{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# M-Estimators for Robust Linear Modeling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.compat import lmap\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* An M-estimator minimizes the function \n",
    "\n",
    "$$Q(e_i, \\rho) = \\sum_i~\\rho \\left (\\frac{e_i}{s}\\right )$$\n",
    "\n",
    "where $\\rho$ is a symmetric function of the residuals \n",
    "\n",
    "* The effect of $\\rho$ is to reduce the influence of outliers\n",
    "* $s$ is an estimate of scale. \n",
    "* The robust estimates $\\hat{\\beta}$ are computed by the iteratively re-weighted least squares algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We have several choices available for the weighting functions to be used"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "norms = sm.robust.norms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_weights(support, weights_func, xlabels, xticks):\n",
    "    fig = plt.figure(figsize=(12,8))\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.plot(support, weights_func(support))\n",
    "    ax.set_xticks(xticks)\n",
    "    ax.set_xticklabels(xlabels, fontsize=16)\n",
    "    ax.set_ylim(-.1, 1.1)\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Andrew's Wave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Andrew's wave weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = sin(z/a)/(z/a)     for \\|z\\| <= a*pi\n",
      "    \n",
      "        weights(z) = 0                  for \\|z\\| > a*pi\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.AndrewWave.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1.339\n",
    "support = np.linspace(-np.pi*a, np.pi*a, 100)\n",
    "andrew = norms.AndrewWave(a=a)\n",
    "plot_weights(support, andrew.weights, ['$-\\pi*a$', '0', '$\\pi*a$'], [-np.pi*a, 0, np.pi*a]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hampel's 17A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Hampel weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = 1                            for \\|z\\| <= a\n",
      "    \n",
      "        weights(z) = a/\\|z\\|                        for a < \\|z\\| <= b\n",
      "    \n",
      "        weights(z) = a*(c - \\|z\\|)/(\\|z\\|*(c-b))      for b < \\|z\\| <= c\n",
      "    \n",
      "        weights(z) = 0                            for \\|z\\| > c\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.Hampel.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 8\n",
    "support = np.linspace(-3*c, 3*c, 1000)\n",
    "hampel = norms.Hampel(a=2., b=4., c=c)\n",
    "plot_weights(support, hampel.weights, ['3*c', '0', '3*c'], [-3*c, 0, 3*c]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Huber's t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Huber's t weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = 1          for \\|z\\| <= t\n",
      "    \n",
      "        weights(z) = t/\\|z\\|      for \\|z\\| > t\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.HuberT.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = 1.345\n",
    "support = np.linspace(-3*t, 3*t, 1000)\n",
    "huber = norms.HuberT(t=t)\n",
    "plot_weights(support, huber.weights, ['-3*t', '0', '3*t'], [-3*t, 0, 3*t]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least Squares"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    The least squares estimator weighting function for the IRLS algorithm.\n",
      "    \n",
      "    The psi function scaled by the input z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = np.ones(z.shape)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.LeastSquares.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "support = np.linspace(-3, 3, 1000)\n",
    "lst_sq = norms.LeastSquares()\n",
    "plot_weights(support, lst_sq.weights, ['-3', '0', '3'], [-3, 0, 3]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ramsay's Ea"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Ramsay's Ea weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = exp(-a*\\|z\\|)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.RamsayE.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = .3\n",
    "support = np.linspace(-3*a, 3*a, 1000)\n",
    "ramsay = norms.RamsayE(a=a)\n",
    "plot_weights(support, ramsay.weights, ['-3*a', '0', '3*a'], [-3*a, 0, 3*a]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Trimmed Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Least trimmed mean weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        weights(z) = 1             for \\|z\\| <= c\n",
