{
 "metadata": {
  "name": "ch5"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "''''\n",
      "-------------------------------------------------------------------------------\n",
      "Filename   : ch5.ipynb\n",
      "Date       : 2012-07-15\n",
      "Author     : C. Vogel\n",
      "Purpose    : Replicate the regression analyses in Chapter 5 of_Machine Learning \n",
      "           : for Hackers_.\n",
      "Input Data : heights_weights_genders.csv, and top_1000_sites.tsv, avaialable at\n",
      "           : the book's github repository at https://github.com/johnmyleswhite/\n",
      "           : ML_for_Hackers.git.\n",
      "Libraries  : Numpy 1.7.0b2, pandas 0.9.0, matplotlib 1.1.1, statsmodels 0.5.0\n",
      "           : (dev) (with patsy 0.1.0 dependency)\n",
      "-------------------------------------------------------------------------------\n",
      "\n",
      "This notebook is a Python port of the R code in Chapter 5 of _Machine Learning\n",
      "for Hackers_ by D. Conway and J.M. White.\n",
      "\n",
      "Two datasets, heights_weights_genders.csv and top_1000_sites.tsv, should be located in the\n",
      "in a /data/ subfolder of the working directory. See the paths defined just after the import\n",
      "statements below to see what directory structure this script requires. Copying complete\n",
      "data folder from the book's github repository should be sufficient.\n",
      "\n",
      "For a detailed description of the analysis and the process of porting it\n",
      "to Python, see: slendrmeans.wordpress.com/will-it-python.\n",
      "'''"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "import os\n",
      "import numpy as np\n",
      "import statsmodels.api as sm\n",
      "import matplotlib.pyplot as plt\n",
      "from pandas import *\n",
      "# formulas.api lets us use patsy formulas.\n",
      "from statsmodels.formula.api import ols"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "heights_weights = read_csv('data/01_heights_weights_genders.csv')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## WEIGHT VS. HEIGHT REGRESSION\n",
      "Using patsy formulas."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit_reg = ols(formula = 'Weight ~ Height', df = heights_weights).fit()\n",
      "print fit_reg.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:                 Weight   R-squared:                       0.855\n",
        "Model:                            OLS   Adj. R-squared:                  0.855\n",
        "Method:                 Least Squares   F-statistic:                 5.904e+04\n",
        "Date:                Sat, 24 Nov 2012   Prob (F-statistic):               0.00\n",
        "Time:                        09:50:14   Log-Likelihood:                -39219.\n",
        "No. Observations:               10000   AIC:                         7.844e+04\n",
        "Df Residuals:                    9998   BIC:                         7.846e+04\n",
        "Df Model:                           1                                         \n",
        "==============================================================================\n",
        "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------\n",
        "Intercept   -350.7372      2.111   -166.109      0.000      -354.876  -346.598\n",
        "Height         7.7173      0.032    242.975      0.000         7.655     7.780\n",
        "==============================================================================\n",
        "Omnibus:                        2.141   Durbin-Watson:                   1.677\n",
        "Prob(Omnibus):                  0.343   Jarque-Bera (JB):                2.150\n",
        "Skew:                           0.036   Prob(JB):                        0.341\n",
        "Kurtosis:                       2.991   Cond. No.                     1.15e+03\n",
        "==============================================================================\n",
        "\n",
        "The condition number is large, 1.15e+03. This might indicate that there are\n",
        "strong multicollinearity or other numerical problems.\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note we get the condition number warning. This is really just a scale issue (with\n",
      "only one variable, the multicollinearity warning doesn't make sense). If we run\n",
      "the log-log version, this goes away. Note we can specify the log transforms \n",
      "within the Patsy/sm formula."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fit_reg_log = ols(formula = 'np.log(Weight) ~ np.log(Height)', \n",
      "                  df = heights_weights).fit()\n",
      "print fit_reg_log.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:         np.log(Weight)   R-squared:                       0.848\n",
        "Model:                            OLS   Adj. R-squared:                  0.848\n",
        "Method:                 Least Squares   F-statistic:                 5.576e+04\n",
        "Date:                Sat, 24 Nov 2012   Prob (F-statistic):               0.00\n",
        "Time:                        09:50:17   Log-Likelihood:                 11038.\n",
        "No. Observations:               10000   AIC:                        -2.207e+04\n",
        "Df Residuals:                    9998   BIC:                        -2.206e+04\n",
        "Df Model:                           1                                         \n",
        "==================================================================================\n",
        "                     coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "----------------------------------------------------------------------------------\n",
        "Intercept         -8.6155      0.058   -148.708      0.000        -8.729    -8.502\n",
        "np.log(Height)     3.2619      0.014    236.129      0.000         3.235     3.289\n",
        "==============================================================================\n",
        "Omnibus:                       38.178   Durbin-Watson:                   1.713\n",
        "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               42.749\n",
        "Skew:                          -0.105   Prob(JB):                     5.21e-10\n",
        "Kurtosis:                       3.241   Cond. No.                         320.\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pred_weights = fit_reg.predict()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "heights = heights_weights['Height']\n",
      "weights = heights_weights['Weight']\n",
      "plt.figure(figsize = (8, 8))\n",
      "plt.plot(heights, weights, '.', mfc = 'white', alpha = .2)\n",
