aula13-regressao-linear.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Aula 13 &mdash; Regressão linear\n",
    "\n",
    "Renato Vimieiro\n",
    "\n",
    "rv2 {em} cin.ufpe.br\n",
    "\n",
    "maio 2017"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import matplotlib\n",
    "matplotlib.style.use('ggplot')\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "% matplotlib inline\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introdução\n",
    "\n",
    "Regressão linear é um método de aprendizado supervisionado que é muito simples, mas ainda assim muito eficiente e versátil na detecção e análise de padrões nos dados. O objetivo central do método de regressão linear é ajustar um modelo (um hiperplano) aos dados de forma a predizer o valor de um atributo quantitativo (variável dependente). Por exemplo, poderíamos tentar ajustar um modelo para predizer o valor do crédito a ser concedido a um cliente com base nos seus dados pessoais (salário, idade, tempo de serviço, empréstimos contraídos, dívidas, ...).\n",
    "\n",
    "Embora o objetivo central seja a construção de um modelo de predição de valores da variável dependente, o modelo ainda pode fornecer informações sobre a influência das variáveis independentes sobre ela. Em outras palavras, podemos usar regressão linear para entender como certos atributos influenciam uns aos outros.\n",
    "\n",
    "Essa aula é baseada no capítulo 3 do livro *An Introduction to Statistical Learning*, cujos detalhes estão nas referências da disciplina. Usaremos o mesmo exemplo base do livro. O exemplo consiste num conjunto de dados sobre o impacto de publicidade em três tipos de mídia (TV, jornal impresso, e rádio) nas vendas de um produto. A seguir carregamos o conjunto em um data frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 4)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TV</th>\n",
       "      <th>radio</th>\n",
       "      <th>newspaper</th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      TV  radio  newspaper  sales\n",
       "0  230.1   37.8       69.2   22.1\n",
       "1   44.5   39.3       45.1   10.4\n",
       "2   17.2   45.9       69.3    9.3\n",
       "3  151.5   41.3       58.5   18.5\n",
       "4  180.8   10.8       58.4   12.9"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ads = pd.read_csv(\"http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv\",\n",
    "                  usecols=[1,2,3,4])\n",
    "print(ads.shape)\n",
    "ads.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Antes de iniciarmos qualquer análise, devemos plotar os dados para avaliar se existe alguma relação entre o investimento em publicidade e o total de vendas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117e72470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figs, axes = plt.subplots(1,3,figsize=(15,4))\n",
    "ads[['TV','sales']].plot.scatter(x='TV',y='sales',ax=axes[0])\n",
    "ads[['radio','sales']].plot.scatter(x='radio',y='sales',ax=axes[1])\n",
    "ads[['newspaper','sales']].plot.scatter(x='newspaper',y='sales',ax=axes[2]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Percebemos que existe uma certa relação entre o investimento em publicidade e o aumento de vendas. É verdade também que a relação talvez não seja exatamente linear, mas, em geral, supomos como tal para simplificar o modelo. Nesse ponto, surgem várias perguntas:\n",
    "\n",
    "1. Em cada caso, qual a reta que melhor descreve os dados?\n",
    "2. Quão forte é essa relação entre publicidade e vendas?\n",
    "4. Qual a precisão do modelo e da influência dos meios nas vendas?\n",
    "3. Das três mídias investidas, qual é a que mais contribui para o aumento de vendas?\n",
    "5. Existe alguma interação entre as diferentes mídias? O efeito de cada uma delas é isolado ou elas se inter-influenciam?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regressão linear simples (método dos mínimos quadrados)\n",
    "\n",
    "No caso mais simples de regressão linear, queremos determinar a equação de uma reta que melhor se ajusta ao conjunto de dados. Nossa suposição é que a relação entre a variável dependente e independente seja dada pela seguinte equação:\n",
    "\n",
    "$$ Y = \\beta_0 + \\beta_1X $$.\n",
    "\n",
    "A escolha de diferentes valores para os coeficientes $\\beta_0$ e $\\beta_1$ resulta em diferentes retas. Exemplos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11860c160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figs, ax = plt.subplots(1,1,figsize=(6,5))\n",
    "ads[['TV','sales']].plot.scatter(x='TV',y='sales',ax=ax)\n",
    "ax.plot(ads.TV,np.repeat(ads.sales.mean(),ads.shape[0]),color='green')\n",
    "ax.plot(ads.TV.sort_values(inplace=False),ads.TV.map(lambda x: 0.05*x+7).iloc[ads.TV.argsort()],color='red')\n",
    "ax.plot(ads.TV.sort_values(inplace=False),ads.TV.map(lambda x: 0.03*x+10).iloc[ads.TV.argsort()],color='black');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O problema é como encontrar os coeficientes que melhor se ajustam aos dados. Isso nos leva a refletir como definir o conceito de 'melhor se ajusta aos dados'. A definição mais comum leva em conta a minimização da soma dos quadrados dos erros (chamados de **resíduos**). Ou seja, deseja-se obter o mínimo para a função:\n",
    "\n",
    "$$S(X) = \\sum e_i^2 = \\sum (y_i - \\hat{\\beta_0} - \\hat{\\beta_1}x_i)^2$$,\n",
    "onde $\\hat{\\beta_0}$ e $\\hat{\\beta_1}$ são estimativas para os coeficientes.\n",
    "\n",
    "A função atinge o mínimo quando sua derivada é zero. Assim, para calcular os coeficientes, derivamos a função, igualamos a zero e resolvemos o sistema resultante. O resultado é:\n",
    "\n",
    "$$\\hat{\\beta_1} = \\frac{\\sum (x_i-\\bar{x})(y_i-\\bar{y})}{\\sum (x_i-\\bar{x})^2}$$\n",
    "\n",
    "$$\\hat{\\beta_0} = \\bar{y} -\\hat{\\beta_1}\\bar{x}$$\n",
    "\n",
    "Logo, podemos calcular os coeficientes para os dados do exemplo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 7.033 +0.048x\n"
     ]
    }
   ],
   "source": [
    "b1 = np.sum(ads.TV.map(lambda x: x-ads.TV.mean())*\\\n",
    "            ads.sales.map(lambda x: x-ads.sales.mean()))/\\\n",
    "np.sum(ads.TV.map(lambda x: (x-ads.TV.mean())**2))\n",
    "b0 = ads.sales.mean()-b1*ads.TV.mean()\n",
    "print('y = {:.3f} {:+.3f}x'.format(b0,b1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10cecadd8>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAh4AAAF9CAYAAABLS2EjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4CFJkpoxeEiSpGb+AmGSA2EcqP7QAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cb516a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figs, ax = plt.subplots(1,1,figsize=(6,4))\n",
    "ads[['TV','sales']].plot.scatter(x='TV',y='sales',ax=ax)\n",