      "    \n",
      "        weights(z) = 0             for \\|z\\| > c\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.TrimmedMean.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 2\n",
    "support = np.linspace(-3*c, 3*c, 1000)\n",
    "trimmed = norms.TrimmedMean(c=c)\n",
    "plot_weights(support, trimmed.weights, ['-3*c', '0', '3*c'], [-3*c, 0, 3*c]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tukey's Biweight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function weights in module statsmodels.robust.norms:\n",
      "\n",
      "weights(self, z)\n",
      "    Tukey's biweight weighting function for the IRLS algorithm\n",
      "    \n",
      "    The psi function scaled by z\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    z : array_like\n",
      "        1d array\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    weights : ndarray\n",
      "        psi(z) = (1 - (z/c)**2)**2          for \\|z\\| <= R\n",
      "    \n",
      "        psi(z) = 0                          for \\|z\\| > R\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(norms.TukeyBiweight.weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 4.685\n",
    "support = np.linspace(-3*c, 3*c, 1000)\n",
    "tukey = norms.TukeyBiweight(c=c)\n",
    "plot_weights(support, tukey.weights, ['-3*c', '0', '3*c'], [-3*c, 0, 3*c]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scale Estimators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Robust estimates of the location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([1, 2, 3, 4, 500])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The mean is not a robust estimator of location"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "102.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The median, on the other hand, is a robust estimator with a breakdown point of 50%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Analogously for the scale\n",
    "* The standard deviation is not robust"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "199.00251254695254"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Median Absolute Deviation\n",
    "\n",
    "$$ median_i |X_i - median_j(X_j)|) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standardized Median Absolute Deviation is a consistent estimator for $\\hat{\\sigma}$\n",
    "\n",
    "$$\\hat{\\sigma}=K \\cdot MAD$$\n",
    "\n",
    "where $K$ depends on the distribution. For the normal distribution for example,\n",
    "\n",
    "$$K = \\Phi^{-1}(.75)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6744897501960817"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.norm.ppf(.75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1   2   3   4 500]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.482602218505602"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.scale.mad(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4142135623730951"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1,2,3,4,5.]).std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The default for Robust Linear Models is MAD\n",
    "* another popular choice is Huber's proposal 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(12345)\n",
    "fat_tails = stats.t(6).rvs(40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kde = sm.nonparametric.KDEUnivariate(fat_tails)\n",
    "kde.fit()\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(kde.support, kde.density);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0688231044810875 1.3471633229698652\n"
     ]
    }
   ],
   "source": [
    "print(fat_tails.mean(), fat_tails.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.0688231044810875, 1.3471633229698652)\n"
     ]
    }
   ],
   "source": [
    "print(stats.norm.fit(fat_tails))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(6, 0.03900835312789366, 1.0563837144431252)\n"
     ]
    }
   ],
   "source": [
    "print(stats.t.fit(fat_tails, f0=6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.04048984333271795 1.1557140047569665\n"
     ]
    }
   ],
   "source": [
    "huber = sm.robust.scale.Huber()\n",
    "loc, scale = huber(fat_tails)\n",
    "print(loc, scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.115335001165415"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.mad(fat_tails)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0483916565928972"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.mad(fat_tails, c=stats.t(6).ppf(.75))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.115335001165415"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sm.robust.scale.mad(fat_tails)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Duncan's Occupational Prestige data - M-estimation for outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.api import abline_plot\n",