      "plt.xlabel('Height (in)')\n",
      "plt.ylabel('Weight (lbs)')\n",
      "plt.plot(heights, pred_weights, '-k')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[<matplotlib.lines.Line2D at 0x108fb8450>]"
       ]
      },
      {
       "output_type": "display_data",
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E43E0TVNd1kKhEAaDgfX1dVwuF7W1ter/tsLCQioqKpibm2NxcZHKykomJydx\nOBzMz89z9OhR9SVibm6O1dVVzGYzZrOZXC7H4OCgmlo2OztLMBjkxRdfpKysjKKiIm7evEk6naag\noIBDhw6xsbHB0tISXV1d6h6i0Sjr6+usra0RiUQoKCjgtdde2/beBwcH+clPfkJLSwtra2u8+OKL\nBAIBgsEgx48fR9M0UqkU169fp6enZ9dSM/1363K5CIVCuFwu/H6/2s0YHh6ms7PzgbfUH6SjXT6Q\n7XQhhHgEtm61r6+vE4/H6ejoYGRkRG23X758mS984QvbtsZzuRxms1mtQr1eL8FgkEgkQmFhIYWF\nhdjtdmpraxkYGKCgoIDKykoqKioYGxvjxIkTaqWfSCRYWlrC4/GQTqeJxWKEQiFOnjzJ5OQkdrud\neDxOKpWitrYWg8GA1WplfHyccDhMRUUFNpuN6upqNQglHo+ztLSkuqTpNeNwezv85s2bfPzxxxQU\nFFBaWsrk5KRKvNO34202G5cuXeLcuXMADxSE9eCub4c/aDC+2xevfCTb6UII8Qhs3WovKCigq6sL\ns9lMOp3GZDLx0Ucfce7cOZVgpp/tjoyMYLVaMRgMmEwmTCYTRqORyspKPB4PGxsbmEwmzGYzx48f\nx+/3q0z0jo6ObV8IAIqLi1lfX2dyclIF1lAoxODgIGVlZaysrNDc3ExFRYU6Hw8EAlRVVXHkyBHS\n6TTxeByr1crU1BRHjx6ltraW5eXlbQH8b/7mb/jOd75DOBwmk8mwtrZGLpdjfX0dm81GW1ubOiqI\nRqMcO3YM4IHLxfSSOK/Xu+f41vt5/tMQwPdLVuJCCHEPe6349I5qeqY53N7ihduBv7KyUiWp9ff3\nYzabuXbtGisrK9TV1eF0Ounp6cFsNhMIBJibm2NwcJCqqipcLhexWIyqqiqKi4v55JNPKC0tpaio\niFQqxdraGs899xwDAwNsbm5y8uRJFhcXCYfDVFdXk06ncblcLC4uUlNTw+rqKsPDw7S2tlJSUkIi\nkVDZ8YcOHVLv6Z//+Z/JZDKUlpaSSCRwOBx4PB76+voYHx/nK1/5CqlUCrPZrLq4bf39hMNhQqGQ\nqo33er3PdJB9ELISF0KIA7A1WU0fILK1W5nObDarGmj9eblcjsuXL5NKpRgZGaGjo0MlfPl8Pl58\n8UVOnDgB3F5Z6wlZoVAIs9lMe3s7xcXFFBcXk06nVYA8dOgQZWVlnD59GqPRyMDAgJrbXVxcrEaN\nejweuroOhmc/AAAgAElEQVS66O7uVu1VFxYWGB0dpbW1levXr5NIJIhGo2xubm4L4D/72c9YW1tj\neXkZq9XK2bNniUajbGxsoGkap0+fpre3944t860rYr3ValtbG5qm0d/fj9/v58aNG8zNzUk9+AGT\nIC6EEDtszXrWt4j3yoAOBAIMDAzw3nvvMTg4SDAYpK6uTiWnhUIhVXetaRqLi4tMTEzQ2dmpepn7\n/X7C4TClpaUquWtxcVH1JTcajayurrKxscGlS5dIp9PU19fzyiuvqLngk5OTdHV1UVBQQCAQ4NKl\nS2QyGZxOpyr9Kisro6enR435bGpqUu/j3XffpaWlhdLSUjVnfGRkhCNHjnDx4kU1pczr9aodCf29\n61n2mUyGbDbL+vq6aujidDrV7w84sEzyxzlN7kkmQVwI8Uy6WxDY2hLU4XDctT2oHqAdDgelpaXE\n43E2Nzc5fvw4w8PDeDwestks6XSaF154gUgkosrEYrGYqgEvLi7m+vXrfPjhh2QyGeLxON3d3QSD\nQRYWFnj55Zex2+2YTCba2towGAwEg0E++eQTlRT2f//v/2Vubo6NjQ0aGxspKSnBbrezvLxMc3Mz\npaWlXL9+XdWLb30PjY2NhMNhSkpKePnllxkbGyObzVJfX093dzeaplFYWEgqlVLb6LlcjqKiIqqr\nqxkZGeHnP/+5ylz3+/2qPe3a2hp+vx+73X5gbValvOw2CeJCiGfS3YLA1iEnuyVdbf0CsLm5ycbG\nBn6/H6/Xy+bmJh6Ph48//hiXy6Vqn2/evMnm5iaFhYWcP39eJcGVlJSQTqfx+XyYTCY+97nPoWka\nq6urGI1GLBYLiUSCH/7wh3zyySdYrVYGBgbo6upieHgYt9tNTU0NnZ2dNDc3k81mGRoaIhwOU19f\nz/DwMDabjXQ6zaVLlzh+/DgvvfSSeq9TU1MA6kjA6/VSUFBAbW0tBQUFavu8ra2Nmzdvsri4qL74\nBINBwuEws7OzlJaWUlxcTG1tLcXFxWqLXe8J39HRQTQaPbBSMOm9fpuMIhVCPJO2BoGtwz0CgQDh\ncJh0Ok02m8Xr9e46NlTTNNW5zeFwUFFRQSqV4siRI5hMJhwOB2azmfX1dWKxGOfOnWNhYYHFxUUW\nFxdVOZjL5WJiYoLGxkYSiQQrKyusrKzg9Xq5evUqHR0dJJNJzpw5QyqV4pe//CUOhwOXy8X4+Dir\nq6tcu3YNg8FAUVERhw4dwmq1AjA2NobRaCQajVJcXExraysNDQ3qfYyPj2MymfD7/YyNjXHs2DG1\nte92u1Vg3tzcVOfyVquVYDDI6OgoNpuNRCJBeXm5qv9eX1+npKSExcXFO3rC71Z6tt+ua3p72aeh\nPvxhGL/97W9/+7O+id0kEgkASktLP+M7EUI8jUpLS3etS15ZWaG8vJza2lri8Thra2v09vYyPT3N\nzZs3qa6uZnp6mqWlJTY2NmhpaWFzc5PNzU2Gh4dJJpNUVlaSTCY5dOgQiUSC1dVVXC4XiUQCo9FI\nJpNRTVH0rPXCwkLKysq4evUqJ0+eVMFzfn6ekpISxsbGCAaDNDY24nQ6uXXrFlVVVRQUFJDL5YjF\nYqRSKUpKSshms1gsFtbW1lRddzgcVgl1AG+//Tbd3d2sr6+rpjULCwusrKzg8XgIhUKqrK6jo4Ox\nsTEKCwuZnZ2lsbFRzQVvbW1lcHCQc+fOEQgEKCwspKCggCNHjtxX2Zh+vaKiIoLBIOXl5ff1+RkM\nBsrLy9VZvS4QCLCyssLy8jKlpaV3/PuTbD9xL3/enRBCHBC9/lqf9rX1XDybzbKxscHs7Kya3R2P\nxzlz5gzPP/88v/jFL3A4HJSUlNDY2KjOvQ0GA6dPn+bMmTMsLy+rAR/ZbJaqqioGBwfJ5XK4XC7V\nnjWbzfLVr35VZXQvLS1RVVWFz+cjFAoRCoWorKxUZWVTU1MUFRXxySefkMvlWF1dZW1tjbKyMpqa\nmlT/dE3TCIVCDAwMEAqFePHFF/nCF76g3v/o6Cher1c1WtHr1QsLCzGbzVgsFuLxOEVFRapMzmaz\nqSOAaDRKJBKhvr6esbExLly4QHFxMSdOnKCoqIja2lp13n+vVqoHvS3+rJ2VSxAXQjxz9P/oKysr\nKSgoUP/h61u7g4ODRKNRNE3D4/FgNpuZm5vjypUr/Mqv/AqapqlxnZ2dnRiNRtLpNKurq4yOjlJW\nVkZnZyeRSASTyUQ0GqWzsxO3243BYMDj8ajRnX19feRyObXSdjgcbG5uEgwGeeGFFwgEAqytrZHJ\nZDh9+jSxWAyTyYTdbqe5uZlQKERzczOTk5PbZoBHIhGy2SyvvvoqW9uBvPvuu6pRTSgUIpPJMD8/\nj81mw+/3U1tby8jICC+++CItLS1MTEzQ0dFBVVWVmlpWVlYG3N6ud7lcKljrpXj6n41Go3rdvWzN\nP5Cz8gcn2+lCiGfO8vIyRUVFTE5OUltbqxqkJBIJldjlcDgoLi4mFoup6WHnzp2juLhYdUo7cuQI\n0WiUlZUVCgoKCAaD2O12GhoaiEajrK2tUVJSQmFhIYuLi8zMzGCxWIjFYsTjcbLZLNeuXVMtUPXm\nKhMTE8TjcQoKCkilUsRiMbq7u7l165YaAWo2m9E0TY0qXV5e5sSJEzidTiYmJjAYDLzxxhvb3vf/\n+3//j42NDZX9furUKcrKysjlckxNTdHd3U04HCaZTOJyubh+/TpNTU1YLBZu3bpFLBbDbrcTi8XU\nHPWpqSkmJycBaGpqori4mMnJSZxOp+oxf+TIkT23tffaFt+vvY5J8oFspwshxF3oWeV6A5WdGdNb\np23pIz4jkQhFRUX09PQQi8XIZDIYjUZVPhUIBHC5XHi9XtWkJRAIEAgEMJvNZLNZBgYGWFxcJBqN\nAv+yWiwsLCSTyVBVVUVRUREFBQVMTExw9OhRampq1DZ0W1sbyWSS5eVlCgoKsNvtGI1GJiYmmJub\nw+fzqXv++OOPaWxs5Nd+7de2vfcf//jHlJSUMDw8zPLyMk1NTQwMDPDBBx8QiUSIxWKqoY1+3v3y\nyy+zuLjI4OAgAOfPn1f3pGka7e3tauKaPv/c5/MRi8WYnZ3l4sWLtLW1PdZg+qy1YpUgLoR4Zujb\n6HoWtNls3vYfvtvt5oMPPkDTNK5cuUJbWxtut5ubN2+qNqL61rD+WhUVFSwsLBAMBlVjE03TGB8f\nx2Kx8Mknn5BMJikpKaGyshK4HWhKSkoYGRnBbreTSCQwmUzMzMzgdrspKipiYWGBaDSqVvpVVVWU\nlJQQCATY3NxkenoaAIvFwiuvvMKrr77KO++8w4kTJ2hvb1fv+fd+7/f43ve+R2VlJb29vbzyyit4\nPB4uXbpEKBTi8OHDuFwuDAYDfX19lJaWYjQacblcDA8PYzQaKS0tpaCggOvXr2MwGNTjJycn8fv9\nOBwOKisryWazOJ1O2tvbqa+v5+jRo+qLi3g0pMRMCPHY7Lec6KCurSdZpdNpamtrd70fp9NJR0cH\nNpuNwcFBjEYjra2tlJeXc+nSJdra2pifn+fKlStYrVbC4TDd3d2sra0Ri8VUm9Kenh4SiQSZTIbW\n1lbKysq4dOkSr776KmVlZayvr1NUVEQikSCZTBIOhzly5Ahzc3OqhK2pqYlkMqm2+cvKykgkElgs\nFpxOp8o+Hx8f5/r167S2tnLmzBn1nt9++22SySTt7e1cvnxZjQK9du0an//853E6nfh8PsxmM06n\nk9LSUvr6+rBarfziF78gl8vhcDhYX18nmUyqLyher1cdQ9TV1W2bvb61dt5kMuHxeD7Tz/1pJ0Fc\nCPHY6KvXVCqF3++/75GVe9ktOGyt87bb7WoARy6Xo6Ojg+npaVVypU/islqt6n7S6TSJREIlaeVy\nOVKpFD6fj6NHj1JUVMTGxgYrKyucP3+eWCzGp59+SmFhIW1tbczOzjI3N4fL5eLGjRvkcjkSiQRT\nU1OcO3eOmzdv4nA4VLlZKpWivLyc7u5uxsfHaWpqUh3PYrEYuVwOk8nEP/zDP7CwsIDX62VtbY2+\nvj5+9Vd/lWvXrmGxWCgrK+M3f/M31e+mr6+Pzc1NNe2suLgYq9VKb28vX/rSl2hoaODKlSs4nU4K\nCgpobGzkJz/5CYcPH0bTNFVfnsvlmJiYUDXsNpsNj8fDqVOn7hgKo38eenc2fZrbQX/u4l9IYpsQ\n4rHRE8r0xKOHTWbarcZ4tzrv8vJylpeXKS4uZm1tDa/XSyKRUD/39/djs9koKytTq9Pjx49TUFBA\nU1MTi4uLWCwWTCaT6m2uDxG5evUqdXV1JBIJNar06NGjjI+P09PTw/HjxxkYGKC5uZlEIsHp06fx\n+/2srq5SWlpKLpdTs7t7enooKSmhr6+Pjo4OlpeXSaVSZLNZzp07h9lsxmg0srGxQX19vZpZ/txz\nz20L4P/9v/93Njc3GR0dJZFIkMvlaG1tpaKiAq/XSyqV4uLFi7z22muYzWZqa2sZHh7GarWytLSk\nssoXFhYoLy/nyJEjwO3Etfr6enw+HzU1NXckpK2srJBMJjEYDExNTanV+UF/7k+r/cQ9CeJCiMfm\noDOHdwsOy8vL+P1+FhYWSCaTNDU1YTQaWVlZYWpqiuLiYhXsbTYbfX19VFVVkUwm+elPfwqg+pIP\nDQ0Ri8XUF4FoNMqNGzcoLi7GZDIxMjJCRUUFR44cYW1tjdXVVWZmZlhYWCAej7OysqLGhq6urrK6\nuoqmaWr17Pf7KSsro6ioCLPZzOrqKjdu3CCbzaruZ6lUCofDwfLyMvPz85jNZpLJJMeOHVOZ5FuT\n2H70ox9RWVlJPB6ns7OTWCzGyMgIRqORzc1NhoaGmJiYoKGhgdXVVQ4fPkwkEqG5uRlN01heXsZi\nsdDb28sXv/hFtXMwMjLCsWPHGB0dVWV1u30eege3w4cPMzQ0RHV19Z6fez43ZnkU9hP3ZJ64ECJv\n7TbnO5PJqECrtzxtbm7GYDBQU1NDKpVSU7z0ZiexWAy3243P52N1dZWqqio+/fRTzp8/rwZ4GI1G\namtr0TSNTz75RM3httvt/P3f/z2//du/zQcffEBlZSVVVVVMTExQXFxMNBrdlkD30Ucf0djYSHV1\nNcFgcNsOwcrKigpmet/yL33pS+psfmNjg/LycpUh7nK5+I3f+A31+3jnnXc4evQoRqORd955h1On\nTnHr1i16enqYnp5W12hvbyebzTIzM0NhYaFKSoPbmfOZTIbnnnuOeDyuXru8vJzLly9z4cIFNf98\n51FGJpPh3Xff5dSpUyrY6z3Zd6N/dvpn8qxvs8s8cSHEM2W3ciKj0Yjb7aaiogKAM2fOoGkawWBw\nWxMQ/bler5dgMMja2hpjY2McOnQIi8WC2Wxmfn6eiYkJstkspaWlBAIBkskkJ06cYH19HbvdzsDA\nAPX19UxNTalRonNzc8zMzKgpX4WFhRiNRvx+Py+88AILCwvMzs6yvr5OIBBgY2ODoqIiPB4Py8vL\nAEQiEaqqqlhYWCCXy/HlL39ZNXgpKSlhY2NjWwD/53/+Z+bn58nlcgwPD+P1enn//fex2+0sLi6y\ntraGpmkkEglu3LihSs1cLhdHjx5leXmZaDTK/Pw86XRaNaMJh8MAxGIxPv/5z6ugvFtnNKPRyLlz\n51QTnLsFcHj2GrM8CrISF0I8dTKZDL29vaojWzabpbq6Wq3Ad24Fp1IpfvSjH1FfX8/09DQlJSUs\nLS1x+PBhAoGACvSDg4M0NDRQVVXF3NwcmUyGxsZGVe8NMD09TTabVSNK+/v71cq8ubkZQG3nj4+P\nc/r0aaqqqvirv/orOjs71e6C3nAmm81iMBioqqri+vXrHDp0iGAwyL/+1/9a3f/3v/99MpkMTU1N\nasu+tLQUk8mEz+fj2LFj6u+y2SwfffQRXq+XI0eOqBax+o5FYWEhgUAAu92O2WzG5XKpZMD6+vpt\nyWvHjh0jEons+3hkt52UZ5msxIUQAhgaGsJoNHLz5k02Njaora29oyZcb/xy8eJFfD4fuVxOBTGL\nxcLhw4cJhULqnD0UCvHqq6+iaRofffQRzc3NNDQ04PF4CAaDpNNp1eXNbreTSqUYHx9H0zRsNht2\nu5319XXKysoIBoNqktnHH3/M//pf/4t0Ok1paSmVlZWsr69TXV1NKpWioKCAZDJJNBqlvLyc73//\n+9sC+DvvvMPGxgZwu8e7wWBgdHQUi8XC7OwsJSUlmEwmpqenuX79Ojdu3FABPBqNqh2F5uZmotEo\nqVQKm81GTU2N2lovKCigpqZmWztVu93OBx98wMOsA5+1xiyPggRxIcRTJ5fL0dXVxec+9zmVbb3b\nYzwej1r1NDY28qMf/QiHw0FDQwMmk4nNzU3gdsLWysoKRUVFWCwWPB4PJpOJmpoaPvnkE5xOp6r1\nfuWVV8hkMkSjUTUkpa+vD7PZzMmTJ5mbm2NtbY36+npqa2upqKjgN3/zN/m1X/s1xsfHmZmZUSvq\n9fV1dS49MTHBH/7hH/KP//iP6j28++67hEIhNjY2SCaTNDc3s7CwwNGjRxkZGaGoqIjPfe5zZLNZ\nVcZWWFhIJBLh4sWLpNNpTp48SWNjI3V1dTidTjRNUzXguVxO7STopWJ2u53S0lI1+EQfCSo+G7Kd\nLoR4ImxNlAqHwxgMBtLpNM8999yuZ6tbHw+3M8r1JKuLFy9y5MgRRkZGePnll1Ur1K2JWIFAAKfT\nyS9+8QsOHTrE+vq6ygqOxWKsrKzQ19enEuD0qV6ZTIbNzU2OHTtGPB6nvr6e4uJiLBYLKysr6v+u\neDzOyZMnuXLlCmtra1gsFmpqatQ4T/1a6+vraja4PoWspKSEVCrF6uoqc3Nz2Gw2vvGNb2x7///n\n//wfVUt+9OhRrFYr8/PzVFZW0tDQwKefforT6aSiooK1tTXVxtXv92M2m2lvb8fn82EwGDAajVgs\nFtU+Vj+/35l0pg9KGRwcxOFwqGOGfOxT/iTaT9yTEjMhxBNha8338PAwp06dory8HJ/PR3V19V0f\nPzk5SXNzsyo3q6ysVMNCbt26pfqcl5WVqUYtettQt9vN9evXOXz4MDdv3sTpdFJWVsaHH36Iy+XC\n5XKRSqWor6+nvr6ejY0Njh49SmFhIZqmUVZWRjKZ5NatW9jtdlwuF59++imdnZ3Mzs7i9/v53Oc+\nRy6XUyNO9cS0xcVFwuEwgUBANZ0JBAJMTU2pkZ+NjY187Wtf2/be//2///dUV1dTUlICwCuvvMLC\nwgItLS3bdgyOHDnC+vq66qu+urqKyWRS2eTpdBqXy0VdXR0mk4lsNrutrn5n+Z4++KW5uZmKigoJ\n4AdMBqAIIT5z+lnz1hnd92NrpnJFRQWJRIKhoSE6Ojp2fXwwGGR6epr+/n4qKyu3ZTmbTCaampoo\nKytT2emRSASHw6ECjsFgoLu7m7q6OgwGA729vSwsLDA0NKTKsTweD2VlZQQCAWw2G7FYjPLycjWd\n7NatW2SzWRKJBHa7nXg8ztjYGDU1NaysrFBWVqYGhJhMJpaXl1WZl/7c3/md3+Hw4cO43W5sNhuR\nSIQTJ06QTqcxGo28/vrr2973N7/5TbLZLB6Ph6mpKbLZLP/7f/9v/H4/0WgUl8ulRpVaLBY2Njb4\n6le/SlFREYcOHaKlpYXZ2Vmy2SzLy8tEIhF++ctfMjg4SDgcVufg+ohQg8FAKBRifn4eQJ1hbz3P\n3u9nLh6erMSFEAdqty5q92NrQxCXy4XP57trmVI6naawsJDa2lqSySQzMzOsra0xMjKiVrwul4uN\njQ1CoRCFhYWEQiHMZjNLS0vMzs4Si8VIpVJqdW0wGFhaWlLNVvQz4bq6Om7evInJZOLWrVuqKUpF\nRQX9/f04HA6WlpYYHR3l1KlTxONxotEo3d3dpNNpVlZWmJycZGpqCgCPx4PVasVoNBIMBtWW+sWL\nF9nc3KSxsZHh4WG+9a1vqff7n//zf+bMmTOUlJTQ0tJCNBplYWEBp9OJ2+1mZWUFu91OMpmktLSU\njo4Ofvazn+FyuZiammJ6eppDhw6pBjPpdJqioiKSyeS2s3A9Uc9qtVJeXk4ikbjn57nfz1xst5+4\nJ73ThRAHauuKerdt8L3oKzv9zydOnFD/NjAwQC6XUxngBQUFhEIhVeJUU1OD2WzGZDLhdDpJpVJq\nClcikUDTNJqbm9WELoPBwNmzZ5meniYcDmO1WhkfHycajRIOh7HZbDQ0NBAKhfjCF77A3NwcR44c\nQdM0kskkVquVTCZDIBCgublZfZFIpVLq7N1isRCJRFS2u94w5vTp0yQSCf7pn/6JtrY2NE2jvLyc\njz76iNdee41PP/2UkZER/uRP/kS9/29+85tsbm5SXl7OCy+8wNTUFMlkkvLyctWUZX5+XvU8r6ys\nJBqNUlVVxdraGouLi5hMJgwGA+vr69hsNjRNY3h4mBMnTlBaWorP58Plct3xuelNYfSdDH0U60F8\n5uLhHehKfGlpicuXL/Pee+8xNTWF1+vlv/yX/6K2Wux2+7afGxsb93wtWYkLkZ8OurUq3N467+jo\noLy8nL6+Pjo7O7Farfh8Ppqbm1V/br/fz+TkJJlMhuLiYqqrq7FYLNTX15NMJhkaGlIr8qKiIkZH\nR1X70WvXrtHR0aFWk/q4z1AoxMTEBA6Hg3A4zPz8PDU1NQwMDNDd3a3mjU9PT9PS0sL4+DgdHR2Y\nTCYuX75MV1cXAGNjY5jNZpaXl3n//ffxer3q7Lq+vp50Os3c3BwFBQX8/u//vnrv3/72tzl16hS5\nXI65uTlKSkrw+Xy0trayvr4OQG9vL3V1dZSVlWGz2Zibm8PtdtPX18exY8cAWF1dxe/3YzKZVPJa\nfX09y8vLTE9Pc/78+W2z1bd+nr29vTQ1NZHL5VhaWsJqtT7yz/xZ9JmvxP/2b/+WV199lQsXLtDT\n08PExASvv/46DQ0NvP766zz//PPq5zfeeIMLFy4c5OWFEE+ArSvqh6WvavX2pKOjozQ1NZFKpYhE\nInR1dW2bBf7ee+9RXV2tVtf6NnZpaSmTk5O88sorrKysAPDBBx+QSCRUQ5Wenh7sdjt9fX3YbDY6\nOjqorq5WddXvv/8+BoOByspKAoEAJSUlRCIRDAYD/f39tLa2srKygslk4ubNmwAcPnyYyclJYrEY\nJSUlKlmturoaj8dDZWUlJSUlbG5usr6+jt/v55vf/KZ6///zf/5PIpEIly5dori4mO7ubpLJJEaj\nEavVqlq+fuUrX6G3t5eqqirC4TAOh4OamhocDgeDg4MUFxezsrLCF7/4RRwOBx988AHHjh1jY2ND\nrdj12ea7fZ6apqnPw2azPdLPXDyYA01s+/rXv05DQwPxeBy73c7Vq1fVBx6Px+/4WQghYO9kOL2W\n+9SpU1y+fJnOzk7q6uoIhUIqWOvPg9ud0Nrb27Hb7Vy7do10Ok1ZWRnZbJbm5mbGxsZYWlpSAVg/\n904mk7hcLiYmJtSKdHl5mffee4/i4mJKS0vZ3Nzk/PnzvPjii2iaxqlTp3C5XMzMzHD8+HG6urqo\nr69nc3OTeDxOYWEhv/jFL6ioqKCpqYmVlRU2NzexWq1qxXrr1i1u3brFxYsXiUQi2wL4T3/6U+rq\n6hgfH+cLX/gCjY2NRKNR1RCmv7+ff/qnf+K1115jZWWF1tZW4vH4tjP48vJySkpKqK6u5oUXXiAQ\nCDA8PMzZs2eB2/XvbrebsrIyjh49Sjgcpq+vjxs3bjA3N6c+D4vFogabyEr7yfJIzsT//M//nL/8\ny7/clpQBqG9zQgix1c550yaTiXA4rDK9NU1TgzcAterb+byioiIGBweJRCK0tLQwMTFBT08Pq6ur\nbG5uqtVwPB7npZdeYmRkhImJCWKxGGazmWPHjhGLxbBarbz99tt4vV4KCwuZnJzE6/Xi9/sZHR3F\nbDYzMTGhpn/pi5T5+XlVt51IJDh37hzXr19Xnd18Ph9NTU00NTVx/fp1ZmZmqK2tJZVKbQvgf/M3\nf0M4HKa3txe3263O35PJJH6/n9bWVlZXV3n55ZdZWFhgcXGREydOqPtob28nHo9TVVWFw+GgpaUF\nn89HbW2tOi+vr6/HbDar8+zBwUEAqqur1XSxhoYG/H4/LpeLdDqtut6JJ8eBl5j98Ic/5M033ySX\ny3Hy5Emi0SgAlZWV237eeaYihHh27RyEofcd7+rqoqysjKqqKtUIA/5l5e73+1lbW1PPO3v2LBMT\nE5w8eRKbzUZtbS1LS0vMzc1x9OhRqqqqALa1VM3lcrS3tzMzM8Pw8DBFRUXA7f+zXnjhBcxmM+vr\n63g8HjW+9NChQ8zOzvLiiy9SX19PX18f0WgUt9utmtOkUikuXbrE8vIy4+PjmEwmqqqqiEQi9Pf3\nU1hYiNfrxePx8Md//Mfqvf3jP/4jY2NjLCws8NWvflUFXYfDQV1dHYcPH8ZisQBgMpmwWq2qJG5g\nYEAdaXq9XlZWVtA0DZ/Ph91ux+FwEIlE1LCRbDaLzWYjGAxit9upqqoinU6rDPdLly6pBjD63HFZ\niT9ZDrRj27vvvss3vvENGhsbqays5K233uKtt95SP/f09Gz7+fz583u+lnRsE+LpsdvYyq3m5+cJ\nBoOqC5jeozsYDKq+4w0NDaomORQKYbfbqaioYGRkhK6uLtUmdH5+Xg0QgdsLhs7OTqLRKB6Ph/ff\nf5/p6WmWlpbY3NykpaUFq9VKOBzmxo0bnD59mpmZGZaXl2lsbOTGjRu0trYyOjqqZm+3tbXR29tL\nT08PIyMjaJpGd3c3P//5z7FYLMRiMRYXF+nq6qKurk6VoZnNZuLxOLFYjJ6eHm7evMkf/uEfqt/D\nf/tv/43FxUUqKiqwWq0UFBQwMzODy+Uik8lQVFSkztD9fj9dXV2kUik8Hg8XL16kvb2dRCKBwWCg\nsLCQoqIiTpw4oTq1GY3GO8a2bh1Aoo9xtdvtjI6O0tjYyPLyMsePH9/Wc/5un6XYv/3EPWm7KoR4\n5Lm5UBEAACAASURBVO41N3rnv3s8Hm7cuEFVVZU6I6+vrwdul5utr69jNpuZnZ1V4zEHBgZwu90k\nk0kuX76M1+ulsbGRYDCI0WjE5XLhdrt5++231Xb3yMiI6jU+MzOjmszE43FsNpsqx4rFYiwvL3P2\n7FmSySQ//vGP1Za1XvqlB/rFxUVV6qWfyc/Ozqpks4WFBRwOx7YMdIA//dM/xel0YrPZcDgclJSU\nMD4+zvz8PK2trVgsFq5evYrX66Wmpoauri4+/PBDmpubuXbtmmoQEwwG0TSN6upq1Z3tQTLH9Qlw\nNpuNkpISKioqiEaj6jOTGeCPjrRdFUI8kZaXl1ldXWViYoLi4mLKysowGAzb/n1ri0992IbL5VLZ\n2IlEglu3bhEOhykrK1OBPB6Pk81mmZqawuVyMTQ0xMbGBk6nk+LiYubn52lubiabzf5/9t48OM77\nvu9/7X2f2MUusMDiPkkCIAkKpA5HoiwqsZN6alvMZFJn2iaTOnWm97hu02MymYynnrbxTKaJnE5n\nMnKS1moT19ZEY1kULVISCZIgiWtx3wtgL+yFve/fH/o93xLU5SgULcvP6y8BAhbP