysgAA7dq1g1qtRlFREa9dSw5gT0lJwc6dO7F792506NCB2+7n5wcAZoP9qT/5mOpLIejZNI2bmxvCwsLQo0cPLF68GNHR0fjoo4/omawnpvpTCHs8lyR0DaSoqAh5eXncH0j37t3h6urKC2DPzc1FRkZGiwxgnz9/Pnbs2IHdu3fjnnvu4e0LDQ2Fn58fr68qKytx/Phxrq+oP2sx15dC0LNpORqNBtXV1fRM2ghdfwphj+eSpi4NUCqV3DcNjUaDnJwcnDt3Dj4+PvDx8cGKFSswcuRI+Pn5ITs7G0uXLoWvry8eeeQRAIC3tzcmTZqE1NRU+Pr6wsfHB6+88gq6du2KwYMH2/HOmp45c+Zg+/bt2LJlC+RyObcmJ5VKIZPJwDAMkpOT8fbbbyMiIgKdOnXCW2+9BalUinHjxgGg/tRRV18qlUp6Ni3ktddeQ0JCAoKCgqBUKrFjxw4cO3YMX331FT2T9cBcfzrKc0nhBQb88ssvGDFihNH2CRMm4J133sHEiRNx7tw5lJSUwM/PD4MGDcIrr7yC4OBgrm1lZSVeffVV7NixA5WVlYiPj8fbb7/Na9MSMPQI1DF//nykpKQA0M7Dr1ixAp9//jkUCgV69eqFt956C1FRUVx76s+6+7KiooKeTQtJTk7GL7/8goKCArRq1Qpdu3bF7NmzOTd2eiatw1x/OspzSUJHEARBODW0RkcQBEE4NSR0BEEQhFNDQkcQBEE4NSR0BEEQhFNDQkcQBEE4NSR0BEEQhFNDQkcQDkxycjKio6PtbQbH8OHDMXz4cHubQRBWQUJHOAXFxcV44403MGjQIISEhKBdu3bo1q0bpkyZgj179oBlGydcNDc3F2lpaTh37ly9z3Hx4kWkpaXh+vXrNrTMvhhWlQ4KCkJsbCwmT56M7777DhqNxt4mEi0ISgFGNHvOnj2L8ePHo7i4GKNGjcKkSZMgkUiQm5uLn376CZMmTcJbb72FJ5980ubXvnnzJt588020b98eMTEx9TrHpUuX8Oabb2LgwIEIDQ3l7Xv//febrSi4urriww8/BKDNfHHjxg388MMPmDJlCgYOHIitW7fC29vbzlYSLQESOqJZU1JSgscffxwsy+Lw4cO8NE2Atm7b0aNHUVJSYicLG4arq6u9Tag3IpEIiYmJvG2LFi3C6tWrsWTJErzwwgv4/PPP7WMc0aKgqUuiWfP5558jNzcXb7zxhpHI6YiPjzfKX3rnzh0sWrQI0dHR3DTna6+9hqqqKl67I0eOYNiwYQgNDUVQUBB69+6Nl19+GYA2L+qDDz4IAHj22We5abq0tDQAwPnz55GcnIzu3bvDz88P4eHhmDFjBnJycrjzb926FTNmzAAAjBgxgjvH1q1bAQiv0Wk0Grz77rvo1asX2rVrhy5dumDu3LlGYj58+HD06dMHV65cwdixYxEYGIiIiAgsWbLEaJT4wQcf4KGHHkJYWBj8/PzQv39/bNq0qe5fQD34v//7P9x///347rvvkJmZyW3ft28fEhMT0aVLF+53snjxYt7vZOPGjZDL5Th79qzRedeuXQu5XI6LFy8C0Jbaef7559G1a1e0a9cOkZGRSExMxIULFxrlvgjHhUZ0RLPmhx9+gEQiwaOPPmrxMRUVFXjkkUdw/fp1TJ06FR07dsRff/2FDz/8EH///Te++OILAMDly5cxfvx4REVFYcGCBfD09MS1a9ewf/9+AEDnzp2xYMECrFixAlOnTsW9994LAFxl5UOHDiEzMxPjx49HUFAQsrKysGHDBpw+fRq//fYbJBIJBgwYgJkzZ2Lt2rV4+eWXufI75sqTvPzyy9iwYQOGDRuGp59+GpcuXcL69evxxx9/YP/+/bxR4J07d/Doo4/i4YcfxvDhw/Hzzz9j9erVCA0NxdSpU7l2H330ER544AGMGjUKDMNg7969mD17NjQaDa+drUhMTMTBgwdx+PBhREREAAC2bNkCsViMWbNmQS6X4+TJk/jggw+Qm5uLdevWAQBGjx6NBQsWYPv27YiNjeWd86uvvkJ0dDT3hWfKlCm4cOECZs2ahfbt26OoqAi//fYb/vnnH+53RLQMSOiIZs3ly5cRHh4ONzc33vaysjJUVlZyn11cXLj1oI8++giZmZk4fPgwOnfuzLXp0qUL5syZg99++w39+/fHoUOHUFVVhR07dqBNmzZcu8WLFwPQFowcOnQoVqxYgT59+hhN082YMQPPP/88b9vDDz+MYcOGYc+ePRg/fjw6dOiAfv36Ye3atRg8eDAGDRpk9n4vXryIDRs2YPz48fj000+57REREUhJScGXX36JyZMnc9vz8/Px/vvvc9umT5+OgQMHYuPGjTwB++OPP+Dp6cl9fvrppzFq1Ci8//77jSJ0Xbp0AQBcvXqV27Zu3TqeDdOmTUN4eDiWL1+OJUuWICgoCK1atcLw4cOxc+dOLFu2jKuwfvXqVfz+++94/fXXAWintI8fP45ly5bxfgf/93//Z/N7IRwfmrokmjWlpaXw8vIy2v7aa68hPDyc+3n88ce5fd988w369u2Ltm3boqioiPvR1b46evQoAHDn/f777+vlEKL/0lYqlbh9+zbuueceeHt748yZM1afDwA3mpw9ezZv+/Tp09GqVStuvw4PDw9MnDiRt23AgAG4du2aoK01NTUoLi5GUVER4uPjkZWV1SjrmzKZDIC2Xwxt0Gg0KCkpQVFREfr37w+WZXlTlRMmTEB+fj4OHz7Mbdu2bRvEYjFXM87DwwOurq44duwYiouLbW4/0bygER3RrPHy8kJpaanR9lmzZnHxXs899xxv35UrV3D+/HmEh4cLnrOwsBAAMHbsWGzevBmzZ8/Ga6+9hvj4ePznP//B6NGjLXISUSgUeO211/Ddd98ZvWzrKx7Z2dlgGIab7tPh7u6O0NBQZGdn87YHBgZyox4dcrncyJ7vv/8eq1atwl9//QW1Ws3bd+fOHZt7R+oETid4gNb7NDU1FceOHUNFRQWvvX5/DR48GAEBAdi+fTtXQ+7rr7/G4MGD4e/vD0DbH4sXL8bixYsRERGB3r1748EHH8T48eMREhJi03shHB8SOqJZExkZiTNnzqC6upo3fRkREcGJgUQi4R2j0WgQHx+Pl156SfCcgYGB3HE//PADjh07hp9//hn//e9/MWvWLHz44YfYv3+/0XkNmT59On777Tc899xziImJgZeXFxiGwfTp0xslZIBlWTAMw9tmKHJCnDhxAk888QT69euH1atXw9/fH25ubjhw4AA++uijRrH10qVLAICwsDAAWiEbMWIEJBIJXn31VXTs2BESiQQ3b97EM888w7NBLBZj/PjxWLduHcrKynDx4kVkZWVhwYIFvGs899xzeOSRR7Bv3z4cPnwYq1atwjvvvIMvvvgC9913n83viXBcSOiIZs2wYcNw4sQJfPvttxg/frxFx3Ts2BFKpZKbqjSHSCRCfHw84uPjsXTpUqxfvx4vv/wyt8ZmKCw6FAoFDh48iAULFvBewJWVlVAoFLy2ps4hRPv27cGyLDIzM9GtWzdue3V1NbKzs+tc4xPi22+/hYeHB7755ht4eHhw23/55Rerz2Up27dvB8MwGDJkCHetwsJC7N27FwMHDuTaHTp0SPD4CRMm4L333sPevXvx+++/QyaT4ZFHHjFq16FDBzzzzDN45plnkJOTg/j4eKxevZqEroVBa3REs2bq1KkICgrCK6+8wo0SDDHMijJmzBicPn0a+/btM2pbUVHBTavdvn3baL/O008nVrp1JUPxEolEgtcWGiGZOocQCQkJAID09HTe9g0bNuDOnTt46KGH6jyHIWKxGAzD8OxSKBTYsmWL1eeyhNWrV+PgwYMYM2YMN32sG3nq95dGozG6Tx2RkZHo0aMHtm7dim+++QYjRozgrYmWl5cbTX8GBwfD19fXon4mnAsa0RHNGm9vb2zduhWJiYm47777MGrUKPTu3RsSiQS3bt3C/v378c8//6B3797cMc8//zwOHDiASZMmYfz48ejVqxeqqqrwzz//4JtvvsHXX3+NPn36YOXKlTh27BgeeughtG/fHgqFAp999hmkUikefvhhAEB4eDhatWqFzz77DDKZDDKZDF26dEFUVBQGDhyI999/HzU1NQgJCcHx48fx22+/oXXr1rx7iI2NhUgkwurVq1FSUgKJRIJevXqhQ4cORvfbtWtXTJs2jRO2IUOG4NKlS9iwYQN69uyJCRMmWN2HDz/8MNLT0zF69GgkJiaiuLgYGzduRLt27ZCfn2/1+XRoNBps374dAFBVVYXs7Gz88MMPuHDhAgYNGoR3332Xa9uvXz+0bt0aycnJeOqpp+Di4oLdu3fznFUMmTBhAubNmwcASEpK4u37559/MHLkSIwaNQqRkZFwd3fHgQMHkJGRgWXLltX7nojmCQkd0ezp3r07fvvtN3z88cf44Ycf8P3336Ompgbt2rVD79698dJLL2HYsGFce4lEgt27d+O9997Drl27sHPnTkilUnTo0AHJycnc2t5//vMf5OTk4Msvv0RhYSFat26NPn36YN68eWjfvj0ArdPDmjVrsGzZMsyZMwc1NTWYP38+oqKisG7dOixYsAAbNmyASqVC//79sXv3bqOYv4CAALz77rt499138cILL0CtViM9PV1Q6ADg7bffRmhoKDZt2oQDBw6gTZs2mDFjBhYtWlSvTCqDBg3Cxx9/jNWrVyMlJQWBgYFcLJuhI4811NTU4KmnngKgHbW2bdsW3bt3x7x58zBixAhu1AsAPj4++Oqrr7Bo0SKkpaVBKpVi5MiRmD59OgYMGCB4/nHjxmHRokVo27at0ZRtcHAwHnvsMRw9ehQ7duwAwzAIDw/HBx98gEmTJtX7nojmCaNQKBon2y1BEEQjUlJSgnvuuQdPP/00lixZYm9zCAeG1ugIgmiWbN++HVVVVfWariVaFjR1SRBEs+LIkSP4+++/sWLFCjzwwAOIjIy0t0mEg0NTlwRBNCuGDx+OU6dOoXfv3lizZg23XkoQpiChIwiCIJwaWqMjCIIgnBoSOoIgCMKpIaEjCIIgnBoSOoIgCMKpIaEjCIIgnBoSOoIgCMKp+X+FGgnd3jlgGQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "scatter_fit(baby, 'Gestational Days', 'Birth Weight')\n", "s = slope(baby, 'Gestational Days', 'Birth Weight')\n", "i = intercept(baby, 'Gestational Days', 'Birth Weight')\n", "fit_300 = s*300 + i\n", "plt.scatter(300, fit_300, color='red', s=20)\n", "plt.plot([300,300], [0, fit_300], color='red', lw=2)\n", "plt.ylim([0, 200]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The height of the point where the red line hits the regression line is the fitted value at 300 gestational days. \n", "\n", "The function `fitted_value` computes this height. Like the functions `correlation`, `slope`, and `intercept`, its arguments include the name of the table and the labels of the $x$ and $y$ columns. But it also requires a fourth argument, which is the value of $x$ at which the estimate will be made." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def fitted_value(table, x, y, given_x):\n", " a = slope(table, x, y)\n", " b = intercept(table, x, y)\n", " return a * given_x + b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fitted value at 300 gestational days is about 129.2 ounces. In other words, for a pregnancy that has a duration of 300 gestational days, our estimate for the baby's weight is about 129.2 ounces." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "129.21292417031435" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit_300 = fitted_value(baby, 'Gestational Days', 'Birth Weight', 300)\n", "fit_300" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Variability of the Prediction ###\n", "\n", "We have developed a method making one prediction of a new baby's birth weight based on the number of gestational days, using the data in our sample. But as data scientists, we know that the sample might have been different. Had the sample been different, the regression line would have been different too, and so would our prediction. To see how good our prediction is, we must get a sense of how variable the prediction can be.\n", "\n", "To do this, we must generate new samples. We can do that by bootstrapping the scatter plot as in the previous section. We will then fit the regression line to the scatter plot in each replication, and make a prediction based on each line. The figure below shows 10 such lines, and the corresponding predicted birth weight at 300 gestational days." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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slopeinterceptprediction at x = 300
00.451396-6.744488128.674336
10.4193612.863158128.671482
20.440637-3.352362128.838751
30.488713-16.535841130.078027
40.568657-38.928764131.668195
50.560154-37.127551130.918772
60.4081995.556973128.016596
70.473496-12.223482129.825245
80.432073-0.587389129.034531
90.450153-6.120299128.925705
\n", "
" ], "text/plain": [ " slope intercept prediction at x = 300\n", "0 0.451396 -6.744488 128.674336\n", "1 0.419361 2.863158 128.671482\n", "2 0.440637 -3.352362 128.838751\n", "3 0.488713 -16.535841 130.078027\n", "4 0.568657 -38.928764 131.668195\n", "5 0.560154 -37.127551 130.918772\n", "6 0.408199 5.556973 128.016596\n", "7 0.473496 -12.223482 129.825245\n", "8 0.432073 -0.587389 129.034531\n", "9 0.450153 -6.120299 128.925705" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = 300\n", "\n", "lines = pd.DataFrame(columns=['slope', 'intercept'])\n", "\n", "\n", "for i in range(10):\n", " rep = baby.sample(len(baby), replace=True)\n", " a = slope(rep, 'Gestational Days', 'Birth Weight')\n", " b = intercept(rep, 'Gestational Days', 'Birth Weight')\n", " lines = lines.append({'slope':a, 'intercept': b}, ignore_index=True)\n", "\n", "lines['prediction at x = '+str(x)] = lines['slope']*x + lines['intercept']\n", "\n", "lines" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# HIDDEN \n", "x = 300\n", "\n", "lines = pd.DataFrame(columns=['slope', 'intercept'])\n", "\n", "\n", "for i in range(10):\n", " rep = baby.sample(len(baby), replace=True)\n", " a = slope(rep, 'Gestational Days', 'Birth Weight')\n", " b = intercept(rep, 'Gestational Days', 'Birth Weight')\n", " lines = lines.append({'slope':a, 'intercept': b}, ignore_index=True)\n", "\n", "lines['prediction at x = '+str(x)] = lines['slope']*x + lines['intercept']\n", "\n", "xlims = np.array([291, 309])\n", "\n", "left = xlims[0]*lines.iloc[:,0] + lines.iloc[:,1]\n", "right = xlims[1]*lines.iloc[:,0] + lines.iloc[:,1]\n", "fit_x = x*lines['slope'] + lines['intercept']\n", "\n", "for i in range(10):\n", " \n", " plt.plot(xlims, np.array([left[i], right[i]]), lw=1)\n", " \n", " plt.scatter(x, fit_x[i], s=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The predictions vary from one line to the next. The table below shows the slope and intercept of each of the 10 lines, along with the prediction. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
slopeinterceptprediction at x = 300
00.498896-19.845130129.823687
10.490620-18.680815128.505082
20.473614-12.615359129.468738
30.4296170.101009128.986178
40.464804-9.474261129.966908
50.434600-1.293353129.086731
60.549052-34.334031130.381503
70.531405-28.997715130.423636
80.35610419.916587126.747725
90.4100215.028982128.035215
\n", "
" ], "text/plain": [ " slope intercept prediction at x = 300\n", "0 0.498896 -19.845130 129.823687\n", "1 0.490620 -18.680815 128.505082\n", "2 0.473614 -12.615359 129.468738\n", "3 0.429617 0.101009 128.986178\n", "4 0.464804 -9.474261 129.966908\n", "5 0.434600 -1.293353 129.086731\n", "6 0.549052 -34.334031 130.381503\n", "7 0.531405 -28.997715 130.423636\n", "8 0.356104 19.916587 126.747725\n", "9 0.410021 5.028982 128.035215" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bootstrap Prediction Interval ###\n", "\n", "If we increase the number of repetitions of the resampling process, we can generate an empirical histogram of the predictions. This will allow us to create an interval of predictions, using the same percentile method that we used create a bootstrap confidence interval for the slope." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us define a function called ``bootstrap_prediction`` to do this. The function takes five arguments:\n", "- the name of the table\n", "- the column labels of the predictor and response variables, in that order\n", "- the value of $x$ at which to make the prediction\n", "- the desired number of bootstrap repetitions\n", "\n", "In each repetition, the function bootstraps the original scatter plot and finds the predicted value of $y$ based on the specified value of $x$. Specifically, it calls the function `fitted_value` that we defined earlier in this section to find the fitted value at the specified $x$.\n", "\n", "Finally, it draws the empirical histogram of all the predicted values, and prints the interval consisting of the \"middle 95%\" of the predicted values. It also prints the predicted value based on the regression line through the original scatter plot." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# Bootstrap prediction of variable y at new_x\n", "# Data contained in table; prediction by regression of y based on x\n", "# repetitions = number of bootstrap replications of the original scatter plot\n", "\n", "def bootstrap_prediction(table, x, y, new_x, repetitions):\n", " \n", " # For each repetition:\n", " # Bootstrap the scatter; \n", " # get the regression prediction at new_x; \n", " # augment the predictions list\n", " predictions = np.array([])\n", " for i in np.arange(repetitions):\n", " bootstrap_sample = table.sample(len(table), replace=True)\n", " bootstrap_prediction = fitted_value(bootstrap_sample, x, y, new_x)\n", " predictions = np.append(predictions, bootstrap_prediction)\n", " \n", " # Find the ends of the approximate 95% prediction interval\n", " left = np.percentile(predictions, 2.5)\n", " right = np.percentile(predictions, 97.5)\n", " \n", " # Prediction based on original sample\n", " original = fitted_value(table, x, y, new_x)\n", " \n", " # Display results\n", " \n", " #Table().with_column('Prediction', predictions).hist(bins=20)\n", " pd.DataFrame({'Prediction':predictions}).hist(bins=20, ec='white');\n", " \n", " plt.xlabel('predictions at x='+str(new_x))\n", " plt.plot(np.array([left, right]), np.array([0, 0]), color='yellow', lw=8);\n", " print('Height of regression line at x='+str(new_x)+':', original)\n", " print('Approximate 95%-confidence interval:')\n", " print(left, right)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Height of regression line at x=300: 129.21292417031435\n", "Approximate 95%-confidence interval:\n", "127.2751374613809 131.2758278536617\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bootstrap_prediction(baby, 'Gestational Days', 'Birth Weight', 300, 5000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure above shows a bootstrap empirical histogram of the predicted birth weight of a baby at 300 gestational days, based on 5,000 repetitions of the bootstrap process. The empirical distribution is roughly normal. \n", "\n", "An approximate 95% prediction interval of scores has been constructed by taking the \"middle 95%\" of the predictions, that is, the interval from the 2.5th percentile to the 97.5th percentile of the predictions. The interval ranges from about 127 to about 131. The prediction based on the original sample was about 129, which is close to the center of the interval." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Effect of Changing the Value of the Predictor ###\n", "\n", "The figure below shows the histogram of 5,000 bootstrap predictions at 285 gestational days. The prediction based on the original sample is about 122 ounces, and the interval ranges from about 121 ounces to about 123 ounces. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Height of regression line at x=285: 122.2145710160761\n", "Approximate 95%-confidence interval:\n", "121.18725843142495 123.27876593511762\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bootstrap_prediction(baby, 'Gestational Days', 'Birth Weight', 285, 5000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that this interval is narrower than the prediction interval at 300 gestational days. Let us investigate the reason for this.