    "from statsmodels.formula.api import ols, rlm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "prestige = sm.datasets.get_rdataset(\"Duncan\", \"carData\", cache=True).data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            type  income  education  prestige\n",
      "accountant  prof      62         86        82\n",
      "pilot       prof      72         76        83\n",
      "architect   prof      75         92        90\n",
      "author      prof      55         90        76\n",
      "chemist     prof      64         86        90\n",
      "minister    prof      21         84        87\n",
      "professor   prof      64         93        93\n",
      "dentist     prof      80        100        90\n",
      "reporter      wc      67         87        52\n",
      "engineer    prof      72         86        88\n"
     ]
    }
   ],
   "source": [
    "print(prestige.head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,12))\n",
    "ax1 = fig.add_subplot(211, xlabel='Income', ylabel='Prestige')\n",
    "ax1.scatter(prestige.income, prestige.prestige)\n",
    "xy_outlier = prestige.loc['minister', ['income','prestige']]\n",
    "ax1.annotate('Minister', xy_outlier, xy_outlier+1, fontsize=16)\n",
    "ax2 = fig.add_subplot(212, xlabel='Education',\n",
    "                           ylabel='Prestige')\n",
    "ax2.scatter(prestige.education, prestige.prestige);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:               prestige   R-squared:                       0.828\n",
      "Model:                            OLS   Adj. R-squared:                  0.820\n",
      "Method:                 Least Squares   F-statistic:                     101.2\n",
      "Date:                Fri, 24 Apr 2020   Prob (F-statistic):           8.65e-17\n",
      "Time:                        14:17:04   Log-Likelihood:                -178.98\n",
      "No. Observations:                  45   AIC:                             364.0\n",
      "Df Residuals:                      42   BIC:                             369.4\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -6.0647      4.272     -1.420      0.163     -14.686       2.556\n",
      "income         0.5987      0.120      5.003      0.000       0.357       0.840\n",
      "education      0.5458      0.098      5.555      0.000       0.348       0.744\n",
      "==============================================================================\n",
      "Omnibus:                        1.279   Durbin-Watson:                   1.458\n",
      "Prob(Omnibus):                  0.528   Jarque-Bera (JB):                0.520\n",
      "Skew:                           0.155   Prob(JB):                        0.771\n",
      "Kurtosis:                       3.426   Cond. No.                         163.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "ols_model = ols('prestige ~ income + education', prestige).fit()\n",
    "print(ols_model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accountant            0.303900\n",
      "pilot                 0.340920\n",
      "architect             0.072256\n",
      "author                0.000711\n",
      "chemist               0.826578\n",
      "minister              3.134519\n",
      "professor             0.768277\n",
      "dentist              -0.498082\n",
      "reporter             -2.397022\n",
      "engineer              0.306225\n",
      "undertaker           -0.187339\n",
      "lawyer               -0.303082\n",
      "physician             0.355687\n",
      "welfare.worker       -0.411406\n",
      "teacher               0.050510\n",
      "conductor            -1.704032\n",
      "contractor            2.043805\n",
      "factory.owner         1.602429\n",
      "store.manager         0.142425\n",
      "banker                0.508388\n",
      "bookkeeper           -0.902388\n",
      "mail.carrier         -1.433249\n",
      "insurance.agent      -1.930919\n",
      "store.clerk          -1.760491\n",
      "carpenter             1.068858\n",
      "electrician           0.731949\n",
      "RR.engineer           0.808922\n",
      "machinist             1.887047\n",
      "auto.repairman        0.522735\n",
      "plumber              -0.377954\n",
      "gas.stn.attendant    -0.666596\n",