8yyIz/dzvd/c\nvHmTaDSKyWRia2uL5eVlVCoVS0tL1Ot1XC4XOp2OTCaDy+XCZDKRz+fp6+tDp9ORSCS4desWZrOZ\nrq4uoUkeDodRqVRiWl2hUIhA19LSQqVSQa1Wk0ql2Nzc5Hd+53eOPJ8//uM/xufzUalU2NvbIxqN\nEovFhM+4VqtlcnISh8NBf38/ExMTpNNpXC4XP/rRj+jt7WVubg69Xk9nZydDQ0M0NTWRzWbZ3NzE\naDRitVqJRqNkMhkODw8xmUxH3gMJyfZ0a2uL9vZ2YTUqfe27ybHKPBg+TNyTg7iMjMxHjslkYn19\nHY/HQ71eZ2NjA4/HIwLAu+0Z3/u5nZ0doedtsVhQKBQUCgX0ej1jY2MYDAbW19cpl8vk83khDHP3\n7l3a2trI5/OEw2Hg7SAVDofFBLnX6+XMmTNks1nq9TrZbJZarUYkEqHRaHDq1ClisRiFQoGFhQXO\nnDmDWq1menqaYrGI1+ulUqkIh6/l5WWsVqvoLTcaDeLxuLA5/bf/9t8eeTbf/va3qdfrGAwGDg4O\nOHPmDF6vl2AwyGOPPUZ3dzdzc3OMjY0xNDREPp8nnU6Ty+Xo6ekR1yANDttsNrHLncvl6O/vx2Aw\nEIlEhJ1ptVp9x763NMx2eHiI2WwWsqvvtjcu74R/NMja6TIyMh9LVCqVGJrS6XQMDw8L+8pwOMzC\nwoIQUpHK5yqVShiXhMNhkX1LJiY+n0+U2yORCAMDA6RSKVQqFS6Xi0KhwK/8yq+I1bH+/n6q1SoK\nhYKFhQW6u7vx+Xy0trZy48YNqtWqEE/RarWcO3dOGJsUCgW2trbE7rXZbKa1tZXjx4/jcDjQaDRC\n9nRiYoKhoSGh2tbS0oLX62VhYYFf+7VfO/Jcvve974mhvHQ6TbFYpFAoMDMzQ7VaxWq1Mj09TUdH\nByaTiVqtRj6fZ3R0FJvNxuTkJCsrK6yuropVN8lbPBwOEw6H2d3dZX9/n5aWFg4ODqjX64TD4Xdo\nnEuT/m63W/TPped///sie4B/fJAzcRkZmYeCyWRiY2PjHSXaTCaD1Wqlvb2dtbU1EWgymQwHBwcU\ni0U0Go1QW6tUKng8HjQaDQqFgkuXLqHVasVes2TJ6XQ6WVxcJJvN4na7WV9fZ3NzE41Gg8vlEj33\nK1euoNFoiMfjwgzlXiEXSd51e3ub4eFh9vf3iUajOJ1O6vU6m5ub5HI50QOXDhLRaPRIlv7P//k/\nF8+it7eXP/3TP0Wj0aDRaPB6vSJYNxoNenp6qNVqvPnmm7S3t5PL5chkMhSLRQYHB4V3+fz8PEND\nQ2JXXrIU9fv95HI5uru7SSQSQqQmHo+jVqvFzy0WiyL7rlarImO/972RNNGlFbT3K8XL/O2QM3EZ\nGZmPLSqVirGxsXdIe9brdWFYolAoxE7y4uIibrcbu91OtVqlqamJXC6H2WwWa1OS6lm9Xiefzwu/\nb7Vazeuvvy7MTJLJJLOzs9jtdgYGBmg0GkxMTHD79m3cbjdPPPEEY2NjrK2tUalUuHPnDhaLhWq1\nis1mY2pqCp1ORywWY3FxUaxgZbNZOjs7GR0d5fHHHyebzbK+vk6j0UCr1ZLJZFhdXeU3fuM3xHP4\n6le/yr//9/+e/f19Xn75ZUwmE9evX+dzn/ucyMS3t7fJZrN8/vOfp1arMTw8zFNPPcXo6Kg4cJw6\ndYrBwUGq1SotLS185jOfEfcuGavs7u6SSCRQKBSEQiExVS7te9+bfTcajXeUz+9d/XO73UcydZmP\nB3ImLiMj85Fyf6/VbrcfGbCSsuRisUgqleLg4IBKpYJOp0Or1bK0tMT4+Dibm5vodDoxxNbf3086\nnWZ2dhav18vBwYHImCVvBr1eT6PRIJVK0dfXRzQaZWVlhebmZtbW1rBarcIFbGFhAb/fT6VSwWaz\ncfLkSVKpFDMzM5w8eVLYnZ49e1bsfCuVSjQaDYeHh9jtdgqFAjqdDqPRSLFYxGg0HsnAf+d3foeO\njg4GBgao1+vCXe348eNcunSJX//1Xxc73x0dHWxvb+Pz+VAqlRgMBhqNBu3t7UJHfWZmhr29PVE9\n8Hq9oppwr8vbzs4O/f39OJ1OZmZmRJCXpvBjsRg+nw+73X4kw763/53L5eSBto8YebBNRkbmY8e7\n2VTe+7loNIrNZmNgYACtVsvdu3fp7u5mdXWVRCLB+fPnWVlZIZ/Pk8lk2NnZQafTUS6XcTgcIkO2\nWCzs7OywsbFBW1ubkAi9ffs2J06cYH19Ha1WS2dnJ+l0GpvNxujoKKurqwQCATEEtrW1hUqlYnV1\nlWQyCSDK0+l0GnhbZKVareJwOIC3zU2MRiM7Ozt4vV7K5TKVSoUvf/nL4jn85V/+JRqNhtnZWaxW\nK7FYjGq1yqlTp9jd3RXrcPl8nqamJjY3NzEYDExOTrK9vU0wGKRarYryeyAQoLe3Vxie2O12Tpw4\nIbJoqUcfi8UwGo2k02l2dnYwGAz4fD78fj/lcplgMChMZO5HqVRitVpRKpXyQNtD4MPEPXlPXEZG\n5m/F/eIfkuiK9HE4HMbtdh8JAHt7e0c+J33N7Ows5XKZbDaLy+Vif39f9MSNRiO5XI729nZqtRrR\naJSOjg5CoRAOh4OlpSXMZrMIvIODg3z7299mYmKC2dlZ+vr6GB4eZmdnB71ez+7uLslkUmiC9/f3\nU6lUUKlUZDIZkskkRqMRjUaDzWYjk8mI1bLr168zODjIwMAAV69eZXV1lXK5TFNTkwjQv/d7vyee\n0R/8wR/Q0tLC4eEhVqtVaJwfHBzgdDppbW0lk8lQKpU4PDxErVYzMDDAzs4OLpeLbDZLoVAQCm+H\nh4ccHh6Sz+fxer0olUr0ej2PPPLIuwq5AMzOzjIyMiKEbMxmMyqVCo1Gg1KplMVbPgbIe+IyMjIP\nnfszbWlHWvq4paWF+fl5sZtdrVbF4JrP5yMWixGJRFhaWqKlpYVCoQCA2+1GqVSi1Wo5efIkNpuN\nl156CY/Hw/T0NGq1mmKxKFzFlpaW8Pl8FItFurq6mJycxOv10tzcjMfjIRwOs7OzQ1dXF/v7+1gs\nFgwGA1arFa1WS7VaJZfLEYvFGB0dpVKpcOHCBYLBIIlEglwuR19fH8lkktHRURYWFggGg2IPvb29\nXQjQ/P7v/754Pl//+tcplUpUKhVqtRqbm5uoVCoGBwfp7u4mGAwSiUT4whe+gMlkIpPJMDAwwO3b\nt9FoNKTTaZqamhgaGhKDaB6Ph8HBQSE/e/z4cex2u/AYn5ubEy0Lt9uNRqMRa2zZbFZ4r0s+6PdX\nSmR+MsjldBkZmYeKtMZUq9VIp9NCr1uv13P16lUajQbhcJimpib8fj+lUgmdTofb7aZQKAi7ULPZ\nzPDwMIVCQayQSc5ZuVwOhULBnTt3GB8fx2KxYDQaWV9fp7Ozk/X1dcxmsyivOxwOfvjDH/Krv/qr\nbG5uCgnSpqYm4UYWDoc5ceKEmIxvamri8PCQ5uZm4vE4MzMzYoJd0mZvb29nf38fj8dDMpnEarVS\nqVRwu920tbWxvb0NwNe+9jXxfJ5//nkcDgednZ0i0x8ZGWF6ehq/38+1a9dobm4Wg2Xz8/P09fWx\ntLREe3s7er2eUChEZ2en6H1fuHCBWCyGTqejUCjQ2tpKoVDAYrGI/vm9/uuBQIDW1lZRDvf5fDQ1\nNYn+tyze8vFBnk6XkZF5qDQaDUZGRiiXy0JqVBIJaWpq4uTJkwwMDLC0tES5XCYWi2G1WkWGDhCJ\nRAiFQiwsLFAul2lra+P06dOo1WrGxsawWq3k83nGx8fZ399Hr9ezsLDAyMgIu7u7lEolMSne39/P\n7u4uX/rSl0TAXV5eJhgMUigUqNVqtLa2YjabWVtbY2pqilqtxiuvvIJKpSIej9PT08Nv/dZv0dTU\nhFKpZHx8nImJCYrFIsePH2dhYQGj0YharcZkMhGPx7l16xbr6+v81m/9lng2//W//lccDgcmkwmD\nwcDt27ep1WrMzc2h1WpZXV3F7XZjs9mw2Wxcu3aN7u5u0uk0tVqNEydOoFQqee655zg4OBDPJZVK\n4XA4CAQCjI+Pix38e81JpKqC9JwAYrGY0J6/d0f8vURdZH46kHviMjIyH5r7e9v3BoE7d+4wMDDA\nwsICx48fJx6P09zcTCAQwO12o1Ao8Hq9hEIh1tfXqVQqlMtlPv3pT7O8vCxU1xwOBz6fjzfeeIP+\n/n6uX7/O9vY2LpeL3d1dzpw5g0qlQqFQMDMzc6RsfPr0aS5fvozT6cThcGCxWIQr2czMDD6fT6if\nmc1mYb7yzDPPCLW3g4MDdnd3xYCXxWIRr61UKgkEAvy3//bfuHHjhrj3P//zP0epVJLNZnE4HBw/\nfpxQKMSNGzeEQ1t/f7/4GZIKndlsFiXulZUV+vv7yefz5PN5Dg8PcTgcjI2NvaehiUS5XGZ2dpbm\n5mY0Go1Qn2tubsbpdB7RQpf5+CD3xGVkZD4ypFWx9fV1qtWq6Le+VxbX1NREIBBgdHQUvV4vBr4K\nhQJGoxGn00k0GkWhUJDP53E6nfh8PmHbaTKZqNfr3L59W/Rpu7u7MRgM4oBQr9eFnrjdbmdtbY2J\niQmGh4eZm5tDoVBgsVhwu9309PQwOTmJ2+0mm81iMBhQq9Xo9Xp6e3ux2+2EQiF0Oh2lUomuri52\nd3dZXV3FYDBgNBoplUqo1WqhZQ7wpS99ib29PXHf/+W//BcsFgvFYlGseYXDYTwej7Ax1el0TE5O\nYrfbcTgcojyez+cpFAooFArUajWhUIjDw0Pq9TqdnZ2USiVKpZIYcrt/JUxCpVLR2toq+t2lUolG\no4HH4yEQCNDf3y++794VQFnE5SfLh4l76o/qYmRkZD4ZSNPn4XBYlM41Gg0Oh+N9Xay0Wi3j4+NH\nXkfKNEqlEi+99BJOpxObzcb09DQXL15kcXERr9dLKpUiEomQTCbp7u5mYWGBY8eOsbu7i0ajwe/3\nMzY2BrxdDdjb2xNuW2q1mvn5eRKJBMePHxdWoW+++SZtbW2cPXuW119/HbfbTblcptFocOvWLRwO\nB7Vaje7ubnEgMRqNGI1GXC4XLpeL+fl5nnjiCbLZLEqlkl/91V89cs+/93u/h8vlwmazsbm5yZkz\nZ8QEealUYn19XWihDw0NYbFYyOfzYu98Y2ODa9euceHCBaGJHgqFxHT6/v4+1WpVTPRL2wCxWIz1\n9XVMJhONRoOBgQHUajW1Wk20MYaGhlhcXGR0dPTIgUsSfCmXy4RCITlD/ylDzsRlZGTeF2n6vFar\nkUgkiMfjtLe3E4vFfuxBKCmAazQa2tvbuXr1KmfPnqWlpQWr1UqxWOSVV14hl8tRqVRobm5mamqK\nnp4ednZ2iMfjlEolEomEeL2DgwPR3zUajYyPj2M0GpmcnGRjY4Ouri7RK6/X61y4cIHl5WW2t7ep\nVCqUSiX8fj+vvfYaZrNZZOwWi4XV1VUKhQLr6+u0trZitVq5desWNpuN9fV1dnZ2+MpXvnLkHv/i\nL/6CZDKJy+Xi5s2bKBQKsS+eSqWo1WpC512r1RKLxYS6WrlcZmhoSEjEKhQK9vf3hZqdJIF67Ngx\nwuGwCOI3btwgGAweEa2ROqTt7e1ir97lcrG9vc3IyAharfbIdUuDbYFAQEzHyxn5TwZ5Ol1GRuaB\nI/2RT6fTKJVKent7WVxcxGQykcvlPvAPvhTAq9Uqfr+fGzduMDIyQqPRIJFI0Gg0SCaTqFQquru7\nsVgs7O7uolAoWFpaQqPRYLfbUavVBINBUqkUPp+Pvb09JiYmhHhMrVZjcnKS9vZ2IYpSrVbZ3t7G\nZrMRDAbR6XTUajUGBwcBuHXrFl1dXdRqNUwmk8jivV4vTqdTGH3Mzs4yMDBAMpnE7/cfGWADeOGF\nF1heXuYXf/EXuXv3LoODg5w9e5bl5WVaWlrQarUYDAZOnz5NIpE4Us5Wq9Wsra0JtzNpwt/lcpFI\nJDh37hwrKyuYzWYajQZ+vx+bzcatW7fo7+/HarWyubnJ3t4eXq+Xvb09fD4f29vbmEwmzGYzfr8f\nl8tFNBp9xwqZNLVuMploa2uTV81+gsjT6TIyMg8caXq5vb2djo4OtFotXq+XtrY2IdASCoWYnp4W\nJiT3Tj9Lg1y9vb1cu3aNp556SkiDlkolUqkUmUyGQqFAKpVibW2NeDwuzE70ej1KpZJKpUIikaCr\nq4uWlhbRD9/f3wfg9ddfx+VyMTAwIErCAwMDHDt2TPSztVotLpeLvb09pqenKZfL6HQ60Z9Xq9X4\nfD4WFxfZ2Njg8PBQrHtNTU3hdrv5lV/5FXFvv/3bv823v/1tYrEYjz/+OOFwmEqlgtfrZX19nWg0\nitvtFgcIaT+9paWF7e1tnE4ner2ec+fOCcnUZDJJU1OTsCHd39/H7/fj9/up1+u43W4WFhbE0F25\nXMZms9Ha2koymeTJJ58kHo8zOjoqxHYk/XNpI+BeJFcyqXLwXl8n8/HkAzPxv/zLv+Stt94inU7T\n1dX1kC5LzsRlZD4u3Cu9KXHvbrHJZMLn84nAHY/HmZycZG9vD4VCQaPREIpq586dQ6vVolQqCQaD\n7O7uCvcvpVIphrlWVlbQaDS43W4qlQpra2s0NTVRLBap1Wpcv36d7u5ukskk+XyeVCol3LmCwSAH\nBwc0NzeTSqWETOvBwYHY+U6n04TDYc6ePYvFYmFjY4NsNovFYqFcLnPhwgW2t7eZn5/n2LFj7O3t\n0draeiQD/5//83/i9/uF6Yper2dtbY1yuczGxgb1eh2Px0OhUMDv93P37l18Ph99fX0EAgF8Ph+p\nVIre3l4ajQbHjx9HpVLR3NzM0NCQuP/5+XkeeeQRarUavb29HBwc0N/fj8fjOZKNu1wujh07dkTY\nZX5+HpfLxdbWFt3d3Wg0mvd8n2VZ1Z88D7ScfvfuXX73d3+XRCKB0+lkamqK//N//g9tbW14vd4H\ncsHvhxzEZWQ+vphMJqHCFo1Gsdvt3LlzB6vVyuLiIufOnaO3t1eUdIvFIn19fUeCyPXr19FqtUI/\nXa1WUyqVaGlp4dixY6KPXC6X8Xg81Ot1oZGu1+vp6enBaDRy+/ZtFAoFNpuNc+fOEYlEWFtbo1Ao\nEIvFACgWi2Iq3e/3c+bMGRwOBzs7OywvL1OtVhkfHxcOZj6fj2AwSE9PD+l0GqfTyT/+x/9YXPvX\nvvY1vF6vCNZms5lQKMRjjz3GyMiIOCCkUimxX+5wOLhx4waVSoVCoYBKpRL96ZaWFra2tujt7RX7\n6YBoMUjWrRqNRhyoVCoVVquVer0u1Nek77u3RP5+pfR7ebfDmszD5YFPpz///PPv+Nxrr732N7ws\nGRmZTxqSqEtLSwtNTU288cYbKJVKkfXu7u7SaDRoampCrVazurrK6uoqFovlyHDVyZMnhe54R0cH\nN2/eRKfTsbm5SXNzM9PT01y4cEH0pSWxk1qtxsbGBlqtluPHjxOJRNjf32dxcZGdnR2effZZ/H4/\n3/3ud6lUKjz99NMkEgnW1taoVqt4vV7u3LmD0+nk0UcfJRAIUKlUUCqVuN1upqamhKZ4NBrlX/yL\nfyHu/ZVXXmFpaYnFxUUUCgU9PT1CvOX69euibB8MBsVUfzQaJRAI8MQTT+Dz+fje975HqVSir6+P\nzc1NJiYmaGlpIRAI4PV6WVxcxOFw0Gg0cLlcaDQaMY0uZcnhcBilUkkikWBkZORI9iwJu4RCIZqa\nmsQhQOaTx3tm4lJP5O7duxiNRv76r/8ao9HIqVOnHsqFyZm4jMy786D3et/r9cLhMJubm+zv71Op\nVDCbze9aUo/FYjQ3N2MwGBgaGiKVShGNRuns7KSzs5N8Pk+j0eD06dM0Gg02NjaIx+NEIhEymQy7\nu7tcvHiR9vZ21Go1W1tbol8uWXpKe9Zra2vA22Im5XKZwcFBdnZ2qNfrNBoNoQzX0tLC5OSk2I/u\n6OjgypUr2O12Pv/5z/Pmm2+iUChwOBycPn2aaDTK4uIiTU1NZDIZuru7aW5uJhKJ8B//438U9/yn\nf/qnzM/P4/f7aWpqorm5mWKxyMbGBkNDQ2xubjIwMCAU2M6dOyf2v6WhM+kg8fTTTxMMBtHr9SST\nSRqNhpBOTSQSdHR0iMPG2NjYOwbOJO35d8uypY0Cu90u9sLlEvnHn49ksO073/kOL774Irdu3eLV\nV1/98FcnIyPzQJD2et1uN6FQ6IG9nqR4Jg2mSQNpx44do1qtvuNn3SvXqVAohByq1+vls5/9rNi3\nrtfrYsd5cnIShULB6uoqn/nMZ9DpdNhsNuFv3drayiOPPIJSqaSvrw+tVkt7ezsjIyNUKhU+/elP\nU6/XyefzJBIJLl26xNLSElarlVOnTtHd3Y3b7RaCMdLrfO9732N4eJinn36ahYUFPB4PXV1d5HI5\nofHu9/sBRE86mUzy1a9+Vdzv7//+7xMOh+nq6mJ5eVnorkuqa5KWus1mY29vD4/HQzabJZfL4fF4\nuHbtGvV6HaVSSVdXF1euXBFVAek5ScNlBwcH5PN53nrrLWw2m+jlS8lVOBwmEomIQ9b9g2j1el28\nzsmTJ+UA/gnmAwfbUqkUL730El/+8pfZ39/n9OnTD+XC5ExcRubdeZCGFVIwkILEyZMnMRgMRCIR\n4G0N7kQigUqlwufzCWcsycpSUgwzmUysr68DiOxX2jc2m81UKhWi0Sgulwu9Xk8mk2FpaQmbzcZj\njz0myr1Wq5VgMEitViObzQr99EQiQaVSEdfj8/k4efIka2trYoo9m82KHvTQ0BCJRAKNRkOj0cBk\nMlEqlVhZWWF3d5fx8XHsdrswW5FkVbe3t4Uc6j/7Z/9MPKc//MM/xGq1YjQaqVQqQq51bm5OCLms\nrKxQqVRoNBoMDQ2h0+lYW1sjl8tRKBRoamoSPW1pViASieD3+7Hb7SSTSQqFAktLS2LmYGRkhK6u\nLhYXF49k05ubm3i9XuLxOFqtlqamJvF+ZjIZoajn8/nkAP5TxEeSiff09PDLv/zLJBIJ8Y9URkbm\nJ8eDNKxoNBqcOHECtVpNo9EQYiTSVHkoFOLg4AC1Wk04HKZarb5rFSAWi7G7u0s2m2VtbY1YLEa5\nXBbT593d3UxMTKBQKIjFYuj1elGKl2wxo9Eoc3NzqFQqKpUKfX19OBwOrly5wvr6Omq1mr29PQ4P\nDykUCmxtbRGJRDhz5oxY4zpx4gQnTpwQ61xGo5GBgQFSqRT1ep2LFy9y5swZdnZ2+O53v0s+n2d3\ndxelUsng4CCPPfYY3//+949k4K+88gonT54Uh4qhoSGq1aoI1p/73OcwmUxYrVbGx8cJhUJsb2+j\n1+uFzOq5c+eo1WpiUE5aB/P7/USjUV599VWxPvZzP/dzGAwGRkZGaG5uZnFx8R3ZtKQpL3mC3/t+\ntrS0iOxeDuCffD4wE5d0dw0GA1/60pce0mXJmbiMzHvxIKeIDw8PMRgM5HI5ent7xeEgn8/j8/lw\nu93E43EGBgbQ6/Wsr6/jcrneUQXIZDIUi0UmJiYIBAIYjUbhdZ3JZIR/uN/v56/+6q/o7e2lXC7T\n19fH7u4uoVCIaDRKKBRif38fl8sFwNbWFiaTCaPRyO7uLm63m/7+fqLRKJVKBavVitPpJJvNEgqF\n2NvbQ6fTsby8TKVSwWKxAOB0Otnb2+Pg4IB4PI5CoWBsbIzr16/T39+PXq8nn89z8eJFZmZmxPP5\nV//qX+F0Orl+/TpWq1XoqVssFtra2iiXy+Tzeaanp+ns7ESpVGK329nb2yMWi+H3+4WIS6lUEtai\nbreber1OW1sbtVqNU6dOCWnVRqPB4eEhfX19Qib1/tUwSQVOpVIdmUqXbUV/uvlItNMvXrwo/run\np4evf/3rH+LSZGRkPo54vV5mZ2dxu93EYjHhiCX1VCORCC6XS/z3yMjIu1YBpDWnmZkZCoUCSqWS\npqYmbDYbGxsbFItFDAYDu7u7dHZ2EolEMJvN3L17F41Gg1arJZlMkkwm0Wg0LC4uCoMShULBwcEB\nTz31FJOTkxQKBYLBIGNjYywvL1Or1VhZWaG3txer1crh4SFjY2OUSiV+8IMf8Pf+3t9je3sbu91O\ntVpFq9UyOjrK9773Pcxms/iee1fIAL75zW+iUqkwGAw4nU7q9To7Ozvs7u5y9uxZyuUyKysrlEol\nBgcHicfj+P1+VCoVw8PDQgL24sWLxONxhoeH2djYoLOzk5GRESYnJ5mfnxcmMtKaXKPRYGxsjGg0\neiQDlzTs6/W6qMbc72Amaa3Lu94/O3xgJr61tcU3v/lNnnvuOTY3N+WeuIzMJwgpU/P5fEemn+8V\n/pD8v+/fU753ql3KLHd3dzl9+rQQYKlWqwSDQdxuN8ViEYVCIbLltbU13G63MOpYXl6mvb0dvQGC\nRQAAIABJREFUj8dDuVzm0UcfxWQy8frrr/P4448zPT1NLBbD7XbjcrlIp9Oo1WrR+3U4HFitVnK5\nnOgV63Q60uk0kUgEu92OyWSis7OTq1evYrFYmJiYoFAo8A//4T888lz+6I/+CJvNRj6fx2w2iyAM\nb1cnG40Ge3t7nDx5UliI9vb28qMf/YjOzk7sdrvor29tbQEI8ZlsNsvi4iLVapXh4WFKpRJNTU0c\nP36c/f19bDYbuVxOBGjpOUciEeHiJhnP3J9py7veP9080Ez8a1/7GvC2J/DGxgY2m+1veXkyMjIf\nR+7NuqVdYkmKU+J+Z6u5uTkSiQQWi0WUt7u7u4WE6cHBAd3d3RweHnLixAmMRiPr6+soFAr6+vq4\nceMG58+fR6FQ8OKLL3Ly5Elh4jE1NYVKpSKRSDA/P09LSwsbGxuYzWYmJibI5/Mis5Ym6IPBIGaz\nmZmZGZLJJEajUfTZh4eHMRgMrK2tcf78eXK5HCqVikwmw9ra2jt00P/1v/7XDA4OYrFY+P73v086\nnSaZTKJUKikUCng8HlZXV+nt7aVer6PX65mYmOC1115jfHyc9vZ2rl27Rnd3N4VCgXq9Tm9vrzjw\n9PT0CJOUtrY2DAYDJpOJg4MD3G73OxzFpD53sVhkf39ffN309DQul0v4st+fed+fucuZ+SeT9wzi\nyWSSixcv8ulPfxp4e0o9mUw+tAuTkZF5OEglWEnYJBKJ0Gg0UCgU1Ot1mpub3xEopIE4lUrF1atX\nGR0dJRQKUavVCAQC5PN5wuEwiURCaHzncjmxiiXJhP71X/814+PjWCwW6vU6N2/epFAooFar2dzc\nZHBwkGAwSCaTweFwMD09jcViEUN2UmneYrGwsLCA2Wzm1KlTmM1mAoEAXV1daDQaisUiJpNJ7GM3\nGg0mJib4xV/8RfEchoaG+Af/4B+IzFuyTfX7/Zw7d45gMIjRaGR5eZm///f/PrFYjNnZWZ5++mmu\nX7/O8PAwfX19/OAHP+CZZ57h5Zdf5sSJExSLRWG00tHRQaPR4O7du5TLZaLRKOVyGYvFIpzJ7j9Q\nSYcs6f1wu92ily5Zwr6bhahsMfqzgaIh+db9GKTT6YeWkUv/gJqbmx/Kz5OR+VknFAoJY45MJsPA\nwAALCwtC1ORe7/A7d+7gcDi4ffs2Y2NjZLNZfD4fpVKJcDgsxFk2NzdRqVTUajWUSiV6vZ5qtUo2\nm0WhUJDJZOjr6yMej5NOp7Hb7RgMBvb29oSCWr1ep6enh1AoRLlcplgs4vf7mZ+f59SpU2KC3mQy\nCfnUxcVFDg8P8Xq96PV6crkckUhE6LPn83n+3b/7d+Le//zP/5xIJML58+e5dOkSgDBYMRqN4oAj\n+YvHYjHy+TyPPvoowWAQm83GwMAA6+vrNDc3YzabmZ2dFe2HbDaLXq+ns7OTmzdvcvbsWVQqFfF4\nnGPHjhGPx0Vglt4H6cB0/+f29vaE8cyxY8fEet79mbb0dbIe+k8PHybuvWcmfuHChXd8bnNzk9XV\n1Q9xaTIyMh93pIwvFouJ7E7q196bGQK4XC5u3Lgh9qGnp6cZGBhgZ2eHg4MDYbdZKBTQarUUi0Vh\n/jEzM8PIyAj7+/tCDc5oNFKr1ajX62g0GkqlEh0dHcILW1oR6+joYG9vj1u3buF0OonH41SrVT73\nuc8RDoeZn58nHA6zu7srVNxqtRpWq5VqtYrBYMDhcByRUf3v//2/s7W1hcViYWlpiaamJsxmM8eP\nH+fP/uzPhBpdo9Ggt7eXnZ0dlEql6DtbLBYGBwfR6/XC01sydJGm7HU6HU899RThcJj+/n78fv87\ngjD8P7nUcDgMIA4x9wZ1qXLyXkOGEvKQ288G7xnEv/jFL/LLv/zL3JuoSydUGRmZTyaBQICmpiZR\ncpampO8PBBqNhr6+Pg4PD1lcXKS5uZnZ2VmUSiXnz5/n1VdfZX5+nmg0KnS933rrLdGH1mg0RKNR\nPvWpTwlv7L6+Ptra2pibm6Ner1OtVkmlUng8Hvb29oRndiwWw263MzY2hkKh4KWXXqJarYrAHw6H\nGR4eZn19nbNnzzI9Pc3BwQF2u51QKMS//Jf/UtzHf/gP/0FM3/t8PjQaDZubm4yPj/P888/z5JNP\nUqvVhJxsPB7H5XJx/PhxotEoGo0Gv99PJBKho6NDDO7NzMxw4sQJSqUSarWa/v5+Go0GBwcHqFQq\nXn/9dbq7u0V1Q3q2knVpuVwmkUhw+vTpd5TD751XeL8S+f1zDTKfTN5zOr23txebzSZEGfR6PcPD\nw2xubuJwOD7yC5On02VkHi65XI6+vj7hOiatS1mtVqLRqJD43N/fF7vf0WiUp556imQyiUKhQKVS\nCd3zRCLBsWPHMJlMQmVNr9fT1dVFOp2m0Wiws7NDIBDg4sWL5HI5TCYTN2/epL29HbvdTj6fF2Yp\nkv56a2srGxsbNDc3c/XqVZ599lm6u7tJJBIEg0FaWloIh8PEYjGamprY3t6mWq3i9/uPBPDvfOc7\nKBQKcX9nz57lypUruFwuEokEHo8Hp9NJW1sb2WyWtrY2dnZ2uHPnjtBG7+rq4uDggI6ODrETLkmz\nzs7OolAoePLJJ3E4HMJVTFK/W15eFlKrkmZ9KBSis7OTXC5HNps9Ug6XJ84/+TxQK9Jvf/vbXL58\nmVKpRDqdJhAI8Cd/8icolUqxavFRIgdxGZmHiyQUMj8/T6FQIBQKCeOTXC6H1WrFYDCws7ODVqsl\nGo1isViYnp6m0WhQLpcpFAqiPFwoFJiYmOD27du