\n", "\n", "The mean number of gestational days is about 279 days: " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "279.1013628620102" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(baby['Gestational Days'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So 285 is nearer to the center of the distribution than 300 is. Typically, the regression lines based on the bootstrap samples are closer to each other near the center of the distribution of the predictor variable. Therefore all of the predicted values are closer together as well. This explains the narrower width of the prediction interval. \n", "\n", "You can see this in the figure below, which shows predictions at $x = 285$ and $x = 300$ for each of ten bootstrap replications. Typically, the lines are farther apart at $x = 300$ than at $x = 285$, and therefore the predictions at $x = 300$ are more variable." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "tags": [ "remove_input" ] }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "x1 = 300\n", "x2 = 285\n", "\n", "lines = pd.DataFrame(columns=['slope', 'intercept'])\n", "\n", "for i in range(10):\n", " rep = baby.sample(len(baby), replace=True)\n", " a = slope(rep, 'Gestational Days', 'Birth Weight')\n", " b = intercept(rep, 'Gestational Days', 'Birth Weight')\n", " lines = lines.append({'slope':a, 'intercept': b}, ignore_index=True)\n", "\n", "\n", "xlims = np.array([260, 310])\n", "left = xlims[0]*lines.iloc[:,0] + lines.iloc[:,1]\n", "right = xlims[1]*lines.iloc[:,0] + lines.iloc[:,1]\n", "fit_x1 = x1*lines['slope'] + lines['intercept']\n", "fit_x2 = x2*lines['slope'] + lines['intercept']\n", "\n", "\n", "\n", "plt.xlim(xlims)\n", "for i in range(10):\n", " plt.plot(xlims, np.array([left[i], right[i]]), lw=1)\n", " plt.scatter(x1, fit_x1[i], s=30)\n", " plt.scatter(x2, fit_x2[i], s=30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Words of caution ###\n", "\n", "All of the predictions and tests that we have performed in this chapter assume that the regression model holds. Specifically, the methods assume that the scatter plot resembles points generated by starting with points that are on a straight line and then pushing them off the line by adding random normal noise.\n", "\n", "If the scatter plot does not look like that, then perhaps the model does not hold for the data. If the model does not hold, then calculations that assume the model to be true are not valid.\n", "\n", "Therefore, we must first decide whether the regression model holds for our data, before we start making predictions based on the model or testing hypotheses about parameters of the model. A simple way is to do what we did in this section, which is to draw the scatter diagram of the two variables and see whether it looks roughly linear and evenly spread out around a line. We should also run the diagnostics we developed in the previous section using the residual plot." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.12" } }, "nbformat": 4, "nbformat_minor": 1 }