      "coal.miner            1.018527\n",
      "streetcar.motorman   -1.104485\n",
      "taxi.driver           0.023322\n",
      "truck.driver         -0.129227\n",
      "machine.operator      0.499922\n",
      "barber                0.173805\n",
      "bartender            -0.902422\n",
      "shoe.shiner          -0.429357\n",
      "cook                  0.127207\n",
      "soda.clerk           -0.883095\n",
      "watchman             -0.513502\n",
      "janitor              -0.079890\n",
      "policeman             0.078847\n",
      "waiter               -0.475972\n",
      "Name: student_resid, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "infl = ols_model.get_influence()\n",
    "student = infl.summary_frame()['student_resid']\n",
    "print(student)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minister      3.134519\n",
      "reporter     -2.397022\n",
      "contractor    2.043805\n",
      "Name: student_resid, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(student.loc[np.abs(student) > 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dfb_Intercept      0.144937\n",
      "dfb_income        -1.220939\n",
      "dfb_education      1.263019\n",
      "cooks_d            0.566380\n",
      "standard_resid     2.849416\n",
      "hat_diag           0.173058\n",
      "dffits_internal    1.303510\n",
      "student_resid      3.134519\n",
      "dffits             1.433935\n",
      "Name: minister, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(infl.summary_frame().loc['minister'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    student_resid   unadj_p  sidak(p)\n",
      "minister                 3.134519  0.003177  0.133421\n",
      "reporter                -2.397022  0.021170  0.618213\n",
      "contractor               2.043805  0.047433  0.887721\n",
      "insurance.agent         -1.930919  0.060428  0.939485\n",
      "machinist                1.887047  0.066248  0.954247\n",
      "store.clerk             -1.760491  0.085783  0.982331\n",
      "conductor               -1.704032  0.095944  0.989315\n",
      "factory.owner            1.602429  0.116738  0.996250\n",
      "mail.carrier            -1.433249  0.159369  0.999595\n",
      "streetcar.motorman      -1.104485  0.275823  1.000000\n",
      "carpenter                1.068858  0.291386  1.000000\n",
      "coal.miner               1.018527  0.314400  1.000000\n",
      "bartender               -0.902422  0.372104  1.000000\n",
      "bookkeeper              -0.902388  0.372122  1.000000\n",
      "soda.clerk              -0.883095  0.382334  1.000000\n",
      "chemist                  0.826578  0.413261  1.000000\n",
      "RR.engineer              0.808922  0.423229  1.000000\n",
      "professor                0.768277  0.446725  1.000000\n",
      "electrician              0.731949  0.468363  1.000000\n",
      "gas.stn.attendant       -0.666596  0.508764  1.000000\n",
      "auto.repairman           0.522735  0.603972  1.000000\n",
      "watchman                -0.513502  0.610357  1.000000\n",
      "banker                   0.508388  0.613906  1.000000\n",
      "machine.operator         0.499922  0.619802  1.000000\n",
      "dentist                 -0.498082  0.621088  1.000000\n",
      "waiter                  -0.475972  0.636621  1.000000\n",
      "shoe.shiner             -0.429357  0.669912  1.000000\n",
      "welfare.worker          -0.411406  0.682918  1.000000\n",
      "plumber                 -0.377954  0.707414  1.000000\n",
      "physician                0.355687  0.723898  1.000000\n",
      "pilot                    0.340920  0.734905  1.000000\n",
      "engineer                 0.306225  0.760983  1.000000\n",
      "accountant               0.303900  0.762741  1.000000\n",
      "lawyer                  -0.303082  0.763360  1.000000\n",
      "undertaker              -0.187339  0.852319  1.000000\n",
      "barber                   0.173805  0.862874  1.000000\n",
      "store.manager            0.142425  0.887442  1.000000\n",
      "truck.driver            -0.129227  0.897810  1.000000\n",
      "cook                     0.127207  0.899399  1.000000\n",
      "janitor                 -0.079890  0.936713  1.000000\n",
      "policeman                0.078847  0.937538  1.000000\n",
      "architect                0.072256  0.942750  1.000000\n",
      "teacher                  0.050510  0.959961  1.000000\n",
      "taxi.driver              0.023322  0.981507  1.000000\n",
      "author                   0.000711  0.999436  1.000000\n"
     ]
    }
   ],