    "ax.plot(ads.TV,ads.TV.map(lambda x: b1*x+b0),color='red')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "É importante ressaltar que, ainda que a relação entre as variáveis fosse realmente linear e soubéssemos os *verdadeiros* valores dos coeficientes $\\beta_0$ e $\\beta_1$, os valores encontrados pelo método dos mínimos quadrados seriam diferentes. Isso porque não consideramos erros que podem ser introduzidos aos dados por diversas vias (medições, representação numérica, ...). Assim, a equação mais fiel aos dados seria\n",
    "\n",
    "$$ Y = \\beta_0 + \\beta_1X + \\epsilon$$.\n",
    "\n",
    "Para exemplificar, vamos considerar que a verdadeira relação entre uma variável dependente e independente seja dada pela equação $y = 5x + 3$. Agora, consideremos que os erros sigam uma distribuição normal com média zero e desvio padrão 10. Vamos gerar um conjunto de dados seguindo tais especificações e ver como o modelo é ajustado."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = lambda x: 5*x+3\n",
    "np.random.seed(111)\n",
    "x = np.random.uniform(10,0,size=100)\n",
    "e = np.random.normal(0,20,size=100)\n",
    "yv = np.apply_along_axis(f,0,x)\n",
    "y = yv+e\n",
    "\n",
    "b1 = np.sum((x-np.mean(x))*(y-np.mean(y)))/np.sum((x-np.mean(x))**2)\n",
    "b0 = np.mean(y)-b1*np.mean(x)\n",
    "g = lambda x: b0+b1*x\n",
    "yreg = np.apply_along_axis(g,0,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAssAAAD8CAYAAACB6OnnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAIABJREFUeJzsnXt8VPWZ/99zS0ggECDcMiEEQiSCotCKtdufVSm70lrtYnt+q62Lrru89mUttopAy6/WurqLyrYott2ldrvWtuqppFpdQ1VabbvepTWIBBIghEzCJUAgkNtczu+PM7czt8xM5p7n/XrxgjnzPed8vzPDmc955vM8j0nTNARBEARBEARBCMec7QkIgiAIgiAIQq4iYlkQBEEQBEEQoiBiWRAEQRAEQRCiIGJZEARBEARBEKIgYlkQBEEQBEEQoiBiWRAEQRAEQRCiIGJZEARBEARBEKIgYlkQBEEQBEEQoiBiWRAEQRAEQRCiYM32BEKQdoKCIOQ7pmxPIIPINVsQhHxn2Gt2rollOjs7E96noqKC7u7uNMwmN5D15T+FvkZZn05lZWUGZpNbyDXbSCGvDQp7fYW8Nijs9SW7tniv2WLDEARBEARBEIQoiFgWBEEQBEEQhCiIWBYEQRAEQRCEKIhYFgRBEARBEIQoiFgWBEEQBEEQhCjkXDUMQRAEgIaGEjZuLKOz00JlpZv163tZsaI/29MqGBRFKQceBy5ALwH3D8Be4BmgBmgDFFVVT2VpioIgCDmBRJYFQcg5GhpKWLt2Ag6HFU0z4XBYWbt2Ag0NJdmeWiHxCLBdVdV64CJgD7Ae2KGqah2ww/tYEARhVCNiWRCEnGPjxjL6+42Xp/5+Mxs3lmVpRoWFoigTgMuBnwCoqjqkqmoPcB3whHfYE8AXsjNDQRAEI+fOmTh5MjuyVWwYgiDkHJ2dloS2CwkzGzgO/FRRlIuA94E7gGmqqnZ5xxwBpoXuqCjKKmAVgKqqVFRUJHxyq9Wa1H75QCGvDQp7fYW8Nsjv9e3bB2fP6o325s7VMIdo5nSvTcSyIAg5R2WlG4cj/PJUWenOwmwKEiuwGPiaqqpvK4ryCCGWC1VVNUVRwtpZq6q6Fdjqfagl0zVLOonlL4W8vkJeG+Tn+gYGYN8+m//xnDkuTp4MuyxJBz9BEEYf69f3UlLiMWwrKfGwfn1vlmZUcHQAHaqqvu19/Cy6eD6qKMoMAO/fx7I0P0EQRjmtrRa/ULZYNC680Mm4ceFCOROIWBYEIedYsaKfhx46jd3uwmTSsNtdPPTQaamGkSJUVT0CHFYUZZ5301LgI+A3wErvtpXA81mYniAIo5i+PhNNTTb6+nSJOnOmiwULXJhM2ZuT2DAEQchJVqzoF3GcXr4G/EJRlCLgAHALegBFVRTlVuAQoGRxfoIgjDJ27bKhBQWP5893Ys0BpZoDUxAEQRAyjaqqfwE+HuGppZmeiyAIo5uhIWhuDniTrVaN+fNdWZyRERHLgiAIgiAIQlZobbX4LRcAdXVOSnKspL6IZUEQBEEQBCGjuN2we7fNsG3hQmeWZhMbEcuCIAiCIAhCxnA4LJw4EYgmz57toqwsO5Uu4kHEsiAIgiAIgpB2NE1P4gsmV6PJwYhYFgRBEARBENJKe7uFnp5ANNludzN5sifGHrmDiGVBEARBEAQhbTQ1GaPJF17ozGrd5EQRsSwIgiAIgiCknFBvcnGxxrx5uVMSLl5SIpYVRfkG8I+ABuxCL24/A3gamAy8D9ykqupQKs4nCIIgCIIg5C6h0eRcaTCSDCNud60oih1YDXxcVdULAAvwd8CDwPdVVZ0LnAJuHem5BEEQBEEQhNzl+HFzmFBeuDB/hTKkQCx7sQIliqJYgVKgC7gKeNb7/BPAF1J0LkEQBEEQBCHHaGqy0dVl8T+eO9eVlmoXp06ZOHzYMvzAFDFisayqqgPYBLSji+TT6LaLHlVVfcaUDsA+0nMJgiAIgiAIucXZs6aI0eTS0tTUTnY6dSH+3ns29u+3cPiwlYEBE253Sg4/LCMOiiuKMhG4DpgN9AC/Aq5OYP9VwCoAVVWpqKhIeA5WqzWp/fIFWV/+U+hrlPUJgiCMTkJF8rRpbqZNS11JuKYmG04ntLXpknXMGCeVlXrZuUxV1EiFg+QzwEFVVY8DKIrSAPwVUK4oitUbXa4CHJF2VlV1K7DV+1Dr7u5OeAIVFRUks1++IOvLfwp9jbI+ncrKygzMRhAEIfsMDMC+felrMHL2rIkDB6y0tOhS1WzWqK11M2+eC5ttmJ1TTCrEcjvwCUVRSoF+YCnwHvB74IvoFTFWAs+n4FyCIAiCIAhCFgmNJkNqhXJTk43jx0309Oi+5FmzXBQVZa/bXyo8y2+jJ/LtRC8bZ0aPFK8D7lQUpRW9fNxPRnouQRAEQRAEITt4POFCeeFCZ8pE7P79Fj74wEZLi9UvlOvqXCxYkJ5EwXhJSSEPVVW/A3wnZPMBYEkqji8IgiAIgiBkj3RGkzUNdu2y+S0XALNnu7BasxdNDiaPq94JgiAIgiAI6SadDUaammycPQtdXYED1tW5uOACJ+ZUFTgeISKWBUEQBEEQhDDSGU12ueCjj4zR5NpaF2VlHmprI9eE83j0P1YrDA5CUREZqYghYlkQBEEQBEEwECqUZ892UVaWmrrJTU022tosOJ260rVaNWbPdkcV4j6bBkBfn8lfvzmVc4qFiGVBEARBEAQBgNZWK319xnBtqqLJZ8+a2LfPysGDRstFba2LsWMji16faD93Dt777/1UnDnEeXdeQXGJieJiDYfDwoQJKZleVEQsC4KQdRoaSti4sYzOTguVlW7Wr+9lxYr+bE9LEARhVBEaTZ4wwcOsWalpk9fUZLRclJRoVFVFjybv3m3F7dZF+2s/P8HYXzzJfNowAed972OcGCyjudkXbU7JFKMiYlkQhKzS0FDC2rUT6O/XMzkcDitr1+phAhHMgiAI6efECTMOh8WwLVXR5LY2Cy0tVs6cCWTr1dW5uPBCZ0S/8aFDFk6f1sc274beNZupo4tiBgFY9JuvcfB4IJRss2nYbHpL7HQhYlkQhKyycWOZXyj76O83s3FjmYhlQRCENJPOJL7QaHJ5uYfZs13MmRMere7tNfntGefOwUdf3MwETjObUwD8VXUbe//zOQ57x7tcYLGA02niyBEYPz4lU46IiGVBELJKZ6cloe2CIAjCyElnu+pQkQx6NDnS8d1u2L1bn4emwRv3vEnRe28zmzYAZtCJq+EJ9paUALqQtlhgzBh9/5ISjdmz4cSJlEw9IiKWBUHIKpWVbhyO8EtRZWVqfHJCZBRFaQN6ATfgUlX144qiTAKeAWqANkBRVfVUtuYoCEJ6SGc0+d13bbS3B67pkyd7uOSSoYgJfMHzeO9N0O7bzDyvSAaouaiUsxtV/+OWFit1dS7/47o6JyUl6S8fJ2JZGBGSmCWMlPXrew2eZYCSEg/r1/dmcVajhitVVe0Oerwe2KGq6kZFUdZ7H6/LztQEQUg1wSXYfETzDidKItHkYJF8/LiZtr//HrM4hBldUE+gB1vjf3PWO2bfPitz5rgMQnnhQienT5twu6GiYuTzj4WIZSFpJDFLSAW+z4rcdOUE1wFXeP/9BPAaIpYFoSDYudNET0/qbRdDQ/DKK2MYGAgo7spKN5ddNhQ2ds8eq7+2stsNb931W6r3/p7ZDABQzilsTz+K5q0FNzAADocFkwkOHtSjynPnujh92mQQ3DU1I15GTEQsC0kjiVmjg0z8erBiRb98ZjKPBrysKIoG/KeqqluBaaqqdnmfPwJMC91JUZRVwCoAVVWpSCKkY7Vak9ovHyjktUFhr6+Q17ZzpwmLxUJ5eTkA9fUapaUjP+7775vYuxdsNv0PwCc+oTFnjnHciRNw6JCJsWP1x3s+GOLkP3+beRz1jxlXMYaKF573P37rLSgvx7/PpElw0UUahw7pYtu7FObP19L+3olYFpJGErMKn0i/Htx55wTuuWc8PT1mv3hetSrLExWS4VOqqjoURZkKvKIoSnPwk6qqal4hTcj2rcBW70Otu7s7dMiwVFRUkMx++UAhrw0Ke32FuLbg6Gt5eTk9PT0sXOikr29ktYlPnjTx+9+PMWybM8fFokV6pNr3Mg4N4a+FDLrnuGf1JmbT5r8TN+FhcuOjAPT09PDnP1sZO1ZP4uvthTFjNK68coDWVhsffBA4X2mph7lz3Zw9C2PGJPfeVVZWxjXOPPwQQYhMtAQsScwqHCL9euB0mjl1yoKmmfzWm6eeyr9LSUNDCUuWTKWqagZLlkyloaEk21PKKKqqOrx/HwN+DSwBjiqKMgPA+/ex7M1QEISREJrEN3WqlhLbxZ/+ZAsTyp/7XL9fKAef3yeU+/th/99tYuLq2/1VLsZzmgn/fa9fKJ85A2+9VcS4cXrCntWqcfHFQ8yc6aa1Ndw+Mndu5rSGRJaFpJHErMInnl8J+vvN3HOPiWXLMjChFDHa/faKoowFzKqq9nr//dfAfcBvgJXARu/fz0c/iiAIuUi0ShcVFYGIbzLs3Wvlww+Nx46UwBd6/tZdLsrWrmUCHsP2osafArov+X//t5jqajeTJ+tjampc2Gxw7pwxEJOqih2JImJZSJrRmJg12qp/RCvrFsrhw8MOySnEb8804NeKooD+PfBLVVW3K4ryLqAqinIrcAhQsjhHQRASJF0l4bZtC//l7frrjdfK0HO3tFgxr95AOacN2ysaNwMwOAh/+YuNiRM1qqv1KHF1tQurVbdgBFNf76SoaKSrSB4Ry8KIGE2JWaMxGhnp14NIzJyZoQmliNHut1dV9QBwUYTtJ4ClmZ+RIAgj4dgxM0eOpL5d9Z//bOPAAaNU/MQnBrHbA1HilhYr/f2BShgnTpjRvrKaiUH7FDNA93c3MntJOS4XtLVZOXbMzJQp+nHsdjcOh4XiYuP5q6pcTJoUXp850+Sf0VAQskSsaGShsmJFPw89dBq73YXJpFFe7sZmM164Sko83HdffvnUxW8vCEKh0NRkS4tQ3ratJEwoX399v18o9/fr5duChXJrkxPtK6vDjlXW+B/MXFxOS4uV118vRtNgyhQP06e7GT/eQ2mpZqihbDbr/upgoezxeLjrrrtYuXIlLpcr7BzpRCLLghAnozUaGfrrQSQryg03jB2RFy7TiN9eEIR8p78fWlpSXzf55ZeL6e01Boauu64fa5BijGS5uGj1tZRTbdg+5lePUFqq0dJipa8PSkuhutrNlClubDYwmTSmTTMGYELXoGkaVVVVhm1OpxOrNXMSVsSyIMSJtGXWiWy9GZuVuSTLaPTbC4JQOKTDm+zxwK9/bfQml5d7WLp0MOp5Dxyw8PGv/g0TOY92r1AuZoBj925kzpJyWlv1YNKpUyYmTtRFcW2ti/37jW2ro83fbrcbHo8dO5ampibGjBkTNjadiFgWhDiRaGRhMZr89oIgFA6hgnXBAmdYQlyiDJfAF3pOjwdOtPcz8atr2cd5hufGvfQfHGm10toK7e0WqqvdTJyoMXeui9ZWK2YzYW2rQwkVyQDvv/8+06dPT3htqUDEsiDEiUQjBUEQhGyRjmjysWMm/vhHY5R28eIhZs92Rz1nS4uVT67+DCepx01ApZ969DH971ZwucBq1S0Xc+a4OHDASleX2SCS6+pclJQYLRiRRPIvf/lLPv3pTye/yBQgYlkQEkCikYIgCEKmCRWtM2e6/LaGZIkVTe7tNXHwoFEi+kRyN/XsoR6AYgY5ds+/4QlqNe2zXMyc6eLwYSsHDhgtF2VlHr8Y9xFJJN96663cd999yS8whYhYFgRBEARByEHSEU3evr04rNlHcAJf6DmHhqB44AwfX/1lv0j2se/+xxk/Xhfthw9bmDnTzfnnuzhyxMLhw1bmzHEZLCKhc48kki+55BKee+65ZJeXFlIilhVFKQceBy4ANOAfgL3AM0AN0AYoqqqeSsX5BEEQBEEQCplQ0VpUpFFfP7KSabGiyZGEudsN9uuuZg/1HKfWv715ww+ZNs3DeALR7fp6J+PGaf4ydrF8yTU1NTid4aLf4XAkuKLMkKrI8iPAdlVVv6goShFQCnwL2KGq6kZFUdYD64F1KTqfIAiCIAhCwZGOaPK2bSWUlZkM22KJ5KNHzVxw81/TSq0/mlzEIHtuf5DyuZOYZtZrLff2migr0/wVLs6diy2Sa2trGRgYCDtfropkHyNuSqIoygTgcuAnAKqqDqmq2gNcBzzhHfYE8IWRnksQhMKmoaGEJUumUlU1gyVLptLQEB4FyafzCIIgJEKqhfLJk+awaPKkSW6uv76fpiZb2Pl6ekyYTp3igpv/mj3U40R/vody3l3zX0w6bxJmM5w8qQvvxYv1ue3fb6Wy0uUXyhde6DTM+9prr8Vut4cJZYfDkfNCGVITWZ4NHAd+qijKRcD7wB3ANFVVu7xjjgDTIu2sKMoqYBWAqqpUBJnE48VqtSa1X74g68t/Cn2NqVjfU0+ZWbfOQl+ffhF2OKysW1dOWVkZN9zgGWbv9J6n0N8/QRCyy9GjZo4eTW0XvmiWi54eU0RRDlB3w994LRd6NHmQYprXbKa62k01gaS8Sy910tJipaVFl5E+kVxT4/J7mAEefvhhNm/eHHaefBDIwaRCLFuBxcDXVFV9W1GUR9AtF35UVdUURYmYtqmq6lZgq/eh1p1EG7CKigqS2S9fkPXlP4W+xlSsb8OGqX4B66Ovz8SGDbBsWepeu2TOE+/6KisrUzJHQRBGD6mOJjc12fwi1se8eU6uuELjd7+LLJKnLL8aN2a/5cKFmT03fxfz9MlUextv9fWZuOiiyCLZYtFYsCBgv3j55Ze55ZZbws6TbyLZRyrEcgfQoarq297Hz6KL5aOKosxQVbVLUZQZwLEUnEsQhAIlU+3ER2vbckEQcouhIWhuTl27ak0joqXMZ7nYudMYJLDZNFxdJ6i46St+kezBxCFmcWbNOqqr3YCH/n5YsECvlewTyTabRk2NO2zO+/fv5/LLLw+bQ0dHByaTKWx7vjBiz7KqqkeAw4qizPNuWgp8BPwGWOndthJ4fqTnEgQhP0jGExytbXiq24ln6jyCIAjRaGqypVQo79xpC7vOXn75IHV1rrDI9eTJut2s/DPLcd60xi+UD1LDrjU/ZOy/r/EKZf26WFPj5sCBQGy1rs5FTY2bhQsDvuTe3l7sdnuYUD5w4AAOhyOvhTKkrhrG14BfeCthHABuQRfiqqIotwKHACVF5xIEIYdpaCgxtAV3OKysXTsBIGZDl0y1E5e25YIgZJNQ8TpvnpPi4uSOdfCghZ07iwzbZsxwMW4cdHVF/rXMvOSzTAGDSD578y14Kqb6RbLN5qG62sP+/QGZWFvrwmw2inpN06iqqgo7x7vvvltQtrSUiGVVVf8CfDzCU0tTcXxBEPKHjRvLDEIUoL/fzMaNZTHFcqbaiUvbckEQskGqvcl/+EMRx48bBfGllw5y8mQUS9mRI0z52y/4RfIB5mDCE2S5cKNpcN55LlparOzfH7iO19W5uPBCJ8EB4lxtTZ0OpIOfIBQYDQ0lWRWCI/EEZ6qduLQtFwQhk4QK5SlT3MyYkVyVn0gJfHPnujCZCBPKF17oZNcuG1OWX42GHk0+SA0AvWvuBvBHk+vqXIbkPd82u93tt25AZJG8Zs0avvGNbyS1nnxAxLIgFBDJWiBSSWWlG4cj/NKSLk9wtm8OBEEQopHKaPLQELz4YglaSG2x4CYgPi64wMmHH9o4UvV5v+XCJ5LP/v3NeKZO84vk6moX7e1GkeyzcgTPNZJIvuyyy3j22WeTWk8+MeIEP0HIZxoaSliwYBp2+wzs9hlccMG0vG5QEcsCkSnWr++lpMQYMUmXJ9h3c+BwWNE0k//mIJ/fQ0EQCoNUCuWmJhsvvDC8UJ40Sb/2fvTqCaYsv5qTTOSPfIojTAXgzJp1TJo/hepqt3/f9nZr2DE/+clA8p7dbg8TyhaLBYfDMSqEMkhkOeNIFCx3aGgo4c47J+B0BsTlqVMW7ryzHMhcJDaVpKIs2kg/o5n0BCfrjxYEQUgXqRbJoZaLoSEMNY19zJvnZO9e3XIB8D6LORokkseOLaF68lnq6lz09JjCjltX5xo2kgz5Wyt5JIhYziC58BO5EGDjxjKDUPbhdJryVmyN1AKRqs9opjzB0W4CHA4LVVUz5IZUEISMkk6h3N1tpqLCEyaUFy500tRk4+Qc3XLxIQtoZyYA5266Gfc03XJxySVgsQzy1lvG0hsmk/H6LiI5HBHLGUSiYLlFrGhrvjaoGGlZtHz7jEa7OQATmiY3pIIgZIaTJ810dKSmXXWoSNY0XdBedtlQ2PGbmmx8uP04U279BwBe4mrGcwbQo8kAV1wxiMUCzc3Q22sUyn/7t/2YvZd8EcnREbGcQaRzWG4RXWjlb4OKkVog8u0zGunmIJThxH6w7eTGSS+xdv6vmfqDO/BMnpyuaQuCUECkKprc22viwAErra2B76WODjO1tW5/Mh7oFS5OnTLR1BSwXLzE1YF91jwAwCWXDDJ+PH7hXRaUuvLJTw76q3GISB4eEcsZJNNVAoTYrF/fG+ZZBr2NZz43qBiJBSLfPqOhNwd68kt4p6hoYv/3PzjE7f/6SW73bTgB/BE+u/BvabKfLxYOQRCi4nLBRx8ZhXJoLeJ4CY0mt7dbqK52c+WVgWjy+PEeamrcfpE8BXifRRxlGhCoclFR4eGii5w4nYT5kkFvfw0wb948zp49G/a8iORwRCxnEOkcllv4RNC3vz2enh79PZk40cN9950ZtQIpHz+jwTcHS5ZMHVbsVwZFUb4c4XjLeJlXWQYO/BaOVatSO+dcQFEUC/Ae4FBV9RpFUWYDTwOTgfeBm1RVHYp1DEEYraQqmtzUZKOvz4TDod/Qt7dbqKpy+6PCwcduarLxYWMnU/7xH/2l4EItF0uXDobVSvZx440a3d393Hvvvfz4xz8Oe15EcnRELGcQ6RwWmaeeMrNhw9SsvCbRorCjtWpJvn9GI4n9i4o/4i+OBRD5l0YA/g9/4E/8n7DtPgvHqlXJNQ/Ice4A9gC+r+QHge+rqvq0oij/AdwK/ChbkxOEXCVUKNfWuhg7VosyOvZxfKK2q8uM02kylHQDXSTv32/xR5P3UM/bESwXV145yOnT4RUuAJYtG2D8eI1XXnmDa665Jux5EcnDI2I5w0jnMCMNDSWsW2ehr0//3SoXErJGe9WSVH1Gs3HD4Tv+7V+bFNg4GHlsZ3s7Sy6bEdW37h/XaQEKSywrilIFfA54ALhTURQTcBVwo3fIE8C9iFgWBD+pjCZ3dpo5d86MxwMdHbrlYs4cFxaL8bg+kXyIerqjNBbxde/r7jbazXyl4I4dO8b55y8Km0dLSwulpaUJz380ImJZyCobN5b5hbKPbFdfyLeKELnIN785niefHIumZeYmyHz8ONMvvhgg4D8OYeCqqzj55JOGbfEkCOaqX3uEbAbWAr6Un8lAj6qqvpBWBzFj8YIwuggVymVlHmbPTuza4HBYOHHC7I/+trdbGDPGY4gm+zzPTU02zIcP073q3/0i2YY+5syadd59dMtFcEIgwJw5LhYtcuLxeLDbZ4bN45VXXmH+/PkJzX20I2JZyCq5WH0hF+eUTzQ0lBiEso9U33BURsngDqbrww/RJk6M+nyw7cThsGAyYZh3wK89dsTzzRUURbkGOKaq6vuKolyRxP6rgFUAqqpSUVGR8BysVmtS++UDhbw2KOz1RVrbzp369aC8PLBt8eLELRc7d5pobtb/feKE/veCBVBfr/97/HiNuXMD52P5NRyjAhdWDlMFwMB37qemBoqK9MYk584ZK1yMGwezZ8OFF2oUFxtLxAFs2bKFVYWYgEH6P5ciloWskovVF3JxTvnExo1lYULZx4huONxuKqurhx3WmaD/zmc7eeWVV/je937F7t17cbu3Y7fPCrKOFI5YBv4KuFZRlM8CY9A9y48A5YqiWL3R5Sog4gupqupWYKv3odbd3Z3wBCoqKkhmv3ygkNcGhb2+0LVFs10ksnzfMVparLS369c/Xxm46dNd9PQELBe/+52NCcs/z35qgQqD5aLq4xXAWXp7dXtFS4uV3qC8a5/lIlIZuMsuu4xnn312VL138VJZWRnXOBHLQlZZv76XdevKDVaMbFdfSKYiRCb9ubmefBhLECd6wzH5S1+i+I03Yo7pfuYZhj71qYSOC7BixQrefvvtiM/dccde1q4tSfiY+YCqqt8EvgngjSyvUVX1y4qi/Ar4InpFjJXA81mbpCBkkX37rAwMGG/4E/Umaxrs2mUziGTAYLkI9iVbDh6k+7ZH6KaWDqpweuVZ2ffXUG4BpxNsXu0enMQXSySDJO+lChHLQlZZsaKfsrIyNmwgZ8RfohUhMpkQmA/Jh9Ei8yZTfPWr47FXJBo9Bli5ciWvvvrqMKP+CXiErVuLmTv3dM68phliHfC0oij3A38GfpLl+QhCxklFEp/vGM3NVn9JOF802Sdug8d1L/+6f98upuPEiuWBNZSVQW+vbrWorXXR3m4UyQDLl0+NOAcRyanFpGmJe2/SiNbZ2ZnwToX80wLI+nKdaLV97XYX77xzDEjdGuM5VzYIXl+ooAddKN900zn+7d/OhO077pFHGP/QQzGPf/af/5kz3/52QnO69tpref/994cdN23aRxw9en7Y9mTeP+9Pekm0JMhb5JodQiGvDQp3fWfOmOjpqaCnp8e/LVGRvHu3FbfbZIgmT5rkZtw4o0j2NTMJFsk+y8W5r6zEvmSKv8W1z3LhYyQiuVDfOxixDWPYa7ZElgVhhGQyITAfkg/jicynI3pcX19Pb+/wkevnnnuOSy65xP+4qmpG5PPn0GsqCEL68EV4g5P4kokmu1zw+uuBxLrqajfFxRoLFzr9keWmJhsHftfF+IcfBMCDiUPM0s//6BrK0atkzJnjwuUK1E2ePduF1QrLl9cAfWHnl0hyehGxLAgxiMcfnMmEwHxJPgyt1Vz82mtMtkfqlxfAM2YMR/bvj/scc+bMYXAwShHlIB5//HGWL18e9fl8eU0FQUgtPl9xMBcO3jFvAAAgAElEQVRc4MQcvZJkGD6hvWOHUSRDuOWipcXKxNW3+7sA9TKObioof3QNEGhx7evCB1BSolFV5Wb58quBnWHnF5GcGUQsC0IU4vUHZ7JFdDznypUEwLhKu+3bhzY2vkoTs2bNwuVyDTtu7dq13HHHHXEdE/KzxbcgCCMjkjd58WIt7koXg4Owd6+N99+30tNjTOCrrHRx2WW6SO7tNfHyy2OYuPp2fEUsjzKVPkqZvOZLlFfPor3dQkWFJ6xVdV2dS0RyjiBiWRCiEG9zkky2iB7uXNlMADQ7HExfsmTYcfHaKz72sY9x5MiRYcfdcMMNbNq0Ka5jRiLfW3wLgpAYoUK5qsrFpEnx5281NdlwOuEPfwiPJl9/feC6sW1bCZZDbUz898D16SA1zKaNU48+xsF2C7TD/PlO+vpMEUTyEPCh4dwikrODiGVBiEIi/uBMtjGPda5Mdx8Mjh5PjzLm+PPP4/z4x4c91tVXX82uXbuGHbd8+XIef/zxeKcYF9KGXhAKn5FWuohkuZg2zU1xsX4NMXnTxHbsKKKnx8LE1YF+ogMUMYYhyh9dw+GzcNJruQhO4Kurc/Gtb32LP/95J6HRZBHJ2UXEsiBEIR+9rGlPAPR4qJwZ3j417HxxXNjnz5/P6dOnhx1XW1vLH/7wh7imF4lcsaUIgpA9UiGUI9VMLi/X7RMA+/ZZ2LWryGC58DG05g76vZYLwGC5qKtz8eqrr7J69SZEJOcmIpaFjJFvoiUfvazpEPjxeI/d3/gGR9esiTnmqquuYu/evcMea+7cubz++utxzy8W+VCXWhCE9JEukQwRLBcH9jNx8/f929xYsODm1KOP6fu3w6JFToqLPbS0WJk1y8WJE10sX36Ld4+AUG5paaG0tDTueQrpJWViWVEUC/Ae4FBV9RpFUWajd4KaDLwP3KSq6lCqzifkF7FES662qs8VL2siNxmpEviJlnarqKggNDMm3sgxpC96kmlbiiAIucNIhPKpUyZ+97sxABE78PmOs22b3ukz2HJxAU18yELOPPqIXySXlXlYssRJS4uVoiITc+YMcM0113j3CIjk//mf/+Hiiy9OaJ1C+kllZPkOYA/4q6I8CHxfVdWnFUX5D+BW4EcpPJ+QR8QSLatWebI0q+HJtpc10chosgJ/4j/9EyUvvTTsfGLZKz772c/ywQcfDHsMyNxPi/lQl1oQhNTS1mbhzBnj900i0eT33rNx6FDkNtWxRLIJ0IA37voZB0210K5vD7Vc6Ml7ALsB3cJx1113ceeddya0TiFzpEQsK4pSBXwOeAC4U1EUE3AVcKN3yBPAvYhYHrXEFi25K5azTTKR0XgFflzR444O/FkrIdxyyy28/PLLwx4DYMuWk9kpX5eHvnNBEJJnJNHknTtNvPuuLoJ9Qrmqys28eS7/cXy2DOuBVso2bzbsrwEfrAnInEsuGaKsTIsgksEXTZ40aVJcic1CdklVZHkzsBYo8z6eDPSoquoritoBRPxmVhRlFbAKQFVV/efcBLFarUntly8UwvpmzoT29sjbC2F9w5HsGmPdZCR6PPOzz2L9cuzGIABDQY0+gs9w66238vOf/zyuc5WWeujrC4jsdes0ysrKuOGGzN4YPfAA3HabZphLaanGAw+Q0Os3Gj6jgpDP9PebDG2hIbFo8rZtJZSVGS0XixcPMXGi5hfJkaLJ1/ICv+HzHP7Xxzh5MrCvL5o8fryL1as/E3SmgOVCkvfyhxGLZUVRrgGOqar6vqIoVyS6v6qqW4Gt3odaMr29C7nfORTG+u6+uySil/buu0/jco3N+/UNR/J966dGjYzGc7x4osdHdu7EM21aYIP3uA888