4XC4ODw8BxP9fXl5mdHSUnp4eVldXMZvNzM/P\ns7+/TzabRafTEY1Ghd+41FdOJpP09vZy+fJllEolAwMD7O7usr+/j9Vqxefzib3zUCiETqcD4J/+\n038q7vUb3/iGKLdLPuKSF7jZbMZms7G1tYXH4yGVSmG1WkVfv7+/n0QigdlsRq1W86lPfYp6vY7d\nbieTyRzpfwNotVrsdjtWq5VMJkMmkxFWom63G4/HI1b7yuUyuVyOaDRKc3Mzm5ub9PT0vK8PuMSD\nNsaRefg80CB++vRpWlpa+M53vsNLL71EMpnkH/2jf8Sjjz76QC72g5CDuIzMg+P9nMru3fUOBAIo\nFAoqlYooY0uT6tVqlbm5OQwGg7C37O3tJZfL0dXVRTgcJp1O09XVRSqVwmAwAKBWqykUCgwNDREO\nh3E6nQQCAWw2GzabjZWVFXK5HHt7eyKIGY1G6vU6pVIJn89HOBxGq9WytrYmDhUKhYKOjg62traY\nnp6mo6ODWq2GWq0mmUxSqVQYGBhgfHz8iNrk//7f/5udnR0eeeQRTCYTDoeDlZUVqtUqOp0On8/H\nlStXOHbsGBqNhkgkQqVSQa1+u/u4traGx+NBp9MJzfP+/n6USiWZTIaZmRkajYaYA7jf53tnZwez\n2Szc0mKxmMi0zWYz2WwWs9n8rj7g7xeoJeey+93OZH56eOCKbd3d3fyn//Sf/nZXJSMj8xPn/nUj\nSSs9HA6jUCio1WqiPKxUKoUYiyTC0tfXRzQaJZvNcuLECWFm0tbWxp07d6jVaoTDYX7+53+e7e1t\ngsEgTzzxhNBdb2trQ6vVotFoMJlM9Pf3U6vVSKVSGI1GxsfHmZycpNFo0NXVxf7+PolEAqVSyfb2\nNvl8nq6uLhQKBRqN5siUuGSSolQqxVR7W1sbW1tb1Ot1zp49K57DCy+8wMrKCk6nk6WlJVZXV0UW\nrVQq6e7uJplMMjY2hsfjIRqNiv1wlUrFG2+8Qb1eF4IuoVCI9vZ28fpKpZIvfvGLvPbaa0SjUbG7\nfu+a3unTpwmFQu86byD1saUDzf0Dhe+3NvZu+/4yn3w+ULHtJ4WcicvIPDju19SWFMFqtRrb29sM\nDg6KzPvEiRO88cYbtLe3o9PpOHPmDKFQiGQyidfrRa1Wk8vlOHXqlAhya2trWCwWDg8PCYVCGAwG\nstksOzs7rKysADAzM0OtVkOhUDA4OIhCoWB5eRmbzcb+/r4Irnfu3AEQ61mSxOjQ0BCNRkOsom1t\nbaHRaHjyySdJpVJsb2/j8XiE2tzU1BTf+MY3xDN46aWX2NjYQKPR0NLSQjabpbm5mZaWFnp6esjl\nciwsLGAwGFCpVMRiMVFK12g0BAIBHn/8cXQ6HfF4XGiX12o1rly5gsPh4ODggKamJgqFAseOHaOn\np4dEIoHBYBD+5FJpXZo3eLeydyaTYXNzE6PReORr3k8b/V6VPXka/aeTj8TF7PLlywDcvXuXf/Nv\n/s2HvDQZGZmfNIFAQGybSFlbOBwmmUySy+UIBAKcOXOGlZUVvvCFL4g9aUmQRAoa3//+96nX6yKL\nz+VynD17VuyJS2tnLS0twuxDCuTd3d0cHBwQjUaZnJxkfHycWCzGzMwM586dQ6VSoVarGRkZEb1n\ntVqNWq1mZWWFubk5qtUqh4eHOJ1OFAoFiUSCjY0N+vv76e3tZWNjg6997Wu8/PLL4t4vX77M2toa\nqVQKnU5HJpNhaGiIbDYrhuxsNpuoGEjmKh6PRwR8l8tFIBCgWCzidDqx2Wz09PRgNptxuVzcuXOH\ner3OCy+8wMHBAXNzc+zs7FAsFsWanjR0FwqFmJ6eZnd3l729Pfb29oSBi9R7P3XqlFgTk3g/Bzsp\ni5cD+M8W7yn2cvfuXb71rW8xNTXF+Pg4AFNTU0xNTT2UC5PFXmQ+KXwc5C9DoRAKhYJSqcTBwYEo\nicPb/8ampqZwu90YDAaxk1yr1djd3QVAoVCgUCiYmprC7/cf6d+qVCpSqRSrq6u0tLSInrRarWZ7\ne5tTp04RDAbp7OwkEAiQTqeFvCjAzZs3sdlsdHR0cP36dZqbmxkeHmZ1dRWVSkU6nUar1Ypd7Vgs\nxrlz54jFYgQCAZxOJ+l0mqamJnZ3d/nmN7955N7/4i/+gkgkQjAY5LnnnhNqbJubm+RyOYrFoliD\nc7lcFAoFCoUCn/vc5/irv/orOjs7KZfLXLt2jTNnzvDMM8+wuLhIMpkUgfnu3bs8++yzYte8tbWV\ncrnM8vIyn//854nH4+K53iuqUygUsFgsBAIBnn76afb29ojH48Lm9L2EXO5H+h2TDGveS4pV5uPN\nh4l776vYtrGxwaVLl3jmmWcA6Orq+lte4o+PHMRlPilIf7Qlmc2Pcnf3/gNDLBYTvuB2ux2j0YjN\nZhMKYe+m6iWtZ1WrVdbX14VsablcRq/XC3exra0tXC4X1WqVvb09xsbGiMfjQiLU4/FQq9VIJBLA\n26XgWq2GyWQSEqLSdeh0Oubn5zEajYyNjfHaa6/hdruFpnhvby/Nzc1ih7y3t5cbN27Q1taGxWJB\nrVYTj8f58pe/fOR53Lp1i5dffpnHHnsMhULB1atXaW9vJ5VKYbPZhBTrxsYGXq+X5uZmkQVPTk5i\nNBppaWkhEomg1+tRKpXivazVatjtdt566y2efPJJKpUK6XSaYDCIw+GgVqvR39+PRqOho6NDXJP0\nzK9cuYLH46HRaAjL1FQqxejoKOVymUAg8A4f8ffi3oOBXq8XFRR5T/yniw8T9963nN7d3c1v/uZv\nkkql2NjYkMvpMjIfgnsHjqTs86NCGnxyu92EQiHx8dDQECsrK9hsNg4ODlAoFELrXNpnDofD1Go1\nYrGYUB9TKBR0dnZy5swZsYrV2dnJwcEBfr8fn89HPp+ns7OTRqPB4uKiMP7I5/PUajXa29upVqs4\nnU7cbjfpdFqYitTrdebn56lWq/h8PoaHh5mamhLCKC6XC7PZTDAY5OrVq+zu7uLxeAiHw+RyOeG/\n/aMf/egdAfz555/njTfeoLOzE6/XS6lUorm5WUzTVyoVDg4O0Gg0fPazn+XcuXOsrKzQ0dHBtWvX\nGB0dRalUMj09LVbWDg8PKRaLqNVqVCoVlUqF06dP4/P5yGazqNVqXC4Xe3t7eL1e7ty5w/7+vhj8\nk555KBSiv7+fcrksds2lSkAkEhECOj8u96rtSa5zH/XvmszHgw/siV+4cIFvfetb/PCHP+T27dsP\n45pkZD5RvF8f80Fz/4FB+vjg4IDz588Tj8dFb1sqfadSKbRaLU6nU+iQ1+t1QqGQyAyknrNSqeTW\nrVtYLBZisRgKhYJyuUyj0WBzcxOTyUShUMBgMJDL5ejt7RWlcCmobG9vo1AoGB4exuVyCVWzSqUi\nht8GBwf5pV/6JSEoY7PZUKvV+Hw+KpUKly9fxuPxkMvlyOfz/NEf/ZF4Br/5m7/Jt771LQwGA3a7\nHbPZzP/9v/+X7u5uisUio6OjVKtVYWVqs9nIZDJMTk7i8/m4efOmsBjVaDQMDQ2RyWREifyRRx7B\n6XSSTCZpaWnB6XTy5ptvcurUKfx+P21tbUxMTLCysoLH48Hlch05UEllbrVazbFjx1heXmZsbIyO\njg6xTjc6OvqOfvj7If2OjYyMiPdYLqX/bPCB0+nhcJivf/3rPPPMMzz++OMPRa0N5Ol0mU8OD9Pj\n2WQyMT8/j8lkIpfL4Xa7xQHiXi9wacp5Y2OD9vZ2isUis7OzOJ1OSqUSJpOJdDrN4OAgs7OzeDwe\n4QeuUqkoFApCiKVer6NWq9FoNDz77LPCRvSxxx7j8PCQlZUVXC4X8Xgci8VCT08PgUAAi8VCOp0W\n2Se8nTRIffBCocCbb74pMl5pVS2ZTNLa2srw8DDRaJR/8k/+ibj/P/zDP+Tw8JBHHnkErVbL9vY2\ntVqN3t5eMc+TTCbJZrOUy2W8Xi/ZbJbl5WWOHTtGvV4XO+67u7s4HA62trY4e/as6PUrFApmZ2fF\n9zocDtG/hrcHzKanp6nX6zidTiwWC+3t7WQymSOT5WazmWg0Kkru0u9KvV7HYDD8jZTapN+x95t4\nl/n482Hi3nv2xC9evAi8fQKHt0vrm5ub3Lp16297nT8Wck9cRubD8eP04Gu1Gq+//rqQ/UwkEjzy\nyCOoVCoCgQB2u13ollerVZLJJG1tbeTzeebm5jh9+jS3bt1ifHycarXK7du36ejooL+/n8uXL1Or\n1TAajUQiEXQ6ncgUBwYG2NzcpF6vk06nRWZ978/KZrMEg0FUKhUjIyN4vV7u3r1Le3s7c3Nz6PV6\nobv+d/7O3xH39Pzzz5PP5ykUCoyOjrKxsYFCoUCv1xOPxzEajeh0OnQ6nchSLRYLDoeDjY0N0X/P\nZDJiQr27uxulUkl7ezsOh0M8K5vNJoKwyWRCp9OJ3ezd3V3C4TBut5tarYZWqxVCNPc7lL0bP+7X\nyXzyeKAuZuPj4zz33HO8+eabPP7448IDV0ZG5uHzN5lw/3FEPyTJz2PHjnHz5k0MBgNut5s333yT\n8+fPE4lEyGaznDx5ko2NDWGMcuXKFVpbWwkGg2g0GvR6PdPT03z2s5/F6XTy3e9+F41GI0rHiUSC\narVKV1cXer2ehYUFXC4Xg4ODQtZZp9Md6eNaLBbcbjf9/f2YzWYuXbpEU1OTGIxTKpXvCOB/9md/\nRj6fJ5FICC30UCjEs88+y+HhIePj49y+fRu3283du3c5ceIE+/v7aDQaFhYWRPat0Wj4u3/37zIz\nM0M0GmV0dBSNRoNKpRLrYQqFgrm5Odrb27HZbGg0miPl646ODtRq9ZGBQemZ/ziDZrJxiczfhPes\nuXz1q1+lq6uLt956i2984xsoFAo2Nja4ePEi//k//+eHeY0yMj/z3D+w9n58UA9eGrCKRCJsbGyw\nu7uL1+slEAjQ398PvG2JCbC6usrq6iqnTp0im82iVCppbm4W5fCpqSk6OzsJh8MEg0H0ej0DAwM0\nNzezv7+PUqmkt7eXcDjMtWvXxO63VEZPJBK0tLRQrVbxeDz4fD4ikQhNTU2USiVef/11jEYjxWKR\neDxOqVTCYDAcCeB//Md/jEajIZFI0NnZycDAAIlEgqeeeorvfve7pNNpobO+t7dHf38/0WiUpqYm\n1Go1h4eHfPazn6Wnp0e0FVZWVoTPudRCkAb/gsEgExMTOBwOkskkHR0d73jOD3MOQuZnmw9snPT0\n9PDVr36VS5cucenSJV588UVsNtvDuDYZGZn/n7/JhPsHiX5IB4Jz584xPT3NL/3SL4mVML/fL/TT\npYEum80mSsl9fX1ClrRSqbC3t8fc3Bw3btzghz/8IYlEgng8zq1bt8jn8xSLRZLJJPPz80xMTNDb\n20tLSws7OztiAj4Wi9HW1obH42F+fp5yuYzRaOTg4ICTJ0+STCYBsNls9Pb28pWvfEXcywsvvIDZ\nbKZWq7G/v49KpWJ2dha/38/q6ipf+MIXUKvVOJ1OstksZ86cEZPqAMVikfb2dqFW96lPfYq9vT0G\nBwdpbm4W2uXSASoej9Pd3Y3ZbGZtbY2TJ09+qPdARuZB8YFBPB6Pc+fOHbH2ITkRycjIPDweZGYn\nHQiSySQTExMolUo0Go0IOl6vVxierK+v09zczMLCAqOjo2QyGbxeL/v7+xQKBbRaLT09Pfzcz/2c\n2AufnZ3l+PHjNBoNotEoq6urnD17lt3dXbRaLZFIRMiPplIpMRAmWYf29PSws7ODzWZjYWEBnU6H\ny+Wit7eX3/iN3xD38T/+x/8gk8lgsVi4desWNpuN7e1tTpw4QSqVolQqsby8TKPRIJfLMTIyIlTS\npOlzi8XCwMAAf/Inf8LnP/95vF4vX/nKV3A4HKKacOfOHa5evcrly5exWCx0d3fzgx/8gP7+fmKx\nGLVa7T2ftVT1kJTYZGQeNB84nS5pGUuDbi+++CJGo5HHHnvsI70weTpdRub/8X4T7u/nbBUOh9nY\n2CAUCgmbzc3NTZaWlqhWq6KnXa/XqdVqZLNZotEopVJJ2GEqlUpGRkZYXl6mv78fk8nE3bt3eeKJ\nJwiFQqRSKUKhEOFwWBwEpN3w06dP09TUJKa4b968iUqloqOjA51OJ/THk8kkCwsLeDweIXEqicgc\nP36cdDot/gYB/MEf/AGNRgO/38+rr75KrVbjscceQ6VScXh4SKFQwGq1sr+/T3NzM4ODg7zyyit0\ndnaKyX2/30+hUECn0/ELv/ALbG5uCk326elpstks4XAYvV7P6OgoKpVKqKwNDAyIPv/7OYbJzmIy\nfxMeuIsZwKlTpzh16hQAdrv9oaq2ycjIvD/hcJhoNIpOp8NoNPLaa68xPDwsZDcbjQZutxuXy0U4\nHGZ2dpbDw0NaW1tJp9O8/PLL9Pf343a7hWzn6Ogod+/exel0CkewxcVFWlpaiEajxONxYaUpiZic\nOnWKJ554ghdeeIHu7m6uXLmC0WgklUoJx7Oenh7cbjdra2uk02na2tpQq9Vks1lxDcvLy6J0XSgU\nMBqN/Nqv/ZoofwNcunSJvb09gsEgwWCQc+fOsbS0RLFYpFAoEAwG+cxnPkM4HOZTn