   "source": [
    "sidak = ols_model.outlier_test('sidak')\n",
    "sidak.sort_values('unadj_p', inplace=True)\n",
    "print(sidak)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    student_resid   unadj_p  fdr_bh(p)\n",
      "minister                 3.134519  0.003177   0.142974\n",
      "reporter                -2.397022  0.021170   0.476332\n",
      "contractor               2.043805  0.047433   0.596233\n",
      "insurance.agent         -1.930919  0.060428   0.596233\n",
      "machinist                1.887047  0.066248   0.596233\n",
      "store.clerk             -1.760491  0.085783   0.616782\n",
      "conductor               -1.704032  0.095944   0.616782\n",
      "factory.owner            1.602429  0.116738   0.656653\n",
      "mail.carrier            -1.433249  0.159369   0.796844\n",
      "streetcar.motorman      -1.104485  0.275823   0.999436\n",
      "carpenter                1.068858  0.291386   0.999436\n",
      "coal.miner               1.018527  0.314400   0.999436\n",
      "bartender               -0.902422  0.372104   0.999436\n",
      "bookkeeper              -0.902388  0.372122   0.999436\n",
      "soda.clerk              -0.883095  0.382334   0.999436\n",
      "chemist                  0.826578  0.413261   0.999436\n",
      "RR.engineer              0.808922  0.423229   0.999436\n",
      "professor                0.768277  0.446725   0.999436\n",
      "electrician              0.731949  0.468363   0.999436\n",
      "gas.stn.attendant       -0.666596  0.508764   0.999436\n",
      "auto.repairman           0.522735  0.603972   0.999436\n",
      "watchman                -0.513502  0.610357   0.999436\n",
      "banker                   0.508388  0.613906   0.999436\n",
      "machine.operator         0.499922  0.619802   0.999436\n",
      "dentist                 -0.498082  0.621088   0.999436\n",
      "waiter                  -0.475972  0.636621   0.999436\n",
      "shoe.shiner             -0.429357  0.669912   0.999436\n",
      "welfare.worker          -0.411406  0.682918   0.999436\n",
      "plumber                 -0.377954  0.707414   0.999436\n",
      "physician                0.355687  0.723898   0.999436\n",
      "pilot                    0.340920  0.734905   0.999436\n",
      "engineer                 0.306225  0.760983   0.999436\n",
      "accountant               0.303900  0.762741   0.999436\n",
      "lawyer                  -0.303082  0.763360   0.999436\n",
      "undertaker              -0.187339  0.852319   0.999436\n",
      "barber                   0.173805  0.862874   0.999436\n",
      "store.manager            0.142425  0.887442   0.999436\n",
      "truck.driver            -0.129227  0.897810   0.999436\n",
      "cook                     0.127207  0.899399   0.999436\n",
      "janitor                 -0.079890  0.936713   0.999436\n",
      "policeman                0.078847  0.937538   0.999436\n",
      "architect                0.072256  0.942750   0.999436\n",
      "teacher                  0.050510  0.959961   0.999436\n",
      "taxi.driver              0.023322  0.981507   0.999436\n",
      "author                   0.000711  0.999436   0.999436\n"
     ]
    }
   ],
   "source": [
    "fdr = ols_model.outlier_test('fdr_bh')\n",
    "fdr.sort_values('unadj_p', inplace=True)\n",
    "print(fdr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    Robust linear Model Regression Results                    \n",
      "==============================================================================\n",
      "Dep. Variable:               prestige   No. Observations:                   45\n",
      "Model:                            RLM   Df Residuals:                       42\n",
      "Method:                          IRLS   Df Model:                            2\n",
      "Norm:                          HuberT                                         \n",
      "Scale Est.:                       mad                                         \n",
      "Cov Type:                          H1                                         \n",
      "Date:                Fri, 24 Apr 2020                                         \n",
      "Time:                        14:17:04                                         \n",
      "No. Iterations:                    18                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -7.1107      3.879     -1.833      0.067     -14.713       0.492\n",
      "income         0.7015      0.109      6.456      0.000       0.489       0.914\n",