AA//OEP45rn4OCgfz5LlkzF4TBGo/v6TGzYAMuW6WMyley5bBk8+GD4uZYt64+7+QDE//5VVlaOYLaCICTDSKLJPgE8NARtbfo2n+Vi0iQPJ0+aI4rk82lmD/X8/O4/cVCrgZP69uDue0aR3AMcAEQk5yOpiCz/FXCtoiifBcage5YfAcoVRbF6o8tVgHw6RjGxvbTxdXDLJ0LF4AMP6MItURJN2DMfO8b0RYuGPW4k7/GWLVvYuHFjXPOKdbGPFg13OCwsWTKVpUsH+NWvSjNWoSLbvnNBENJHqFCur3dSVDT8ftu3F3PunH4N8kWTy8rwl4ED6O42s3+/FWtrK2WP6paL82mmjxL2UK9bLry9TKqqXMyb52ZwMFQkgy+aLCI5fxmxWFZV9ZvANwG8keU1qqp+WVGUXwFfRK+IsRJ4fqTnEvKbQhEtw0VFIyXl3XabxoMPlkRdf7RjxpOwF0/0+NT3v0+/ohi2PfXUU6wZptybj0Qu8tF8wmDC4bDy5JNj0TRj5FkqVAiCkAjJRpP7+0289JJe5eLYMTMDA/q1aOnSQcrLS+jv9zA4aPZHh33R5PNpppp2fstfG3zJvn1bWqwhnmQQkVw4pLPO8jrgaUVR7gf+DPwkjecSMkS+1UpONbGqU4Auah0OC3pedIC+PlNUMThcxYuwmwxNo9JeNexcQ6PHzz//PLfddltc6xzJxT1SNDyYUKHsQypUCIIQD6FCeepUN9OnD58P4bNTAIbmIAADA/r2Dz/Uw9LBInkip3iDy1D//mk8UwOWtU9/epCzZ00RRDLAThHJBURKxbKqqq8Br3n/fQBYksrjC9lFGjxEr07x7W+PZ3DQFFUgQnQxGE/Fi3iix866Oo6/9pr/8euvv86NN94YfYcgUnlRD46GR7pxiIZUqBAEIRbJRpP/8hcb+/frcscnkidN8rBokXHf5maw7ttH2WOPUkcLVvRr0i+4gTNr1vnH+SpkiEgePUgHPyFupMFDdMHb02NmOFEYTQxGO2aHwxalhkzQvkEX5Z07d/L5OEQ1pP9nQV80XE/2C7/MmEyaIcKc650RBUHILskIZV+ZNx+h0WRfSbeA5eJm6jjCRHqYzAm28zfsX/Ow4ZhLlw5GEckf4HBEKPkkFAQilkcBqbJOSIOHWH7c2JSWalHFoO+Yr3M5l/PHYY/lE8j79u3jyhwRx9GIlqD4pS/1sWPHmFFr5xEEIT5SKZIXLhxiypRA3WPQBXOw5WIurTRTz49WvoJnSsByUV3t5qGHLmbTpvASkg7HC4kvTMgrRCwXOKm0TkiDh8jiz2bz4HRGiypr2O2+ahjhr3el3U7HMOfsPHQIrFY6Ojq49NJLIQ6BnCs/A8ZOUDyT3ckJgpDTJCqUz50zsX+/NUwo+0rBtbRY6emByZM9emORfXspe2wL59PsH/8otxssFzNnuunsfIzVq5/DWHleRPJoQsRygZNK60SiZcwKkUjir6/PxKlT4V5lk0nj0Ud7WLGi31unF4pffpnJt9wy7Hke23KSK65wcOGFF8KsWcOOzxVxHIlCqYIiCEJm6Ooyc/y48RfLZKLJ1dXusFbTLS1WTpwwM3H17X6RbMXFS1zN4Hfu59y5wLWqqqqFO+5YFXauP/1pG7Nnx1GfTigYRCwXOKm0TsRTxmw0ECr+qqpmRBynafpYX3JerHYVx155hTM1NdTV1ekbvjYp5hwOHz6M2Rw9mVAQBCEfSTSa3NRkY3AQ2tt1OePxwMCAiepq/RfPYAHts1z4RPLF/IWn+Dt23fxdPBVT/RX/KysHufPOqcBiw7m+973v83//79wRrE7IV0QsFziptk5IlDCc0Nd4PKc5Tbn+IIZj4lBbGzU1NfqDYTqWHDx4kKJ4Ku0LgiDkIUND0NxsFMrDiWQgYjS5tFTzbzOZ9MCFdd9eljz2Vf/2PdTzElcbLBc1NXDLLRPQRXJAKH/xi1/ikUf+PsmVCYWAiOUCR6wT6Wf9+l5uHyYSDHDmq19lwg9+ENjgE8oR2Lt3L+PGjUvB7ARBEHKbRKLJkURyb6/efW/mTBe+qkRTp7o5dsyCpsEngzrqnaGMDuw0hTQW2bTpSqCbYJFssVh58cUX426dLRQuIpYLHLFOpA+fveL2GGMMaX/BQjmEDz74gIqK8CzrQmW0N7cRBEEnVCjX1bkoKdHCxp0+beLQIV2yBAtlAJv3ECZT4Ip77JjFIJI/xk5+zo3suvlf8ARda3WRvBNdJAe2NzZu94pkEcpCgYjlp54ys2HD1Li/eEfbF7VYJ1JDPI1B4mu/AW+88Qaz4kjcK0SkuU32URRlDPAHoBj9e+BZVVW/oyjKbOBpYDLwPnCTqqpD2ZupUKiMNJoMur3CZIIxevdqPB4wm6G+520m3bPBP24P9fyRT+FY8y/+bZs2XQPsQ/fKBaLJjY3bueACJ2aziGQhQN5nCDU0lHDbbRYcDiuaZvJ/8TY0lEQdv3bthLjHC+nnqafMLFkylaqqGSxZMjWn3otKu93/JxKmkD/RePvtt3E4HP4/IxXKDQ0laXvN0nlsiF2hRcgYg8BVqqpeBFwMXK0oyieAB4Hvq6o6FzgF3JrFOQoFSqhQLivzRBTKTU02mppsnD5t8gtlX75Ne7sFU8hFd/p0N59c/Rm/UN5DPXuo54M1P/IL5U2bHvRGk98iOKmksXE7b775FgsXOpHcaSGUvI8sb9xYRl+f8X9MrNJo0oUut2hoKGHdOov/Pcx2lHHCt77F2CeeiPp8vJHjZ555hk996lP+x3rpuO4Rzk4nnZHZTER9pblN9lFVVQPOeh/avH804CrA1yP9CeBe4Eeh+wtCMsQbTQ4eFxpNfuutIqqr3f5qFz6CLRegC+Vdt9yPZ/JkQBfJsJ2A5eJCQBfJvnlUVGik6DItFBh5L5YT/eKVL+rcItGbnXQQy14Rrzj+8Y9/zGc/+9nUTGgY0nnDl4mbSWlukxsoimJBt1rMBX4A7Ad6VFV1eYd0MGzDdUGIj3iEcjSRXFfnYseOYuz2gEj2Vb6Y3/Mm5fd8G4CD1DCA7sn4wJvAFxDJPnTLhU8k2+1uJk/2jGxxQsGT92I50S9e+aKOTab93Nm4ebG9+y5TvvCFiM/FK47vv/9+bomjuYjx9Zyaktcz2dcsnvc2E+9HpAotJpOGw2FhyZLUvEbBjLYchXhRVdUNXKwoSjnwa6A+nv0URVkFrPIeI6nEVKvVWrAJrYW8Nkh8fTt36lfV8vLAtsWLjQl83d3Q3m7yj2lu1qtb1NfD9u1w4gQsWKA/53KB1QrXXw+2yz4BwFnGcpiZALR+578B2PTde9E9yQcIRJPhzTffijoPee/yl3SvLe/F8vr1vaxbV26ITsYqjVZopdRSKQSykXiVqZuXWJ7jeLjzzju56667Ejpnul7PZF6zeOeSifcjuEKLw2Hx1kEd3oaTzGddkgmHR1XVHkVRfg9cBpQrimL1RpergLDWkKqqbgW2eh9qydiLUmlLyjUKeW2Q2PqiRZODd48UTfZ12tu2zeKPJPf26tHkpUsHmbL8av8+HkwcZiZdd97DMfMMr0huA5rRrfnFwGJ/JLmnp8cf0Q5dhrx3+Uuya6usjNUuLEDe29hXrOjnhz90Y7e7MJk07HYXDz10OuoX4YoV/Tz00Om4x+cyqU5WzEbi1fr1vYYC8pCim5eBgYjJefEm5F1//fWGhLxEhTKk7/Vcv76XkhLjz4bDvWbxziWZYyfDihX9vPPOMex2t18ox5pXsp91SSaMjKIoU7wRZRRFKQGWAXuA3wNf9A5bCTyfnRkK+czJk+YwobxwodNgu/Al7wF0dpppabFSVaU7gHbsKKajw2ywXNTVubh63Ot+oXyKcvZQz17m8cGaH/EvP/4NmzbdhW65aEa35BfT2LjdL5R98xCERMn7yDLADTd4WLYs/juKQimllmp/aTYsEStW9FNWVsaGDYw4Oh4pehxv5PgTn/gE27ZtS/icsUjX6+l7bb797fH09Ojv/5gx4XVJk5lLputyxzuvZD/rkqMQlRnAE17fshlQVVV9UVGUj4CnFUW5H/gz8JNsTlLIP4bzJoc+74smFxVpHDxopasrEE3u6zMxebKbpUtdfpG8J8gt9MGaH/Hmm2/wv5seBP4CHPH+fTGNjX+KOgdBSJSCEMujlVQLgWz5uRO92QkmVCDHK471MrLdlJR40vbLQrpfz8HBQHz81ClLTHtBInPJ5M1kvPNK9rMuOQqRUVW1CVgUYfsBYEnmZyTkO2437N5tFMIXXuj0l3eLJpIrK910dlpobbUyc6axysVFFzkNInkurQCc3vD/eOewlZ9tepCA5ULnuecOUVxc7H8sIllIBXlvwxjNxEpiTIZM/QQ/EoKtFZV2e9y2CgC73YleHUtDb2ua3p/k0/l6JmovyNX3Nt55JftZz9V1C0Ih0dRkCxPKCxfqQvn4caMlw+PRhfLcubrl4sMPrf7KFiaT/vzMmS4WHNMtF3uoZwh9/1bm8v7Xt3D7Az/nZz+7l4DlYg9btjxGY+N2EcpCWhCxnELS3cwhlFQLgVz1cycrjoM9xw6HI+M/yafz9Ux0Lbn63sY7r2Q/67m6bkEoFEIjxrNnu/witanJRldX4JrU0mL1N/xobdVF8qRJmjearFvJ5s1zMfNvr8Z6/7/7LRf7qeXopse4iRo2b/4aekMRPZr85S9/hcbGQ8ydO9d/nlB/tCCMFJOmxfY6Zhits7Mz4Z1yIcMzNOseSNlP/LHWVwhlsULXV7ZxI2VbtgCJ2Cp0cRyLJUumRvxJvrzczdixWlpfw1R/RqOtxW538c47x1J2nnjJxP/BbH7W412fN7M6kY9tvpO31+x0Uchrg8D6YnmTI1kuqqtdtLfr16z2dgtlZW4mTgyMqasz+pJncYhDzOL0//s2t9//JLrdAnwiedKkyfziF78wnGfOHBfjxiWvaUbLe1eIjLAaxrDXbPEsp4hUJNslIwYKJVnR5z1ORGVs2XLS8Ho1NMR+vSKVDbTZPJw7Z6anJzc6CMZLoZVAjIdC+awLQr4TKoZLSz3MneuOKKB93uRgoRzafW/Bkd8zYfUD7KGeeq8YPsQsbqIG7t8M9BLwJTfT2NgWdh6JJAvpRMRyihjpT/yx6sGuWpWaOeYS1n37mHrllUlHjpOpnxup0kNfn4lTp/Kv/Xmmq1YIgiA0NdkoLzdetRcudHrLwBmvo6Ftqn0iOVgo+6LJe6in02u5aKaemwCoQY8mtwEDAIYScMHnF4R0I2I5RYw06z5WZHrVqsJoxenzHMdLLFtFspH80OhkVdWMiOPyobSYRFoFQcgUkaLGU6aER5OHhuDQochC2ddsBOCTqz/DHurppp4ZHKGL6RFEsh5N/u1vG/F4jN8eNpvG+ee7EIRMMGKxrCjKTOBnwDR0h/5WVVUfURRlEvAMgU++oqrqqZGeL1cZ6c/isSPTeSqW3W7s1dVxDx/OcxxMqpL1pLRY9igEv70gFDoHD1ro7TUGJnzR5OPHjdfbaNHkpUsHaWmx0tJiZUHnDjo3/po91HM+zeyhns8wHd2EpxEskn2RZE/IV6BEk4VMk4pqGC7gLlVV5wOfAL6qKMp8YD2wQ1XVOmCH93HBMtKs+1SXgcsWdrs98GcYoeyrUjE4OJiQUIbUvV65VFos09VUskmqu08KgpB6mppsYULZtz2YvXstBqGsaTAwAEuXDgIBEb1o9TV0bvw1Jm/li4/7LRegC+VWdE/y9qiWCxHKQjYYsVhWVbVLVdWd3n/3ordMtQPXAU94hz0BfGGk58p1fC18Ozq6eOedYwlFyXJJtMUiVNAZxHGEDnrBOBwOtmw5id3uxGTyjEgQpur1ypXSYqNNPEobakHIXfr6TBFtF6GcPWvyloMLWCTa2y2cd56LBQuMlouJq2+njRrK6eErmLwieSDoaM00Nr7In/70UsRziUgWsklKPcuKotSgd4V6G5imqmqX96kj6DaNnCKXfgaOnbA1NitzCqWhoYSvfe184CgAwwWDQ6PF0ZLyyso8LFuW2FxSmeCWC97fVLcuj0Qufd6lDbUg5CaRyr7V1Rm9wR4P7N9vlA/9/XDBBS6DL3navjcYeuyXfsvFx6kHyoFjwFRgDL5Iso9Ilg9ByDYpq7OsKMo44HXgAVVVGxRF6VFVtTzo+VOqqk6MsN8qYBWAqqofGxoaSvjcVqsVlysxo/9TT5m57TYLfX2BO+LSUo0f/tDNDTfklkc4mfWlii984Qs0NjbGNXZwYAB/b9MI1NXZaG8Pf766WqOlpbAviMO9h2PG2NC08NfGZNIYGBj5a5Puz3uin9F8+yzEu76ioiKQOsvDIvVecw9Ng127AkL52DEzkyd7sITcv1os5TQ3nzVs6+szcdFFToMVY+Lq2wGooJvrqCD8m31vzO+W885zMmZMMitJnnx97+KlkNeXF3WWFUWxAduAX6iq2uDdfFRRlBmqqnYpijID/VYyDFVVtwJbvQ+1ZBabzIu0YcNUg3AA/T/8hg2wbFluNQDJ5Ad87dq1YYXeo6EBJjRMJo2Oji66T5yIOf7w4ciVJw4fpmD/A/sY7j2srIzcZKSy0p2S1yaZz3siJPoZvfvuyE187r77NN3duZfkl2BTEkHIK+KJJvu2lwU5pbq6zFx++RADAwFf8vjVX8eCvu82hniOCu/oZvCWh2ts3AzoAj1SfEWiyUKuMWLPsqIoJuAnwB5VVb8X9NRvgJXef68Enh/puVJJoj8DF6qndNOmTQbPcSyhrAGVdHj/pfmTNOJNqos2bubMBCedZrKRaJduz3qu2R5yxSsuCKOdYKHc0mKlt9dkEMouF/5KFsHMnu3i8suHaGmxcviwlc6X9zJx9e1YcOGhmZuA5ygi0Eyknueff8gvlCFcKEsCn5CrpCKy/FfATcAuRVH+4t32LWAjoCqKcitwCFBScK6UkWjJsEx4SjPBL37xC9auXRvXWJ9Bp9PhoKpqBqYINgHQ4hZ00crr3Xdf7thekml2kgrS3WQkF0vk5YJXXBBGK6EiGTCIZF90+eDB8OtGsC95aAimrbmdicA0DvHXzEKPIDcDFUA9P/jBaubMmQNAR4eFqirjdWfsWA+1tflV+UkYXYxYLKuq+iei+z2WjvT46SLRusi5FpmLl5dffplbbrklrrE+cXzyRz9i4NprCXYiRhNbEyd64hY80QThDTeMJVdcGNm8KUqneByN7bEFQYiMTyj7BK/VqjF7ttu/zSeag6PJvm3Bloue1ZuYTRuAt7rFLIIjyddccy1f/epVhnOHCmWJJAv5wKjt4JdoJC8XI3ORePvtt1mxYkVcY4NTOzsdDmKl6USPCp9JaH6RBWFuVPuA/L0pGg5pjy0Igk8kd3aaOXdOv5YHC+O6Ohfl5e4wkXzokMU/pqwMuhr3ML/xB0wEbvJ7kbu9f+qZMKGcp5++13+MSN5kEclCPjFqxTKECzefVzWSmMjVyNy+ffu48sor4xobLI4HPv1pOn/5y7jPMxKxlUsly4YjX26KkkFsD4IwemlqsqFp0NpqFML791uorTW2ovY952NoSK+n3N5uYfyme5lPGzexDziPgOUCoN7gSe7pMVFerolQFvKeUSGW4xFrw3lVcyUy19HRwaWXXhrX2NCigJ0JdskLJRmxlS0PcLLk6k2RIAhCMnR2munutoQJ4d5eE2431NaGR5IBg7DWRfKDXERbUMe98wgWyY8++lhYBY3ycuO3kIhkIV8peLEcSazdeecE7rlnPD09Zr/ojcermo3I3PHjx4ftjOcjUsXskQrkkZJviZG5clMkCIIwUpqabGFVLGprA9FkTQv4j+fOdWEygdsNFosulA8ftmD98EMmNT7Pt+ggUP7NJ5JLePTRF7wi2WjnCGb+fCfWglcbQiFT8B/fSGLN6TRz6pT+b1+ks78/co5ipr2qvb291NfXxzU2ojhubyesinwWyUcPsNgVBEHIZwYH4cUXjSUvfTYLs9kYTa6sdDN2bODb5MABK04ndHXp0eR7aCO4RrJPKD/66KsGkezxgNlMmFCWaLJQCBS8WI5HlPX3m7FYNNwRbKnp9qoODAxQW1sb11gPkcuOZDt6HItC9gALgiDkGo2NxfT1RW6hUFfn4vBhMwMDZoqKNGbN0q/DRUUau3fryX8+y8UmjgF9QXvrIvmnP32Lvr5e5swJ9jSD3rwygIhkoZAoeLEcTayF4nbr3tR0e1XdbjfV1dVxjXUBkaT+kXffxZMnncLEAywIgpB+NI2wBkouF5x/vrF2Mhijv5oGu3fbaG+3YNvzEZv+5wXwR5On4mu+29i4nZYWK/X10NNjLDMXLJQnT3Zjt+dO7XxBSAUFL5YjibVI2O0B73IqvaqaplFVVRXX2AGgOMpzZpOHjo6uEc0lG4gHeHSSTxVQBCHf2bbNKJLb2y1ceeUgZu/XXiSR7Nve3q6HZDZtehDCLBfH/CIZXGH7i+VCGC0UvFgOFWsTJng4d86M0xkwNPginanyqsabkNcLjIvynMIz/Cqo6aG90hVlZO6TTx5gEXkjJ98qoAhCvhKawNfebmHKFDdLlw4CemT54MHwhLtgkbxl04Poo/cSCNc009i4Hbcbjh41G/Zvbobp043zEJEsFDoFL5Yhcj3lVAqieMXxCWBSjOc7HY4woQFQWhp/S2kheUTkpYZ8q4AyGlEUZSbwM2Aaeq7wVlVVH1EUZRLwDFCDHmZUVFU9la15CpGJJJIBv0iGgEXCWC8Z3nqrCKfTxBu/3sYb+1vR3+ZWfIl6jY3bDftPm6ZbKk6cMDF5sua1YQTmIkJZGA2MCrEcykgjnfGKYwcQy1nct2IFPVu2hM0NjLaFBx6AZctEZKQbEXmpIR8roIxCXMBdqqruVBSlDHhfUZRXgJuBHaqqblQUZT2wHliXxXkKQbS2WujrM/uFssNhwe2G6mp3WCe+YJFcV+fihRfG4HBYOHKkk5///EnvM9v9Y1544UWsVj3iHHw8gL4+XSgHIyJZGE2MSrGcKPGK40PAcKl78VSuCBXzFRUVdHfHNQVhBIjISw1SASX3UVW1C+jy/rtXUZQ9gB24DrjCO+wJ4DVELGcdj7RaHlwAACAASURBVAc+/DAQTe7rM9HdbQ4TtRDZl7xjRzEu1xCbN2/ybn0TOA3A4//+Pezz5wNw+rSJ6mq3Yd+6OhelpQGhvGiRxokTIpSF0UXsrLdRit1uN/yJxpv/+q9o4P8TTSh3Ohz+P6MVXyvxqqoZLFkyNSxrOxeIJuZE5CXG+vW9lJQYs+GlAkruoihKDbAIeBuY5hXSAEfQbRpCFmlqsvmFssejWy5KSjSDUNYiFN2vqnKzY0cx7e0WNm16kM2bv+995lfAadajWy7s8+f7RfiECfqBfGVUIyXwhbauFoTRgESWiT9y/Oqrr7L0M58JbPjWtyKO62xrA5stBTPTeeopMxs2TB2xxzpbyWv54gWWMnepQSqg5A+KoowDtgFfV1X1jKIEkopVVdUURQmTYYqirAJWecdQUVGR8HmtVmtS++UDqVrbzp26KtU0OHoUTpyA0lJYsAB8fasqKzU6O43q1WyGl17S/71p071Bz+iWi/Mp47/efMt/bJMJLrkkMKq5OXB8H4sXBz4G8t7lL4W8vnSvzaRFuiXNHlpnZ2fCO+k2hfh9CldccQUtLS3DjmtsbOTi6dOZvmjRsGPTFTVuaChh3bpy+vqM1Tseeuh0QuIjUuJgMsdJhiVLpkb8Wd5ud/HOO8cSfv/SSbpuKHJpjekgV9aX7fevUq9/nhexN0VRbMCLwG9VVf2ed9te4ApVVbsURZkBvKaq6rwYh8nINTufGOnampoCgZbgqhU+e0RdnYvycg89PeE/DO/ebeXIEYu3DJyPD4EOALY/9TRaeTkA/f1QEvQDX6Q21dXVLsrLjRpB3rv8pZDXl+za4r1mj4rI8j333MNPfvKTYce98MILLF68mEpfpHn58qhjj77zDu44I9IjYePGMoNQhuSSzrKZvJZPXuB8KnMnGMmXXzByAUVRTMBPgD0+oezlN8BKYKP37+ezML1RSUuLlf5+/VrvdsNrr+ll3IJFso9QoXzsmIldu4pCRDLAD4Ba3gOON25HA44fNzNliscglE+cMEvNZEGIQUGK5ccff5zvfOc7w4578cUXWbRoEbjdVFZXw+c/H3N8vNHjVEa3UiU0kz1OKtYiCV9CJpBqJgnxV8BNwC5FUf7i3fYtdJGsKopyK3rOshJlfyFFuN34W00D7NhhFMmgC+WFC52GqLNv3/fes3HvvQ+HHHUTcAHvUcvxxu0cD3pmypRAPoEvmjx5cmCbiGRBCKcgxPKBAwe4/vrr+eijj4YZ2URJyQIeeug0K/d9h7Jrrok5uvvZZxm67LKE5pLq6FaqhGYyx0nVWsQLLGSCfPoFI9uoqvonov/0uDSTcxnNRLJcBIvk6moXl1yii+RQodzSYmX16k0Y+S2g8R4X0P30MxyfoF+vnU5jGs3Ro2amTfMYoslms8YFF+Rv8ytBSCd5L5YffvhhNm/eHPG5adP2cvToef7HGiboB74W/Xgj9R6nKrrli+g6HBZMJg1NC+84mAjJCNZUrUUSvoRMIL9gCPlCJJFcVuY2COXrr++nu9scJpLfesvGd78bGkk+C6i8563sf7xxu+HZYKEcyZss0WRBiE3ei+VPf/rTbNu2jRtvvJGbb76Z8ePHB56zn+PIML7tngceoO/mm1M2n1REt0IjunrGsoamgd2enNBMRrCmMlInXmAh3cgvGEKuEyx829stDA6awqLJl146RFWVO0ok+Xb05orBbOc9ACrDRHLo/qHNSkQkC0J85L1YXrJkCa2trf4syAlr1jD2qacAiFbvosru5J13jqVlPqmIbkWK6GqayV89IlkSFawSqRPyCfkFQ8hVgpP3zp0z0dlp8Yvk4AQ+ny/55EmzYd+ASK4JOqpPJEO3+iu0sjJAt260tweu20NDcPSoRaLJgjAC8r8pydAQ5u99j0q7nUq73S+Ug7mKHZjQMKFRWuJOa6QpVkOGeBtz5Ir3UppLCLEI/jzX1dlyotHMihX9vPPOMTo6unjnnWMilIWs4nLp0eT+fhMejy58fdfxYJFcV+fiwguNCXxdXWZWrnw6QjR5L9v4yC+Ujzdu9wtlwCCUW1qsFBXBzJmBAMfChU4RyoKQIHkfWa6cPTvi9s72drBYaGgoYd/GMkydWkYiTdGiW0DcyXK5EtGVSJ0QjVCrUHs7UqZNEIII9SUD2GwaTqceYZ41y0VREf5o8q5d+ni3G3760zfYtk3FGE1u4z2a/cccznIxZ47RclFX56KkJKf6KghC3pD3TUmKX36Z0//5W7588D7ePjY3ZwXdcI05gslmA5FsUMiF0n0U2hoT+TwXAoXYlCRFSFOSENrbp9DT0wMERPKUKW6OH7f4/+1r9DFhgofTpwPX+ddfP8rGjY+hJ+zN8h2Rt/mINuZQywG6f/Us2rhxABHLyaU7ga+Q37tCXhsU9vryvimJoihXA48AFuBxVVU3pvL4T529jnVNK/2NO3K1EUEi1orQiO7MmXD33YUplIX8JFesQiMhW+3fhcLEJ1rLywMiGaCy0kVnpxWzWaO2Vv910CdyfUJ59243a9ZsAdrQI8mTgX5+yQeYmYwFqOVAWDQ5NHotCXyCkB7SKpYVRbGgtxBaht5v811FUX6jqupwBZHjoqGhhK9/vRy3e+Qd7tJNPNaKaF/e+h1T7qxFEHLFKpQs0u1PSBXByXstLVZ89uG6OpfXoxwe6fWJXD15705gCCjFZ7m4izZuoJlexlHGfoNInjfPyd69Rm/z2bPGDnwTJ3oMPmVBEEZGuhP8lgCtqqoeUFV1CHgauC4VB/Z92YUKZR+5FuEaLlnOtx6Hw4qmmfxf3tlMmoo3IVEYfeR78mesGuKCEA9OZyB5r6XF6o8m19dDba0rLNJbXx+I8ra0WFm+/OvepiJD6CJ5Kktp4z22c7F33OCzT/iFsi9KHCyUW1qszJjhCYsmi1AWhNSSbhuGHTgc9LgDuDQVB470ZRdMrkW4hkuWi/XlvWqVJ+x46UYib0Is8t0qVAg2EiF7BEeGffgEa3MzTJ9OWDS5udlGd7eZm25aTSBp7xxQg4U2/sABDjAHN2bOp9kQTTabtTDLRXW1WC4EIVNkvRqGoiirgFUAqqpSUVER136xvtRKSzUeeIC4j5UpVq3CK3x94nes90/sL2+r1ZzxtTz8sM3/06KP/n4zDz9czqpVY1N6LqvVmnPvVaopxDUGf56tVisuV+DznOvMnKlX8Ii0PdL7VIjvn5A4PsF69KiZM2f0QML06S6CKrdRXw/e/D5cLrBaweOBz33u68B4oIiAN7mNJznO+TSzh/owkezzNns8+rV4cFAvDSc1kwUhs6RbLDuAmUGPq7zb/KiquhXY6n2oxZvNWFkZORvfYtF48MEeli3rZyRJn5lO/om2nspKNy6XJ+MZrIcPz4iynZTPpZAzdH0U+hrzbX133x254szdd5+OmB+QYDUMocDwieSBATh8ODyaHA2rFZYv/7r3UQ0BkdzOk7T5RTLAlIZ/43iJbnXziWRJ4BOE3CDdYvldoE5RlNnoIvnvgBtTceBorW1TUV4tGxaE2K16Mx+ty/cELkGIhdQQF+Jh3z4rAwN6Q5H9+8NFcqTSbR0dMG5cJJHcBkzhSdqop5lm6sOiyWPHepg92x2xRnOwSK6vd1JUlNq1CoIQnbSKZVVVXYqi3A78Fr103H+pqro7FcdO55ddLP9wur5MY68n82I5tngXhPwn0fbvwujB6YQ9e6L7kufPd/LRR8bI7+AgFBfDl750s3dLJbrlrg2o4UnagON+oewTyce9o33C+8MPja2uxXIhCNkn7Z5lVVVfAl5Kx7F9X3ap/gk4W8k/ufTlLZE3QRBGI7GS92pqXIwfr0VsBPL/27v36KjLO4/j77klBoyEMIGQCSFcwl0UalmqWLG4x6TV1dr6tPV0T72stMday55SxfWctZdTT3a1Fjy6pehWbcXqs5aKp6ttveza03qjFUGRsnITE0ASSAgiJDOT2T9+c0nIBEgyyW9m8nmdwyHzm9v3GeDhkyfPxTmWOqEaJyTDLwG6TLnYwVTKnq6nqfAMwAm/jY2+HqPJ5eVRTbkQyRKuL/DLRpqC4Mim8C4iMpjSheRQKMKIEal9ixsbfezenRr53bHDx803fwkYG79SDewBdvMfN36d4gd/lgzJXadcxIBgMEpFRWe3kPz++z46OjzdQnJZWZTx44d+RyQRSVFYTkNTEEREhod0IRm6z0vu+riEFSseZdOmjThBuTp+dTd/+tMj7Fp0LYEHH2AyO9jKDMazn/BzT/SYctHcnPpppaZciGQvheU0NAVBRCS/7djh4+hR7ylDcuLQkYS1a//KY4/9ssszqoHd/Pa3K2m5bBm7Fl2bHE3exnTKnq4n3GXKBfQ8prrr+3Z9nIhkB4XlXmgKgohI/unocA4I2b7dTyyWun5iSIbuoXbbtgaWLXuKxFxkJyQf5OGHlzHm3ddpuWxZtykXU9lO63O/JUb6uc5Hj5L2KGwFZZHso7AsWWmo97kWkfy3eXOA1lYPTU2p6Q/pQnIsBm+/7QTb9vbjXHnlapzDaKMkplzcddc3mDfvDJrrllFAE1M5nNwzOfjcSuLnkjB3bpjDhz09RpNHj+55TLWIZCeFZck66fa5vuWWEr71rRJCIQVnEembzZsDydPvEqqqIhQW9gypXUNtXd2PcXY93R3/vZply67k0kurCdddRzOjkqPJTZQRfLqeknHltLa2nvaUi9mzw/h0yrpIVlNYziIaTXWk2+c6FnOOex2KA2JEJD84R0V3P1DE54sxeXI07UhuItjW1V0NXAC0AB8B1Sxa9GnuuGM+gddeY1/dSmayj8OM6jaaDDBzZoyjR7sfVhKLwfbtfqZOjeDxpN5Po8kiuUFhOUuc7NTApUvdrGzonWo/68E+IEZEcltDg49Dh9Iv3ks3kpsKybVALU5Q3g1UU1k5nwcfvAqA5rplVLObSdAjJIMTfouK4NVXtYBPJJ8oLGeJk50auHTp8Npjs7d9rrsa7ANiRCT3JE7eSxeSp06NMGJErMdzNm8OxEPyOThBuQM4CFTz1FPLGDkSyupqk/skJ0Jyyz33UjPb6bO7TrkoKXGGjtPtmTxhQoTRo3vWICLZTWE5S5z81MDhFZbT7XN9ouF2QIyInNzmzelDckVFlGCwZx/63nt+Fi+uA2bghGRIjCZ///v3smBBmMCGDez717WUxe/tOpocBGbODBMIOEddb9vWfTR55MhOJk5M9VMaTRbJXQrLWUKnBqZ03ee6sdGHx5Oasww6IEZkoIwxPwcuAw5Ya+fEr5UCT5I6q9lYa1vcqvF0bd4cYOdOH9Foqo+oro5QXt5JKJS+/wyFLscJyYuBM5LXly//KUuWtANhyupqieLFT1EyJHc+eh9jxzrBu7cFfMXFmnIhkm8UlrPEyU8NHOleYS7pus+1Fj6KZNwjwP3AL7pcWwG8aK2tN8asiN++zYXaTsvmzQEOHfJw8GDqp3JnneWM5k6bFkn7nFBoJvBZnKBcHb/azPLld3PeeR2MGtWenHJRBvwf0wBo+fFPqJnlATqT4XfbNj/t7U5AP3IE9u/3M2lShGAQWlthxIgYU6emr0NEcovCcpY4+amBwy8sd6UDYkQyy1r7R2NM9QmXr8AZagV4FPhfsjAsNzb62LPH12Pq2vTpYebM6S0kh3AW7V1GKiTD8uW3UVUVpaamncDrrzPyez9M3pcYTS5+eiXBQpgzJ4w3PpahE/hEhheF5SyiUCgiLhpnrd0X/3o/MC7dg4wxS4GlANZagsFgn9/I7/f3+XkdHbBxo4cdO5zbxcXO77Nmwbnnpl80d/HFF/PKK68B1wAjgLEA3Hnn96iuhpoa8Pkg8KmFALQyin2MByDy8CPMcPIy8+c7r//mm85IckkJ/O1vzn2f/GTq/ebNixEI+IhE+v6Z5Ir+/NnlinxuG+R3+wa7bQrLIiLSjbU2ZoxJm0CttWuANfGbsebm5j6/fjAYpC/P27gxwM6dPRfvJUZwT3yp1atX88Mf/hAnJFeTGE1eunQFs2ZFKCg4Qnl5lDMW1VJABx0UpHa5uHclU6aD19tKVZXz+gcOwDvvOKPJ0Sjs3OnH748xaVKU1vhRfXPnhjl4sO9tyzX53L58bhvkd/v627aKiorTepzCsoiIAHxojBlvrd1njBkPHHC7oHQ7XEyeHGHevPTTHP785z9jjAHm4wTlCYCP5ctvo7i4k9GjI9TURAhseouSuhUAbGJu8vkt993fLYQnakjQlAuR4UlhWUREAJ4BvgbUx39f71Yhb78doKnJS0tLasFzaWmUxYs7up2Al9DY2MiCBQtIhWQvUMXy5beyf7+PqqowFRWR5J7JlTTwFufQFN8ULhGSq0aEk4vympq87NvnzIvevt1PLJY6Ihvodd9mEck/wzIsZ+PuCv2tKRvbkqv0WcpwYYz5Fc5ivqAxpgG4EyckW2PMDcD7gBnqug4e9LJli5+mptTivcLCTurq2nucugfQ3t7O5MmTcaZZzCexy8W3v72Mw4eLKC8PU1XVSU1NhLK6Wiaxi11M4nkuAaDlJyvxFfiomazRZBHp3bALyyc7VtqtYNTfmrKxLblKn6UMJ9bar/Ry15IhLSQuEoE33ihIjuQCBAIxPve542lDciwWo7KyEijECcllwCRuuOE2SkpK8Xhg/nxnlLjgrY2U1N3OmXzEs9Q5z/f4aF21Kj7l4njydRWSRSSdYReWT3astFuhqL81ZWNbcpU+SxF3vP56gIaG1H9FHg9cfvkxAoH0j3e2gQMnJAPM4Oqrb2PixGoAgkHnxL5QqJOyulo+wZv8N3W0JBbw3Xc/paVRFk5rJxRKneyXCMpHj8Levd2D8tixUcrLh9dJqiKSMuzC8smPlXZHf2vKxrbkKn2WIkNr/34vBw74ugXlurpjjBiR/vE9Q/JIFi++k/PO+yRFRTGOHSO+Z7Iz5WI2W9jCbB7jGsCZcoHPrwV8ItJnwy4sZ+Ox0v2tKRvbkqv0WYoMjVjM2a+4tdX5RjQUilJTE2bMmPSL5XqGZJgz5xpqa29k1KhODh8Gny/GokUdjNy5lbF1N3M2b7M2HpKjJaW0/eAHhEIRFi5M/ZToo488ye3oEiE5FIomF+0pJItIwrALyyc/Vjq3asrGtuQqfZYiQ+P48dR2FtOmhTnjjPSPSxeSFy5cxKJFqVP2Dh/2dhtN/gRv8huuYDNnA86UC4CLLmonGOw55SKxZzKkRpO93livJwGKyPA07MLyyY+Vzq2asrEtuUqfpcjQKCqKMX9+jObm9CO33/3ud3n88ceB0cAkAKZMmcqNN66mudlHIBAjHPZQUBDjwgs7KKurZR4bieBPTblYuRK8/h57Mm/Z4icadcK6plyIyOkaUFg2xtwNXA50ADuA66y1rfH7bgduAKLALdba3w+w1ozJxmOl+1tTNrYlV+mzFHHPAw88wF133QX4SIwmV1VNZPXqn/HSS4UUFjpTosJhD3PndjC+ZRsz6wwh9iZDcmRiNUe+sxyAL3yh+7/lxGhyQ4M3+ROkRFCeOTPc64JCEZGBjiw/D9xurY0YY/4NuB24zRgzC/gyMBuoAF4wxkyz1moCqIiIJK1fv56bbropfssJydOnz2DlypW88UaA7dudOcSNjT6Kijo5//xwcsrFVqbzP4nR5PiUi0svPc6ZZ6bmP2sBn4gM1IDCsrX2D11uvgZ8Mf71FcAT1tp2YJcxZjuwAHh1IO8nIiL54eDBg8ydmzhq2gnJBQWFrF+/nuPHYds2P52dHvbscUaBFy1qp/JKJyTHoMuUi1Xg9eH1xvj851N7Jre3w7ZtTlBOhORx46KcdZYW8IlI32RyzvL1wJPxr0M44TmhIX6tB2PMUmApgLWWYDDY5zf2+/39el6uUPtyX763Ue2Tvrj44ot55ZVXgInAGACee+53ABw65GH/fl/ygBKvN8aSmXu44MqFjORjXmIxe6mgfc7ZfLz060DvUy7a2uDDD7uPJldVRSgp0THVInL6ThmWjTEvAOVp7rrDWrs+/pg7gAiwtq8FWGvXAGviN2PNzc19fQmCwSD9eV6uUPtyX763Ue1zVFRUDEE1ue3QoUO88spfgPlcf/0NXH311QCMGNHJpk0F7NmT2tv8oovamXr5hcxgG3sZz2+4EkhNufjUp9qpqEjtcrF3r5fmZuf5idHkKVMieOOb3Gg0WUT645Rh2Vp7ycnuN8ZcC1wGLLHWJr5dbwQmdHlYZfyaiIgMY2edVcqLLx6gvb0dj8dDWVmUfft8vPxyIW1tTqodPz7K+atvYuE9TxADnmcJHzKOlpX3gddLQUGMyy8/3u11E6PJiZAMqdFkhWQRGYiB7oZRC9wKXGSt/bjLXc8Ajxtj7sVZ4FcDvDGQ9xIRkdzn88GECUV0dHzM0aNeduzwsWFDYfL+i85t4u+/OotCOtjDBP7IhXz8hS/SftFiAGprjzNyZM8FfJEI7NrVfcpFcXEnkyZpXbmIDMxA5yzfDxQCzxtjAF6z1n7DWrvFGGOBd3GmZ3xTO2GIiIjHA5WV8PLLft57z8/Ro871OXPCfPbaGZThTHd5gc+wn/LklIspUyKce25qhLizE955p/to8pgxUUpLtYBPRDJroLthTD3JfT8CfjSQ1xcRkfxy/Dhs3OhJBtzJkyMs2vgzFt1zOwAxYAPnsXXVf4HHw8SJzsEivtRU5uRo8gcfeDl+vPueybNnd3+siMhADbsT/ERExD2RiIfOThg9OkpZoIVLvjQDH84ivTaK2VD/a8LnnEsNUYLBaLcFfG1tHnbvdv7b6hq2E+FYo8kiMhgUlkVEZMiceWaM6uoYc5/5d866+24AOvHwVuliDqx9Mvm4s88O4/GknqcFfCLiFoVlEREZOtEoBYWFFMRvHqSUDc9uJZGMa2oiFBWlFvAdOuSlocGXdgHflCmRbov9REQGg8KyiIgMGd8HHwAQxcsLv/obsZISAEpKOqmq6r4O/MTR5PLyKMXFMQoKYsyYEUFEZCgoLIuIyJCJVlfT0d7OSy8dTl6bPj1MYWr3OA4c8LJ/vy/tCXyaciEiQ01hWUREhtyYMVH8fhg3LrWAr7MTtm71Ew572LGj+wl8JwZqEZGhorAsIiJDLhTq7HHtnXcCHD7s4cABHxUVUUaOjFFa2kllpbbpFxH3KCyLiIjrOjqgqclLZ6emXIhIdlFYFhERV+3e7aOtzUtZmTPaPGNGmIKCUzxJRGSIeN0uIBesW1fEggVjqawcz4IFY1m3rsjtkkREcl5bm4fNmwO0tTn/FYVCUebOVVAWkeyikeVTWLeuiFtvHcWxY05n3tjo59ZbRwFw1VXH3CxNRCTjjDG1wCrABzxkra3P9HtEo6lt4QAKC2NMmxbpdgiJiEi20MjyKdTXFyeDcsKxY17q64tdqkhEZHAYY3zAA0AdMAv4ijFmVibfIxaDTZtSqbimJsL06QrKIpK9NLJ8Cnv3+vp0XUQkhy0AtltrdwIYY54ArgDezdQbeDwQDMYIBKKMH99zRwwRkWyjsHwKFRVRGht7fkwVFdrKSETyTgj4oMvtBuDvuj7AGLMUWApgrSUYDPb5Tfx+P5FI6QDKzF5+v79fn0muyOf25XPbIL/bN9htU1g+hRUrjnSbswxQVNTJihVHXKxKRMQd1to1wJr4zVhzc3OfXyMYDNKf5+WCfG4b5Hf78rltkN/t62/bKioqTutxCsunkFjEV19fzN69zkb5K1Yc0eI+EclHjcCELrcr49dERIYtheXTcNVVxxSORWQ42ADUGGMm4YTkLwPXuFuSiIi7tBuGiIgAYK2NADcDvwe2OpfsFnerEhFxl0aWRUQkyVr7LPCs23WIiGQLjSyLiIiIiPRCYVlEREREpBcKyyIiIiIivfDEYjG3a+gqq4oREemH4XRws/psEcl1p+yzs21k2dOfX8aYv/b3ubnwS+3L/V/53ka1r9uv4UR/X4ZR2/K9ffnctnxv3wDbdkrZFpZFRERERLKGwrKIiIiISC/yJSyvcbuAQab25b58b6PaJ32Rz59nPrcN8rt9+dw2yO/2DWrbsm2Bn4iIiIhI1siXkWURERERkYzL6eOujTG1wCrABzxkra13uaSMMsZMAH4BjMPZommNtXaVu1VlnjHGB/wFaLTWXuZ2PZlkjCkBHgLm4PwZXm+tfdXdqjLLGPPPwD/htO9t4Dpr7XF3q+o/Y8zPgcuAA9baOfFrpcCTQDWwGzDW2ha3asxl+dpvD4f+Wn11blIfPXA5O7Ic/0f7AFAHzAK+YoyZ5W5VGRcBvmOtnQUsBL6Zh20E+Daw1e0iBskq4HfW2hnAOeRZO40xIeAW4Lx4p+UDvuxuVQP2CFB7wrUVwIvW2hrgxfht6aM877eHQ3+tvjrHqI/OjJwNy8ACYLu1dqe1tgN4ArjC5Zoyylq7z1r7ZvzrIzj/eEPuVpVZxphK4HM439HnFWPMKODTwH8CWGs7rLWt7lY1KPxAkTHGD4wA9rpcz4BYa/8IHDrh8hXAo/GvHwWuHNKi8kfe9tv53l+rr85p6qMHKJfDcgj4oMvtBvKoYzqRMaYamAe87nIpmbYSuBXodLuQQTAJaAIeNsZsNMY8ZIwZ6XZRmWStbQTuAfYA+4DD1to/uFvVoBhnrd0X/3o/zo/ape+GRb+dp/21+uocpD46M3I5LA8bxpgzgV8Dy6y1bW7XkynGmMSco7+6Xcsg8QPzgZ9aa+cBR8mzH98bY0bjfEc/CagARhpjvupuVYPLWhtDxzxLL/Kxv1ZfnbvUR2dGLoflRmBCl9uV8Wt5xRgTwOl411pr17ldT4ZdAPyDMWY3zo9jP2OMeczdkjKqAWiw1iZGl57C6ZDzySXALmttk7U2DKwDzne5psHwoTFmPED89wMu15Or8rrfzuP+Wn117lIfnQG5HJY3ADXGmEnGmAKcCevPuFxTRhljBTKKzAAAAR5JREFUPDhzqLZaa+91u55Ms9bebq2ttNZW4/z5vWStzZvveK21+4EPjDHT45eWAO+6WNJg2AMsNMaMiP99XUKeLIw5wTPA1+Jffw1Y72ItuSxv++187q/VV+c09dEZkLNbx1lrI8aYm4Hf46zu/Lm1dovLZWXaBcA/Am8bY96KX/sXa+2zLtYkffMtYG08GOwErnO5noyy1r5ujHkKeBNnN4CN5PgpUcaYXwGLgaAxpgG4E6gHrDHmBuB9wLhXYe7K835b/XVuy8u+Wn10ZugEPxERERGRXuTyNAwRERERkUGlsCwiIiIi0guFZRERERGRXigsi4iIiIj0QmFZRERERKQXCssiIiIiIr1QWBYRERER6YXCsoiIiIhIL/4fgnM1hKbzBz0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118a8d5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1,2,figsize=(12,4))\n",
    "axes[0].plot(x,y,'o',color='blue')\n",
    "axes[0].plot(x,yv,color='red')\n",
    "axes[0].plot(x,yreg,color='black')\n",
    "\n",
    "axes[1].plot(x,yv,color='red')\n",
    "axes[1].plot(x,yreg,color='black')\n",
    "\n",
    "for i in range(10):\n",
    "    f = lambda x: 5*x+3\n",
    "    x = np.random.uniform(10,0,size=100)\n",
    "    e = np.random.normal(0,20,size=100)\n",
    "    yv = np.apply_along_axis(f,0,x)\n",
    "    y = yv+e\n",
    "\n",
    "    b1 = np.sum((x-np.mean(x))*(y-np.mean(y)))/np.sum((x-np.mean(x))**2)\n",