/oUKpWKV199\nlV/4hV+gXC6TzWbx+XwsLS1hNBrxeDzcvHmTwcFBwuEwLpeLRx55hM3NTQwGA+l0mkgkQjwe5+mn\nnwZgdnZWKLm9n2OY7Cwm81HznitmX/7yl3n++ee5cOGC+Nzm5iarq6sP5cLkFTMZmQ9mdnZWZNHV\nahWNRkOlUsFoNFIoFPB6vUQiEZRKpZjsTqfT6PV68vk8Pp+Pw8NDoY2uUqlQqVTCQ9vtdrO0tITH\n48HpdGIymXC73czMzLC6usrw8DDLy8ucPn2aqakpFAqFMCGx2+24XC7sdjuXL1/mqaeeEkN5hUIB\nvV7P+vo6m5ubjI2NkUgkGB4e5pVXXuHpp59me3ub3/7t3z5yv9/85jdRq9UUi0Xhc261WkkkEuh0\nOiFIs7GxIYxJpqenOX/+PGq1muvXrzM2NkYsFsPj8bCzs4PFYmF4eBir1crOzg7JZBKlUsn+/j49\nPT1ks1lCoRDnzp3D7/cTiUSETam8LibzIPkwce89y+lPPPEEer2eYrHI7/7u7/Lcc8/R3d3N8PDw\nA7nYD0Iup8v8LPB+pfAfh1AoxODgIBsbG2J9yuFwEIvFRP+8UCjQ2tpKR0cHKysrPProo8zMzIgB\nr1qtRr1e5/Tp08KVbHx8HJPJxK1btzh79ixer5etrS1KpRJWq5VqtUokEqHRaFAqldje3hbrYYVC\ngUAggNlsZn19XfiGx2IxsRMueYU3NTWh1WqFvOrly5exWq1YrVZ+/dd//ci9/q//9b+ESpxer8fn\n85FOpxkdHSUej5PJZHA4HExNTeH1etHpdCQSCRQKBV1dXWxsbPDFL36Rubk5nE4n8Xicn//5n8du\nt7O6uko+n2d+fp5SqcTW1hY6nQ6TyYTZbGZwcJBEIkE0GsVisZDP53+swPwwhX5kfvr5MHHvPYO4\nXq8HYGtrixdffJFjx44JM4CHgRzEZX4W+Nv2TMvlMvl8HrPZTDqdJpfLoVKp6O7uZmVlhdOnTwPg\ncrmIxWLY7XZKpRIKheLI3vnx48fRaDRkMhnhnX1wcMDq6iomk4kbN26wv79PLpejUqmg1Wqx2+2U\ny2X29/dJJBJ4vV7m5uZIJpOYTCY6OjowmUwEAgEGBweJRCLYbDYsFguVSgWXy0WxWCSVSglBl/Pn\nz+P1evniF7945D5feOEFXn/9dTo6OrBYLJw9e5Y333wTj8fD7u4uCoWCtrY2NjY28Hg8lMtl1Go1\nHo8Hq9WK3W6ns7OTSqVCJpMRsqf/H3tvHuTmedj3f3Df97E4FtjF3hf3pCiRoinJsi05lpLYjnNY\n47aZ5mibyaRJ08y06fSYtElb904mjZv2D8eTy0diJ9FYkSxTlCiJxy6593Jv7AVggcUCi/vG7w8G\nz4+USVuWKfl6PzOaEcEF8L54l3je53m+x8bGhvCWFwoFfD4farUao9EoBvBGo4Hb7SYYDLK5uYnP\n56NWq7GxsUEymSQSiVCtVjEajcjl8u/4xkzih5d3pU98a2uLrq4uQqEQX/va19750UlISHwD32k5\nikKhIJFIoFKp8Hg8DA0N0dvby8WLFxkaGhLJYS1lu1qtZm1tjUwmg8lkQqPR8Oqrr/J2DOx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nG5XCSTScrlMsFgkEwmQ7Vapb+/H7vdTjgcJh6P02g0kMvl4gYlGo3y1FNPYbVaRQjNW69Tq/yl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      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## PAGE VIEW MODELING\n",
      "The authors refer to this exercise as \"predicting\" page views, but given that the main \n",
      "explanatory variable is the number of visitors, this isn't really a prediction model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "top_1k_sites = read_csv('data/top_1000_sites.tsv', sep = '\\t')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print top_1k_sites.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "   Rank           Site                      Category  UniqueVisitors  Reach     PageViews HasAdvertising InEnglish  TLD\n",
        "0     1   facebook.com               Social Networks       880000000   47.2  910000000000           True       Yes  com\n",
        "1     2    youtube.com                  Online Video       800000000   42.7  100000000000           True       Yes  com\n",
        "2     3      yahoo.com                   Web Portals       660000000   35.3   77000000000           True       Yes  com\n",
        "3     4       live.com                Search Engines       550000000   29.3   36000000000           True       Yes  com\n",
        "4     5  wikipedia.org  Dictionaries & Encyclopedias       490000000   26.2    7000000000          False       Yes  org\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kde_model = sm.nonparametric.KDE(np.log(top_1k_sites['PageViews'].values))\n",
      "kde_model.fit()\n",
      "plt.plot(kde_model.support, kde_model.density)\n",
      "plt.xlabel('Page Views (log)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.text.Text at 0x108f89890>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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JkvMjODgYQUFBd/zfq6+vx4ULF/D999/DZrOhqqoK3377LSoqKrB//34MHToU\ncXFxmDBhAsaOHYtx48Zh4MCB/D/s41jubnDq1ClkZmZi9OjRMBgMPMuBfMYPP/yAyspKlJeXw2q1\nYt++fdi7dy8AICYmBkOHDsXgwYMxaNAg9OrVC926dUO3bt0QEhLi/OugpY++ffti6NChCA0NFfwV\nBi63l7vdbofBYIBGo4FKpUJaWlqLjyckJCA/P/+O5dwR0FtkWYbRaMSSJUvwm9/8BitWrGCxk8+T\nZRlnzpzB/v37cfLkSXz33Xc4deoU6urqcPXqVVy9ehU3btxAQ0NDqx9nz57F6dOnMWTIEMTFxWHS\npEmYPHky4uPj0b17d9FfYkDoSHe6PM/dYDBAq9UiMjISWVlZztK+9XGtVouJEye2uJwvuHbtGjZu\n3IjXXnsNly5dQkFBAWd8JL8hSRIGDRqEQYMGdWo9169fh81mQ2lpKXbt2oWCggIcPHgQMTExmDJl\nCpKTk5GcnIx77rnHTcmps1yWu8VigU6nA3Bzb721x1tb7naNjY24cOFCp0N3hCzLuHjxIr7//nuc\nPHkSlZWV2LNnD0pKSjB69GgsWrQIGRkZCA4Odv6WJKL/UavVmDFjBmbMmAEAuHr1Kvbu3YuysjL8\n85//xLPPPouePXti/Pjx0Gg0iIyMxNChQ9G3b1+oVCr06dOnU2P/N27cQF1dHerr63HlyhVcuXIF\nly9fbvXf9fX1CAoKQmhoKIKDg9GlSxf07t0bvXv3Rp8+fZp99OzZEz169ED37t0RGhqquGMUNTU1\nUKlU7XqNW65Qbes3Qq1Ww4tD/M1IkoSwsDCEhYVh2LBhmD59upAcRP6iW7dumDhxIiZOnOiV7YWE\nhDjLONCEh4dDrVa36zUuyz0xMRE1NTXo06dPs98atz4eHh7e6nK369KlS6f/PCQiortzeUDV4XA4\nD5SGh4cjKioKer0eK1asaPZ4fHx8s89TU1O9+TUQEdFtvHoqJBEReQfP9SMi8kNeKXer1YpFixY1\ne8xoNMJqtXpj8212e06DwQCz2QyDwSAw1Z1uzWm322E2m2G1WmE2mwUnIyKl8Mp87hMmTGj2ud1u\nR3FxseJuV3drzuLiYqjVaqSlpSnuvP1bc5rNZmg0GkyYMAEGg0ExWR0OB0pLS2Gz2aBWq5Gent6m\nC91EZ7z188zMTNERAdyZsymX0WhEdHT0He8vUVrK2XSxo81mQ05OjuiIAFr/uavVatTW1iri/2YT\nk8kEAKi36/ZwAAAF4ElEQVStrUVWVla73kNCbtZRVlaGjIwMEZtus6KiIvTt2xdmsxl2u10xb/Tb\nZWZmIj4+HtHR0cjNzRUdx6mwsBAZGRlIS0tDfHw8bDab4i50uz3jhQsXkJ6ejrS0NCQkJCjmZ35r\nzqZcStxBuj2nSqVS5A7S7T93SZIQFRWluB0ks9nsnAFg2bJlsNvt7XoPeX3Mvbq6GgkJCd7ebLs5\nHA7Ex8cjLS0Nr776qug4rSovL8ff//53ZGRkYNmyZaLjOOXk5CAyMhJ2ux0RERGwWCzO83RdXejm\nTbdm7Nu3LxYsWNAss1Lc/r0ElLmDdGtOtVqNoqIi2Gw2mM1m5x6oEtz+c587dy4WLFiArKwspKen\ni47n1PRLctmyZcjNzW33e8jr5V5eXo7S0lJYLBaUl5d7e/NtFh8fL+yCq/YoLCxEbGwscnJyoNFo\nRMe5w8qVK6HX60XHcOn2jErN3JRL6TtITTntdruid5CaclqtVkXuIAFAWFgY1qxZg9TU1HZfNeuV\ncjcajSgtLUVFRQUyMzORkJAAu92O2tpab2y+zW7NmZOTg/LycphMJrz44ouiozVjNBpRVlYGq9WK\n7OxsmEwmmEwmr10p2FZGoxE6nQ6yLDsvdAPQ7suoPenWjC19rhRNuRobGxW9g3Tr90/JO0i3fj8L\nCgoUuYO0fPlyVFdXA7g5ktDe9xDPcyePKC4uxqJFi5wXtuXn5yvuQrdbM6pUKuh0Ouh0OmfGgoIC\n0REB3Pm9LCgogMPhwLJlyxAeHq6YveKWcubl5UGj0UCSJMydO1d0RAB3/txffPFFVFVVAYCiclqt\nVtTW1sJms0GSJGi12na9h1juRER+iBcxERH5IZY7EZEfYrkTEfkhljsRkR9iuZOiGI1GBAUFIS8v\nD3l5eXfMSdQRWq0WarUaFRUVcDgcyMjIQHZ2NhwOh1vW38RgMDinyW66W9HdWK1Wxc2xRH5CJlKY\n8PBw2eFwyLIsy/Hx8XJxcbFb1tlk1apVnV7f7aqqqpzrtdvtckZGRptfq9Pp3J6HSMjcMkRtZbfb\nUVdXh+XLlzsvvV+6dCnKy8tRWFiIiIgIVFVVYcqUKThz5gwAQKPR3DEvTFZWFgwGQ7PJq/Lz82E0\nGrF582bYbDYYjUZIkgSNRgOLxQKbzeY8972oqAg6nQ6/+93v8P3336O0tBTZ2dnOSbv0ej1mzpwJ\nAM0u3LHZbFi1ahVUKhWys7Mhy3Kz3FqtFiqVCiaTSTFz2ZB/4LAMKVLTBTCrVq1CTEwMMjIyoNFo\nUFRUBODmpEqJiYmYN28eAKCkpATAzSv3LBbLHetrmp/DbDY7X5Odne18Pjc3F5IkQaVSobS0FCtX\nrnTOGgjcvP+vVqvF+fPnUVhYiOjo6GZXM1ZXV7d4j8tly5YhKysLK1aswIIFC5rlliQJaWlpiI6O\nVtzV2uT7WO6kSNnZ2Vi6dCnmzp2LsrIylJeXIy4uzlmC6enp2Lx5M4qLi7Fs2TLU1tZCo9EgJycH\nOp3ujvVFRUVBpVLBaDQiKioKQPM97AsXLjhfv3DhQgBAQkIC9Ho9cnNzodVqkZ2dDZVKhRUrVqCq\nqgrFxcXO12s0Guel4beSJAmyLEOWZUiS1Cz3Cy+8AACoqqpCdHS0+755RBA05S9Ra4xGI+x2O/Lz\n8/H8888DuFm8TWUqSRKqq6tRVFSE6upqHD16FHa7Hbm5udDpdLDZbK3O7LdixYpmky8VFxc719HS\n63U6HcrKypCZmYni4mL06dMHRUVFiI6ORnR0NOLi4pzr0ul00Ov1SEtLc6734sWLyM3NRW5uLoqK\nivC3v/0NmzdvRnV1Naqrq2G327F06VLY7XZFTMdA/oXTD5BPWrRoEVatWoU+ffogKysLhYWFoiPB\nZDIhLi7O+ZdBS27PrdPpoFarFXPDDfIf3HMnnxQdHe2c2Esps2G25YDo7bmVcmMI8j/ccyci8kM8\noEpE5IdY7kREfojlTkTkh1juRER+iOVOROSHWO5ERH7o/wHHjWruIE5s6AAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Univariate model"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pageview_fit = ols('np.log(PageViews) ~ np.log(UniqueVisitors)', \n",