      "education      0.4854      0.089      5.441      0.000       0.311       0.660\n",
      "==============================================================================\n",
      "\n",
      "If the model instance has been used for another fit with different fit parameters, then the fit options might not be the correct ones anymore .\n"
     ]
    }
   ],
   "source": [
    "rlm_model = rlm('prestige ~ income + education', prestige).fit()\n",
    "print(rlm_model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accountant            1.000000\n",
      "pilot                 1.000000\n",
      "architect             1.000000\n",
      "author                1.000000\n",
      "chemist               1.000000\n",
      "minister              0.344596\n",
      "professor             1.000000\n",
      "dentist               1.000000\n",
      "reporter              0.441669\n",
      "engineer              1.000000\n",
      "undertaker            1.000000\n",
      "lawyer                1.000000\n",
      "physician             1.000000\n",
      "welfare.worker        1.000000\n",
      "teacher               1.000000\n",
      "conductor             0.538445\n",
      "contractor            0.552262\n",
      "factory.owner         0.706169\n",
      "store.manager         1.000000\n",
      "banker                1.000000\n",
      "bookkeeper            1.000000\n",
      "mail.carrier          0.690764\n",
      "insurance.agent       0.533499\n",
      "store.clerk           0.618656\n",
      "carpenter             0.935848\n",
      "electrician           1.000000\n",
      "RR.engineer           1.000000\n",
      "machinist             0.570360\n",
      "auto.repairman        1.000000\n",
      "plumber               1.000000\n",
      "gas.stn.attendant     1.000000\n",
      "coal.miner            0.963821\n",
      "streetcar.motorman    0.832870\n",
      "taxi.driver           1.000000\n",
      "truck.driver          1.000000\n",
      "machine.operator      1.000000\n",
      "barber                1.000000\n",
      "bartender             1.000000\n",
      "shoe.shiner           1.000000\n",
      "cook                  1.000000\n",
      "soda.clerk            1.000000\n",
      "watchman              1.000000\n",
      "janitor               1.000000\n",
      "policeman             1.000000\n",
      "waiter                1.000000\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(rlm_model.weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hertzprung Russell data for Star Cluster CYG 0B1 - Leverage Points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Data is on the luminosity and temperature of 47 stars in the direction of Cygnus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "dta = sm.datasets.get_rdataset(\"starsCYG\", \"robustbase\", cache=True).data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "ax = fig.add_subplot(111, xlabel='log(Temp)', ylabel='log(Light)', title='Hertzsprung-Russell Diagram of Star Cluster CYG OB1')\n",
    "ax.scatter(*dta.values.T)\n",
    "# highlight outliers\n",
    "e = Ellipse((3.5, 6), .2, 1, alpha=.25, color='r')\n",
    "ax.add_patch(e);\n",
    "ax.annotate('Red giants', xy=(3.6, 6), xytext=(3.8, 6),\n",
    "            arrowprops=dict(facecolor='black', shrink=0.05, width=2),\n",
    "            horizontalalignment='left', verticalalignment='bottom',\n",
    "            clip_on=True, # clip to the axes bounding box\n",
    "            fontsize=16,\n",
    "     )\n",
    "# annotate these with their index\n",
    "for i,row in dta.loc[dta['log.Te'] < 3.8].iterrows():\n",
    "    ax.annotate(i, row, row + .01, fontsize=14)\n",
    "xlim, ylim = ax.get_xlim(), ax.get_ylim()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename='star_diagram.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/numpy/core/fromnumeric.py:2542: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n",
      "  return ptp(axis=axis, out=out, **kwargs)\n"
     ]
    },
    {
     "data": {