    "    b0 = np.mean(y)-b1*np.mean(x)\n",
    "    g = lambda x: b0+b1*x\n",
    "    yreg = np.apply_along_axis(g,0,x)\n",
    "    axes[1].plot(x,yreg,color='blue',alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observamos que, dadas as premissas de que os erros seguem uma distribuição normal com média zero e desvio padrão $\\sigma$, o valor médio entre as diversas predições para $Y$ se aproxima do valor real (dado pela equação da reta). Dessa forma, percebemos que não há um erro sistemático (viés) nas estimativas. Portanto, ainda que os coeficientes para um conjunto de dados específico não forneça a real relação entre as variáveis, se tivéssemos uma grande amostra de conjuntos de dados, a média dos coeficientes seria o valor exato deles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Qualidade da estimativa dos coeficientes\n",
    "\n",
    "Da mesma forma que usamos o erro padrão para avaliar quão distante a média da amostra está da média populacional, o erro padrão dos coeficientes revela quão distantes eles estão dos reais valores. Através das propriedades da variância e esperança, pode-se [demonstrar](http://qed.econ.queensu.ca/pub/faculty/abbott/econ351/351note04.pdf) que os erros padrão dos coeficientes são dados por\n",
    "\n",
    "$$SE(\\hat{\\beta_0})^2 = \\sigma^2\\left[\\frac{1}{n}+\\frac{\\bar{x}^2}{\\sum (x_i-\\bar{x})^2}\\right]$$\n",
    "\n",
    "$$SE(\\hat{\\beta_1})^2 = \\frac{\\sigma^2}{\\sum (x_i-\\bar{x})^2}$$,\n",
    "onde $\\sigma^2 = Var(\\epsilon)$ e pode ser estimado por $S(x)/(n-2)$.\n",
    "\n",
    "As estimativas de erro padrão podem ser usadas para definir os intervalos de confiança dos coeficientes. Por exemplo, os intervalos de confiança de 95% dos coeficientes são dados por\n",
    "\n",
    "$$\\left[\\hat{\\beta_0}-1.96~SE(\\hat{\\beta_0}),~~\\hat{\\beta_0}+1.96~SE(\\hat{\\beta_0})\\right]$$\n",
    "$$\\left[\\hat{\\beta_1}-1.96~SE(\\hat{\\beta_1}),~~\\hat{\\beta_1}+1.96~SE(\\hat{\\beta_1})\\right]$$\n",
    "\n",
    "Assim, podemos calcular os intervalos de confiança dos coeficientes estimados para o problema da publicidade."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b0 = [6.135, 7.930]\n",
      "b1 = [0.042, 0.053]\n"
     ]
    }
   ],
   "source": [
    "b1 = np.sum(ads.TV.map(lambda x: x-ads.TV.mean())*\\\n",
    "            ads.sales.map(lambda x: x-ads.sales.mean()))/\\\n",
    "np.sum(ads.TV.map(lambda x: (x-ads.TV.mean())**2))\n",
    "b0 = ads.sales.mean()-b1*ads.TV.mean()\n",
    "\n",
    "f = lambda x: b0+b1*x\n",
    "\n",
    "RSE = np.sum((ads.sales.values-ads.TV.map(f))**2)/(ads.shape[0]-2)\n",
    "TSS = np.sum(ads.TV.map(lambda x: (x-ads.TV.mean())**2))\n",
    "SEb0 = np.sqrt(RSE*(1/ads.shape[0]+(ads.TV.mean()**2)/TSS))\n",
    "SEb1 = np.sqrt(RSE/TSS)\n",
    "\n",
    "print('b0 = [{:.3f}, {:.3f}]'.format(b0-1.96*SEb0,b0+1.96*SEb0))\n",
    "print('b1 = [{:.3f}, {:.3f}]'.format(b1-1.96*SEb1,b1+1.96*SEb1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Esses intervalos podem ser interpretados como:\n",
    "\n",
    "- Na ausência de investimentos em publicidade, as vendas vão ficar entre 6 e 8 unidades\n",
    "- O investimento de \\$1000 em publicidade na TV resulta no aumento da venda de 42 a 53 unidades"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quão forte é a relação entre publicidade e vendas\n",
    "\n",
    "O erro padrão do coeficiente $\\hat{\\beta_1}$ também é útil para testar a força da relação entre o investimento em publicidade na TV e o aumento das vendas. Podemos testar a hipótese de que não existe relação entre o investimento em TV e aumento de vendas (i.e. $\\beta_1=0$). Para isso avaliamos se o valor estimado é significativamente diferente de zero. Fazemos isso usando a estatística t\n",
    "\n",
    "$$t = \\frac{\\hat{\\beta_1} - 0}{SE(\\hat{\\beta_1})}$$\n",
    "\n",
    "e avaliando a probabilidade de observar um valor tão extremo quanto $t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17.6676256009\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "7.3369485009735888e-43"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "\n",
    "tB1 = b1/SEb1\n",
    "print(tB1)\n",
    "t.sf(tB1,ads.shape[0]-2) #sf = 1-cdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A probabilidade de observar um valor tão extremo quanto $t$ é quase zero como vimos acima. Esse valor, chamado de ***p-value***, nos informa a probabilidade do coeficiente computado ter ocorrido simplesmente por chance. Como essa probabilidade é bem pequena (em geral, os limiares usados para definir pequeno são 0.05 e 0.01), rejeitamos a hipótese de que o coeficiente real é zero. Em outras palavras, aceitamos que existe uma relação entre o investimento em TV e o aumento nas vendas."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Qual a qualidade do modelo?\n",
    "\n",
    "O teste de hipótese mostrou que, de fato, existe uma relação entre a variável dependente e a independente. O p-value calculado, no entanto, não mostra a precisão deste modelo. \n",
    "\n",
    "A qualidade do modelo é avaliada de duas formas: *erro padrão residual* e *coeficiente de determinação*.\n",
    "\n",
    "O erro padrão residual (RSE) é uma estimativa do desvio padrão dos resíduos (erros) do modelo. Ele é definido por\n",
    "\n",
    "$$RSE = \\sqrt{\\frac{S(x)}{n-2}} = \\sqrt{\\frac{\\sum (y_i - \\beta_0 - \\beta_1x_i)^2}{n-2}}$$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.2586563686504624"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RSE = np.sqrt(np.sum((ads.sales.values-ads.TV.map(f))**2)/(ads.shape[0]-2))\n",
    "RSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Intuitivamente, esse valor nos mostra que, em média, os valores de venda vão oscilar em 3.26 unidades do valor real.\n",
    "\n",
    "O coeficiente de determinação, por outro lado, mostra a proporção da variância explicada pelo modelo. O coeficiente de determinação é calculado por\n",
    "\n",
    "$$R^2 = \\frac{TSS-RSS}{TSS}$$,\n",
    "onde $TSS = \\sum (y_i - \\bar{y})^2$ e $RSS = S(x) = \\sum (y_i - \\beta_0 - \\beta_1x_i)^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5417.14875 2102.53058313 0.61187505085\n"
     ]
    }
   ],
   "source": [
    "RSS = np.sum((ads.sales.values-ads.TV.map(f))**2)\n",
    "TSS = np.sum((ads.sales.values-ads.sales.mean())**2)\n",
    "R2 = (TSS-RSS)/TSS\n",
    "\n",
    "print(TSS,RSS,R2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O coeficiente de determinação varia entre 0 e 1. Valores próximos de zero indicam que o modelo não consegue explicar a variação dos dados, enquanto valores próximos de 1 indicam que a variação dos dados é totalmente explicada pelo modelo. \n",
    "\n",
    "Assim, percebemos que o modelo consegue explicar cerca de 61% da variação das vendas, ou seja, 2/3 do aumento das vendas pode ser explicada pelo investimento na publicidade em TV."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regressão linear em Python\n",
    "\n",