      "                   df = top_1k_sites).fit()\n",
      "print pageview_fit.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:      np.log(PageViews)   R-squared:                       0.462\n",
        "Model:                            OLS   Adj. R-squared:                  0.461\n",
        "Method:                 Least Squares   F-statistic:                     855.6\n",
        "Date:                Sat, 24 Nov 2012   Prob (F-statistic):          2.46e-136\n",
        "Time:                        09:50:22   Log-Likelihood:                -1498.3\n",
        "No. Observations:                1000   AIC:                             3001.\n",
        "Df Residuals:                     998   BIC:                             3010.\n",
        "Df Model:                           1                                         \n",
        "==========================================================================================\n",
        "                             coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------------------\n",
        "Intercept                 -2.8344      0.752     -3.769      0.000        -4.310    -1.359\n",
        "np.log(UniqueVisitors)     1.3363      0.046     29.251      0.000         1.247     1.426\n",
        "==============================================================================\n",
        "Omnibus:                       68.454   Durbin-Watson:                   2.068\n",
        "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               85.893\n",
        "Skew:                           0.615   Prob(JB):                     2.23e-19\n",
        "Kurtosis:                       3.742   Cond. No.                         363.\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize = (8,8))\n",
      "plt.plot(np.log(top_1k_sites['UniqueVisitors']), np.log(top_1k_sites['PageViews']), \n",
      "         '.', mfc = 'white')\n",
      "plt.plot(np.log(top_1k_sites['UniqueVisitors']), pageview_fit.predict(), '-k') \n",
      "plt.ylabel('Page Views (log)')\n",
      "plt.xlabel('Unique Visitors (log)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "<matplotlib.text.Text at 0x108e2e290>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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XUlNT+d0RyclRi67RaIRGoxE6nU7k5eWJKVOmiFWrVrn1q8KSL/awq6urxeLF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\nfsBNN92EJ554Am+88YbbS3T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0XbdMH5unqqWk2e2lzK1dc5RiNxcbGyv27dsnunXrJjp0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\nAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Multivariate model"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = 'np.log(PageViews) ~ np.log(UniqueVisitors) + HasAdvertising  + InEnglish'\n",
      "pageview_fit_multi = ols(model, top_1k_sites).fit()\n",
      "print pageview_fit_multi.summary()               "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "                            OLS Regression Results                            \n",
        "==============================================================================\n",
        "Dep. Variable:      np.log(PageViews)   R-squared:                       0.480\n",
        "Model:                            OLS   Adj. R-squared:                  0.478\n",
        "Method:                 Least Squares   F-statistic:                     229.4\n",
        "Date:                Sat, 24 Nov 2012   Prob (F-statistic):          1.52e-139\n",
        "Time:                        09:50:25   Log-Likelihood:                -1481.1\n",
        "No. Observations:                1000   AIC:                             2972.\n",
        "Df Residuals:                     995   BIC:                             2997.\n",
        "Df Model:                           4                                         \n",
        "==========================================================================================\n",
        "                             coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
        "------------------------------------------------------------------------------------------\n",
        "Intercept                 -1.9450      1.148     -1.695      0.090        -4.197     0.307\n",
        "HasAdvertising[T.True]     0.3060      0.092      3.336      0.001         0.126     0.486\n",
        "InEnglish[T.No]            0.8347      0.209      4.001      0.000         0.425     1.244\n",
        "InEnglish[T.Yes]          -0.1691      0.204     -0.828      0.408        -0.570     0.232\n",
        "np.log(UniqueVisitors)     1.2651      0.071     17.936      0.000         1.127     1.403\n",
        "==============================================================================\n",
        "Omnibus:                       73.424   Durbin-Watson:                   2.068\n",
        "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               92.632\n",
        "Skew:                           0.646   Prob(JB):                     7.68e-21\n",
        "Kurtosis:                       3.744   Cond. No.                         570.\n",
        "==============================================================================\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As comparison, here's the non-patsy code for the above regression\n",
      "The patsy version is a clear improvement."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#top_1k_sites['LogUniqueVisitors'] = np.log(top_1k_sites['UniqueVisitors'])\n",
      "#top_1k_sites['HasAdvertisingYes'] = np.where(top_1k_sites['HasAdvertising'] == 'Yes', 1, 0)\n",
      "#top_1k_sites['InEnglishYes'] = np.where(top_1k_sites['InEnglish'] == 'Yes', 1, 0)\n",
      "#top_1k_sites['InEnglishNo'] = np.where(top_1k_sites['InEnglish'] == 'No', 1, 0)\n",
      "\n",
      "#linreg_fit = sm.OLS(np.log(top_1k_sites['PageViews']), \n",
      "#                    sm.add_constant(top_1k_sites[['HasAdvertisingYes', 'LogUniqueVisitors', \n",
      "#                                                  'InEnglishNo', 'InEnglishYes']],\n",
      "#                                    prepend = True)).fit()\n",
      "#linreg_fit.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    }
   ],
   "metadata": {}
  }
 ]
}