    "Felizmente não precisamos usar todas equações derivadas acima para ajustar um modelo de regressão linear em Python. De fato, existem diversas formas de se fazê-lo, usando SciPy ou Scikit-Learn.\n",
    "\n",
    "#### SciPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 7.033 + 0.048x\n",
      "Stats\n",
      "r2 = 0.612, p-value=0.000\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import linregress\n",
    "\n",
    "X = ads.TV.values.copy()\n",
    "y = ads.sales.values\n",
    "\n",
    "model = linregress(X,y)\n",
    "print('y = {:.3f} + {:.3f}x'.format(model.intercept,model.slope))\n",
    "print('Stats')\n",
    "print('r2 = {:.3f}, p-value={:.3f}'.format(model.rvalue**2,model.pvalue))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 7.033 + 0.048x\n",
      "Stats\n",
      "r2 = 0.612\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import r2_score, explained_variance_score\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(X[:, np.newaxis],y)\n",
    "print('y = {:.3f} + {:.3f}x'.format(model.intercept_,model.coef_[0]))\n",
    "print('Stats')\n",
    "print('r2 = {:.3f}'.format(r2_score(y,model.predict(X[:, np.newaxis]))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 230.1],\n",
       "       [  44.5],\n",
       "       [  17.2],\n",
       "       [ 151.5],\n",
       "       [ 180.8],\n",
       "       [   8.7],\n",
       "       [  57.5],\n",
       "       [ 120.2],\n",
       "       [   8.6],\n",
       "       [ 199.8],\n",
       "       [  66.1],\n",
       "       [ 214.7],\n",
       "       [  23.8],\n",
       "       [  97.5],\n",
       "       [ 204.1],\n",
       "       [ 195.4],\n",
       "       [  67.8],\n",
       "       [ 281.4],\n",
       "       [  69.2],\n",
       "       [ 147.3],\n",
       "       [ 218.4],\n",
       "       [ 237.4],\n",
       "       [  13.2],\n",
       "       [ 228.3],\n",
       "       [  62.3],\n",
       "       [ 262.9],\n",
       "       [ 142.9],\n",
       "       [ 240.1],\n",
       "       [ 248.8],\n",
       "       [  70.6],\n",
       "       [ 292.9],\n",
       "       [ 112.9],\n",
       "       [  97.2],\n",
       "       [ 265.6],\n",
       "       [  95.7],\n",
       "       [ 290.7],\n",
       "       [ 266.9],\n",
       "       [  74.7],\n",
       "       [  43.1],\n",
       "       [ 228. ],\n",
       "       [ 202.5],\n",
       "       [ 177. ],\n",
       "       [ 293.6],\n",
       "       [ 206.9],\n",
       "       [  25.1],\n",
       "       [ 175.1],\n",
       "       [  89.7],\n",
       "       [ 239.9],\n",
       "       [ 227.2],\n",
       "       [  66.9],\n",
       "       [ 199.8],\n",
       "       [ 100.4],\n",
       "       [ 216.4],\n",
       "       [ 182.6],\n",
       "       [ 262.7],\n",
       "       [ 198.9],\n",
       "       [   7.3],\n",
       "       [ 136.2],\n",
       "       [ 210.8],\n",
       "       [ 210.7],\n",
       "       [  53.5],\n",
       "       [ 261.3],\n",
       "       [ 239.3],\n",
       "       [ 102.7],\n",
       "       [ 131.1],\n",
       "       [  69. ],\n",
       "       [  31.5],\n",
       "       [ 139.3],\n",
       "       [ 237.4],\n",
       "       [ 216.8],\n",
       "       [ 199.1],\n",
       "       [ 109.8],\n",
       "       [  26.8],\n",
       "       [ 129.4],\n",
       "       [ 213.4],\n",
       "       [  16.9],\n",
       "       [  27.5],\n",
       "       [ 120.5],\n",
       "       [   5.4],\n",
       "       [ 116. ],\n",
       "       [  76.4],\n",
       "       [ 239.8],\n",
       "       [  75.3],\n",
       "       [  68.4],\n",
       "       [ 213.5],\n",
       "       [ 193.2],\n",
       "       [  76.3],\n",
       "       [ 110.7],\n",
       "       [  88.3],\n",
       "       [ 109.8],\n",
       "       [ 134.3],\n",
       "       [  28.6],\n",
       "       [ 217.7],\n",
       "       [ 250.9],\n",
       "       [ 107.4],\n",
       "       [ 163.3],\n",
       "       [ 197.6],\n",
       "       [ 184.9],\n",
       "       [ 289.7],\n",
       "       [ 135.2],\n",
       "       [ 222.4],\n",
       "       [ 296.4],\n",
       "       [ 280.2],\n",
       "       [ 187.9],\n",
       "       [ 238.2],\n",
       "       [ 137.9],\n",
       "       [  25. ],\n",
       "       [  90.4],\n",
       "       [  13.1],\n",
       "       [ 255.4],\n",
       "       [ 225.8],\n",
       "       [ 241.7],\n",
       "       [ 175.7],\n",
       "       [ 209.6],\n",
       "       [  78.2],\n",
       "       [  75.1],\n",
       "       [ 139.2],\n",
       "       [  76.4],\n",
       "       [ 125.7],\n",
       "       [  19.4],\n",
       "       [ 141.3],\n",
       "       [  18.8],\n",
       "       [ 224. ],\n",
       "       [ 123.1],\n",
       "       [ 229.5],\n",
       "       [  87.2],\n",
       "       [   7.8],\n",
       "       [  80.2],\n",
       "       [ 220.3],\n",
       "       [  59.6],\n",
       "       [   0.7],\n",
       "       [ 265.2],\n",
       "       [   8.4],\n",
       "       [ 219.8],\n",
       "       [  36.9],\n",
       "       [  48.3],\n",
       "       [  25.6],\n",
       "       [ 273.7],\n",
       "       [  43. ],\n",
       "       [ 184.9],\n",
       "       [  73.4],\n",
       "       [ 193.7],\n",
       "       [ 220.5],\n",
       "       [ 104.6],\n",
       "       [  96.2],\n",
       "       [ 140.3],\n",
       "       [ 240.1],\n",
       "       [ 243.2],\n",
       "       [  38. ],\n",
       "       [  44.7],\n",
       "       [ 280.7],\n",
       "       [ 121. ],\n",
       "       [ 197.6],\n",
       "       [ 171.3],\n",
       "       [ 187.8],\n",
       "       [   4.1],\n",
       "       [  93.9],\n",
       "       [ 149.8],\n",
       "       [  11.7],\n",
       "       [ 131.7],\n",
       "       [ 172.5],\n",
       "       [  85.7],\n",
       "       [ 188.4],\n",
       "       [ 163.5],\n",
       "       [ 117.2],\n",
       "       [ 234.5],\n",
       "       [  17.9],\n",
       "       [ 206.8],\n",
       "       [ 215.4],\n",
       "       [ 284.3],\n",
       "       [  50. ],\n",
       "       [ 164.5],\n",
       "       [  19.6],\n",
       "       [ 168.4],\n",
       "       [ 222.4],\n",
       "       [ 276.9],\n",
       "       [ 248.4],\n",
       "       [ 170.2],\n",
       "       [ 276.7],\n",
       "       [ 165.6],\n",
       "       [ 156.6],\n",
       "       [ 218.5],\n",
       "       [  56.2],\n",
       "       [ 287.6],\n",
       "       [ 253.8],\n",
       "       [ 205. ],\n",
       "       [ 139.5],\n",
       "       [ 191.1],\n",
       "       [ 286. ],\n",
       "       [  18.7],\n",
       "       [  39.5],\n",
       "       [  75.5],\n",
       "       [  17.2],\n",
       "       [ 166.8],\n",
       "       [ 149.7],\n",
       "       [  38.2],\n",
       "       [  94.2],\n",
       "       [ 177. ],\n",
       "       [ 283.6],\n",
       "       [ 232.1]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}