      "image/png": 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YxjQ8tLZCfb37qquDykr399ZWsBaMgZQUyMyEUaMgJweystz3qal+Ry8iIiIS12KZQKcARwHfsta+Zoy5E7gWuCHoMm8Ak621tcaY04BlwIGhN2SMuRS4FGDSpEkxDDmB1dTArl2wcSPs2dP5XHq6S4yNcV/Wuq+qKti0yf0d3J+jR8PUqTBuHOTmusuLiIiISAdjA8nTQN+wMeOB1dbaKd73nwKutdae3sN1NgMl1tqK7i5TUlJiS0tLBzjaBFVXBx9/7JLgmhp3LCcHsrP7lvha61aqa2vd37Oy4IADYPJkl0yLiIiIDCPGmDXW2pLQ4zFbgbbW7jDGlBljZlhr1wMnAe+FBDUe2GmttcaYo3FdQfaEuTkJtm8ffPABbNgASUmQlwfjx/f/do1xyXd2tvu+qQneew/WrnWJ9IwZkJ/f//sRERERSWCx7sLxLeDPXgeOjcBXjDFfB7DW/gY4D7jMGNMKNAAX2FgtiQ8FVVUuof34Y0hLc2UWSTHsRJieDmPHQns7lJfDRx/BxIlw6KGu1ENERERkGIpZCUesDMsSjuZmlzi/9x5kZMDIkf7UJlsLe/e60pGDDoKZM12SLSIiIjIEDXoJhwyQHTvgtdegsdGtOCcn+xeLMa6EY8QItxr98ccwZw5MmKDNhiIiIjJsKIGOV01N8NZb8OGHbsU5L8/viPZLSnKlHQ0N8OKLMGUKHHWUa4MnIiIiMsQpgY5H+/bByy+7bhjxvLqbmeni27YNKirgxBO1yVBERESGvBjuQJM+2bEDnnnGDT0ZNy5+k+cAY2DMGLcqvXw5bN3qd0QiIiIiMaUEOl5Y69rSPfec67kcTyUbkcjNdavPL7zgNjsm2OZUERERkUiphCMeWOvqnd97z/VzTknQlyU9HQoL4Y03XPlJSUls2+yJiIiI+EDZjd+shXfegXXrXPKZqMlzQHIyFBW51fQ33nA9pEVERESGECXQfrLWTflbu9Ztxhsqq7XGuA8D778Pb7+tcg4REREZUoZIxpag3nvPrT4XFg6d5DkgKcl9KFi3zj1GJdEiIiIyRAyxrC2BfPCBq3suLPR3OEosBZLotWvdhwURERGRIUAJtB927YLXX/d/suBgSEpyHxLeekst7kRERGRIUAI92GprYeVKGDUq8TcMRio5GQoKYNUqNyRGREREJIEpgR5Mra3wr3+5VdnhNvY6PR0yMtyExeZmv6MRERER6TMl0IPFWnjzTaisdKvPw1FeHtTVwZo12lQoIiIiCUsJ9GDZvNltHBw3zu9I/DVmDGzc6PpEi4iIiCQgJdCDoa7ObRocM8b1SB7OjHEfItasUT20iIiIJKRhsovNR9ZCaanbMJiW5nc0He5+4gl+++STbN6xA4BDp0zhexdeyOnHHgvADb//PY+++CJlu3eTlpLCUQceyC0XX8xxM2f2/85TUlwN+GuvwUknDb0e2CIiIjKkKXOJtY8/hvLyuKt7njhmDD++9FLeWLqU0t/8hvlHHsnZN9zAOx99BMCM4mLuvuIK1t53H6t++UumFhay8Jpr2FlZOTAB5OfD7t3g3Z+IiIhIojA2wTZzlZSU2NLSUr/DiExjIzz5JIwYEVerz90ZdeaZLPnqV/namWd2Obevro68M87gmR//mAVHHz0wd9jS4jZVnnEGZGcPzG2KiIiIDBBjzBprbUnoca1Ax9Lbb7sSjjhPntva2nhkxQpqGxrClmg0t7Sw9MknGZGdzRHTpw/cHaemunKON95QVw4RERFJGKqBjpXKSleeUFjodyTdWrtxI8d+85s0NjeTk5nJEzffzKwDDug4/+Srr3LBzTdT39RE4ejRPHv77Ywb6FKUUaNgyxaoqHCbLEVERETinEo4YsFaN22wqsrV+sap5pYWtuzaRXVtLY+tXMnvnnySF++4g5lTpwJQ19DA9spKKvbu5XdPPsnzb7zBq3ffTeHo0QMbSE2NG7Jy8snqUiIiIiJxQyUcg6miwm0cjOPkGSAtNZXpRUWUzJjBkksu4Yjp0/nFo492nM/OzGR6URHHHHII9119NakpKdz71FMDH0huLuzaBV5HEBEREZF4pgR6oFkLb73lksIE024tTS0tfT7fL/n5rha6vT02ty8iIiIyQFQDPdB27HCrqUVFvoaxasNuHnm9jIraJgpy0rlgdjFzD9xfY3zt0qWcfswxFI8dS019PQ89/zwvvvUWTy1Zwr66On7yyCN89thjKRw9mt3V1dy9bBnlu3fzuU9/OjYBZ2fDtm1u5X7SpNjch4iIiMgAUAI9kNrb3Sqqz6UbqzbsZunKTTS3tQFQUdvE0pWbADqS6B2VlVz4ox+xo7KSvOxsDjvgAP5x220sOPpo6hsbWbd5M7//xz/Ys28fo0eMYPaMGay84w4OmzYtdoGPHOmevwkTXHcOERERkTikTYQDaccOWLHCJYA+uvyhN6iobepyvCAnnV994SgfIorC9u0wdy4UF/sdiYiIiAxz2kQ4GN57D3Jy/I4ibPLc0/G4MmIErFunvtAiIiISt5RAD5S9e90KdBxsHizISY/qeFzJznY9tAdqZLiIiIjIAFMCPVA++shNHIyDPsYXzC4mLTm507G05GQumJ0gZREZGfDBB35HISIiIhKWEuiB0NgIGza4TXBxYO6BY7j0hKkdK84FOelcesLUTl044lp+PmzeDHV1fkciIiIi0oVaHQyEsjJXsxuy6uunuQeOSZyEOVRSkvvavBkOPdTvaEREREQ60Qp0f1kL//63763rhpxRo+D998FrxSciIiISL5RA91d1tSs1yMjwO5KhJTUVmpu1mVBERETijhLo/iov19CPWElLgy1b/I5CREREpBMl0P3R3u66b+Tl+R3J0JSXB5s2QWur35GIiIiIdFAC3R9VVdDQ4FZKZeClpEBLC+zZ43ckIiIiIh2UQPfHli0q34i19HTXjUNEREQkTiiB7qu2Nti4Ud03Yi0vDz7+2K1Ei4iIiMQBJdB9tXev6xKRmup3JENbcrKrNa+q8jsSEREREUAJdN9VVMTF2O5hITkZdu70OwoRERERQAl0323ZArm5fkcxPOTkuGmPIiIiInFACXRfNDe7FeisLL8jGR4yM13JTEOD35GIiIiIKIHuk+pq96dKOAaX6qBFREQkDiiB7osdO1xdrgye9HTYutXvKERERESUQPdJWZnqnwdbbq4bm26t35GIiIjIMKcEOlrNzbBvH2Rk+B3J8JKaCk1NqoMWERER3ymBjlZNjWqf/VRT43cEIiIiMswpgY6WEjj/JCW5bhwiIiIiPlICHa1du1S+4ZeMDA1UEREREd8pgY7Wrl2uL7EMvqws2L1bGwlFRETEV0qgo9HS4ko40tP9jmR4SklxmzgbG/2ORERERIYxJdDR0AbC+KA6dBEREfFRit8BJJT6+oQsH1jy5z/z+Msvs76sjPTUVI455BCWXHIJM6dO7bjMzspKrlm6lH+WllJdW8sJhx3GXd/+NgdOnOhj5N2oq/M7AhERERnGtAIdjZoaV0aQYF586y2+cdZZ/OtXv2LFz39OSnIyJ191FZX79gFgreXsG25gQ3k5y265hTeXLmXyuHGc/N3vUhdvfZfT0lwfbhERERGfKIGOxr59LoFLMMtvv52vfOYzzJw6lVkHHMCfrr+e3Xv38sq77wKwobyc1e+9xz1XXsnRBx/MjEmT+PWiRTQ0NfHwihU+Rx8iLU2t7ERERMRXSqCjsXdvQibQoWrq62lvb2ekN468qaUFgIygx5aUlER6aiqr1q71JcZuKYEWERERnymBjkaCrkCHuuKuuzhi+nSOPeQQAA6aNInJ48Zx/b33UrlvH80tLfz44Ycp372b7Xv2+BxtiNRUV4ve3u53JBLi/vvvxxjT8ZWWlsa0adO4/vrraRzAzik33ngjZgA381500UVMmTJlwG4vVHV1NTfeeCNvvPFGzO5DREQGlxLoSDU3Q2srJCf7HUm/fOfuu1n17rs8dtNNJHuPJTUlhcduuomPtm1j9FlnkbVwIS+8+SafmTOn4zJxwxi3kbOpye9IpBuPPvoor776Kk899RQLFixgyZIlLF682O+wunXDDTfwxBNPxOz2q6uruemmm5RAi4gMIYm3I84vjY0J38Ju0d1388iKFbzwi19wwIQJnc59csYM3rr3XvbW1tLc2sqY/HzmXHYZJTNm+BRtD4yBhgYNtIlTRxxxBNOnTwfglFNOYcOGDdx3333ceeedJCXF32f2adOm+R2CiIgkmPj73yxeNTUlZAu7gCvuuouHnn+eFT//OQdNmtTt5fJychiTn8+G8nJKP/iAs44/fhCjjJBWoBPKUUcdRUNDAxUVFR3H6uvrueaaa5g6dSppaWlMnTqVH/7wh7SHlOa8+eabfOpTnyIjI4OioiJuueUWbIQ/h/X19Vx22WWMHj2a3Nxc/uM//oN//etfGGO4//77Oy4XroTjBz/4AUcddRR5eXkUFBQwf/58Vq9e3ekyL774IsYY/va3v3H55ZdTUFDAmDFjuPDCC6murgZg8+bNTPXaRV5yySUd5S2B+1++fDnHHXcceXl55OTkMGPGDG6++eaIHp+IiPhHK9CR8jbaxaNVG3bzyOtlVNQ2UZCTzgWzi5l74JiO89+84w7+9OyzLLvlFkbm5rKjshKAnMxMcrxV3EdffJGCvDwmjxvH2o0bueJXv+Ls44/n1NmzfXlMPbI2rl8P6Wzz5s3k5eUxevRoAFpbW1mwYAHvvfceN9xwA7NmzWL16tXccsstVFZW8rOf/QyAiooK5s+fz/jx43nggQdIT0/n9ttvZ8uWLRHd76WXXsqjjz7KjTfeSElJCc8//zxf/OIXI7ru1q1bWbRoERMnTqSuro4HH3yQE044gdLSUg477LBOl73iiis444wzeOihh1i/fj1XX301ycnJPPDAAxQWFvL4449zzjnncN1113HmmWcCbtV748aNnHnmmZx33nl8//vfJy0tjQ0bNrBx48ZIn1oREfGJEuhItbb6HUFYqzbsZunKTTS3tQFQUdvE0pWbADqS6Hv+938BOOmqqzpd9wdf/jI3XnQRANv37OE799zDzqoqCkeP5r9OPZUbvvSlQXoUUTLG1aRLXGpra6O1tZWamhqeeOIJHnvsMe64446OevqHH36YVatW8dJLL3HCCScAcNJJJwFw0003cc011zB27Fh+8YtfUFdXx/Lly5nk/dbklFNOYfLkyb3GsH79eh566CFuu+02rr766o7r1tfXc9ddd/V6/XvvvbfT41m4cCGHHnpoRylKsBNOOKHjNk899VTWr1/Pvffey/333096ejpHHnkkAAcccADHHHNMx/Veeuklmpub+fWvf82IESMAmD9/fq+xiYiI/5RAR6q5OS5roB95vawjeQ5obmvjkdfLOhJo+8ILvd7Ot889l2+fe25MYhxwKSmuJl3i0kEHHdTp+2984xtcfvnlHd8/88wzTJ48meOOO47WoA+mp556Kt/73vdYvXo1Z555Jq+++irHHHNMR/IMkJ2dzWc/+9lOJRjhvPbaa1hrOf/88zsdP++88yJKoJ977jl++MMf8s4771Dp/cYG6CjHCHb66ad3+n7WrFk0NTWxc+dOxo8f3+19HHHEEaSmpnLBBRdw8cUXc8IJJzB27NheYxMREf+pBjpSjY1x2YGjojZ8LXB3x4eE5GTVQMexJ554gtdff52nn36ak08+mXvuuYc//vGPHed37drFxx9/TGpqaqevo48+GoA9XuvE7du3M27cuC63H+5YqO3btwN0SUgjue4bb7zBaaedRk5ODvfddx+rV6/m9ddf5/DDDw/bjm/UqFGdvk9PTwfotXXf9OnTWb58Oe3t7XzpS19i/PjxzJkzh5deeqnXGEVExF9agY5UU1NcJtAFOelhk+WCnHQfohkkA5BAl5aWsmrVKq688soBCkoCZs6c2dGFY/78+Rx22GEsXryYc889l+zsbEaPHs3UqVP5y1/+Evb6gQ19hYWF7Ny5s8v5cMdCFRYWAi5ZD141juS6jz32GCkpKTz++OOkpqZ2HK+qqiI/P7/X60dj3rx5zJs3j6amJl555RW+//3vc/rpp7N582YKCgoG9L5ERGTgaAU6Un8PovsAACAASURBVHGaQF8wu5i0kLjSkpO5YHaxTxENgn4k0KWlpcybN4+5c+fy/e9/f4ADk1CBjX+7du3innvuAWDhwoWUlZWRk5NDSUlJl69A4njssceyevVqysrKOm6vrq6Ov//9773e75w5czDG8Oijj3Y6Hvp9OPX19SQnJ3ca1rJixYqINy+GCqxINzQ09HiZ+fPnc/XVV1NXV8emTZv6dF8iIjI4tAIdqYaGuEygA3XOPXXhGHKSk6OugS4tLWXx4sW89tprNDY2Yq3ttLoosXPmmWcye/ZsfvrTn3L55ZfzxS9+kT/84Q+cdNJJXHXVVRx++OE0Nzfz0Ucf8be//Y1ly5aRlZXFokWLuOeeezj11FO58cYbO5LxzAj6f8+YMYMvfOEL3HDDDbS3t/PJT36SFStWdCTfPfWjXrhwIXfccQcXXXQRX/nKV/jggw+45ZZbKCoq6tPjHzduHKNHj+aRRx7hsMMOIzs7m6lTp/Loo4+ycuVKTjvtNIqLi6moqGDJkiVMmDCBmTNn9um+RERkcMQ0gTbG5AP3AjMBC1xsrX016LwB7gROA+qBi6y18Tmuq60N4nAIBLgkekgnzKGSkiJegQ6XOMvgu/XWW1mwYAG/+c1vWLRoEcuXL+e2225j6dKlbNq0iezsbKZNm8bpp59OWloaAAUFBTz//PNcccUVfPnLX2b06NF8/etfp7W1NaJeyUuXLiU3N5ef/OQnNDc3M3/+fO6++27OOOMM8vLyur3eggUL+OUvf8nPf/5zHnvsMWbOnMkf//hHbr311j499qSkJO69916uv/56Tj75ZFpbW/nDH/7A4Ycfzj/+8Q+uu+46du3axahRo5g7dy5//vOfI/qQICIi/jGxTCiMMQ8AL1tr7zXGpAFZ1trqoPOnAd/CJdBzgDuttXN6us2SkhJbWloas5i79cwz7s+MjMG/b+msudn9RuCss7q9SCSJc05ODjU1NbGMVOLM7bffzjXXXMPmzZs7dfcQEREJxxizxlpbEno8ZivQxpgRwAnARQDW2mYgtHnvWcAfrctuVhtj8o0xhdba7bGKq8+sjcs2dsNSD69DNCvOjY2NfClee13HoXnz5nHxxRf7HUbEnnzySd59912OOOIIkpKSePnll/npT3/K5z73OSXPIiLSL7Es4TgA2A38wRhzOLAGuMJaWxd0mSKgLOj7cu9Y/CXQoAQ6XhjTZax6W1sbp512GitXrqSpqSmiUo3W1lYefPDBWEU55Lz//vsJlUDn5uaybNkybrvtNurq6igqKuLb3/42N910k9+hiYhIgotlAp0CHAV8y1r7mjHmTuBa4Iagy4TLSLtkPsaYS4FLAa0cSVhJSUnMmTOHVatWkZ6e3msPXoDU1FRSUrSPNhLt7e09bryLRyeeeCKrV6/2OwwRERmCYpk9lAPl1trXvO//ikugQy8T3G9tIrAt9IastUuBpeBqoAc+1AhpA1p8CFNOY4zh5ptvZtGiRdx+++3ceeedtLe395hIJyUl8Ytf/CLW0Q4Zs2bN8jsEERGRuBCzBNpau8MYU2aMmWGtXQ+cBLwXcrG/AZcbYx7BbSLcG5f1zxC2bEB80kM9+siRI/nRj37E4sWLe02kU1NT+drXvhbraEVERGSIifXvZL8F/NkY8w5wBPAjY8zXjTFf984/DWwEPgR+B3wjxvH0XYL9+nrI66UePZBIl5eXc+WVV5KVlUWGOqiIiIjIAIhpG7tY8K2N3QsvQF0d5OQM/n1LZw0NLoFeuDDiq1RVVXVZkVYbOxEREelJd23stKwaqfR0N0xF/NfWFnU/7uAV6UWLFpGZmZlwm+JEREQkPiiDiNQQS6BXvv02Z/7P/1B0/vmYefO4PzAoxrOzspKLbruNCeedR9bChSy8+mo2lJf7FG2Itjb3evRBIJHeunUry5YtG+DAREREZDhQAh2pjIwhlUDXNjQwc8oU7rz8cjJDklFrLWffcAMbystZdsstvLl0KZPHjePk736XuoYGnyIO0ocV6FAjR45k3rx5AxSQiIiIDCdKoCOVmTmkEujTjjmGH11yCeedeCJJIRvyNpSXs/q997jnyis5+uCDmTFpEr9etIiGpiYeXrHCp4iD9GMFWkRERKS/lEBHKjXV7wgGTVNLCwAZaWkdx5KSkkhPTWXV2rV+hbXfAKxAi4iIiPSVEuhIDaOJdQdNmsTkceO4/t57qdy3j+aWFn788MOU797N9j17/A7PGUYfaERERCS+KIGO1DBK2FJTUnjsppv4aNs2Rp91FlkLF/LCm2/ymTlzSE5O9js8Zxi9HiIiIhJfhs+yan8Ns5KBT86YwVv33sve2lqaW1sZk5/PnMsuo2TGDL9Dc4bZ6yEiIiLxQyvQkcrIGJajvPNychiTn8+G8nJKP/iAs44/3u+Q3OugBFpERER8ohXoSKWkuKSttTUh6qFXbdjNI6+XUVHbREFOOhfMLmbugWM6ztc2NPDh1q0AtFvLlp07eevDDxmVm8ukceN49MUXKcjLY/K4cazduJErfvUrzj7+eE6dPduvh+S0t0NysrpwiIiIiG/iPxOMJ7m50Nwc9wn0qg27WbpyE81e272K2iaWrtwE0JFEl65fz7xFizqu84P77+cH99/Plxcs4P5rr2X7nj1855572FlVReHo0fzXqadyw5e+NPgPJlRzs3sdQlrviYiIiAwWYxOsLKGkpMSWlpb6c+evvw7l5TBypD/3H6HLH3qDitqmLscLctL51ReO8iGiAbRvH4waBXPn+h2JiIiIDHHGmDXW2pLQ46qBjkZenlsBjXPhkueejieU5mb3OoiIiIj4RAl0NLKzXQ1unCvICV8f3N3xhNLSAiNG+B2FiIiIDGNKoKORk5MQtbcXzC4mLaRfc1pyMhfMLvYpogFkjHsdRERERHwS37vh4k0ggbY2rhPpwEbBnrpwJCxrlUCLiIiIr5RARyM52dXfNjZCZqbf0fRo7oFjhkbCHKy52ZXRqIWdiIiI+EglHNEaOxYaGvyOYnhqaIAxQ+xDgYiIiCQcJdDRGjMmITpxDEkNDe4DjIiIiIiPlEBHKzfX7wiGN7WwExEREZ8pgY5WYANbgg2gGRK0gVBERETigBLoaKWkwOjRqoMebE1NbvU/I8PvSERERGSYUwLdF8XFUFvrdxTDy759MGmS31GIiIiIKIHukzFjoK3N7yiGl9ZWGDfO7yhERERElED3SX4+JCUpiR4sgXrzkSP9jUNEREQEJdB9k5wMhYVQV+d3JH228u23OfN//oei88/HzJvH/c880+m8tZYb77+fCeedR+aCBXz6yitZt2mTP8HW10NBAaSl+XP/IiIiIkGUQPdVcbFL7BJUbUMDM6dM4c7LLyczzGS/nzzyCD/7y1+461vf4vXf/Iax+fmcsngxNX485tpa1T+LiIhI3FAC3VejRvkdQb+cdswx/OiSSzjvxBNJMqbTOWstd/z1r1z7hS9w7oknMnPqVB647jpq6ut56LnnBj9Ya90KtIiIiEgcUALdVyNGQFaWa682xGzavp0dlZWcWlLScSwzPZ0TDjuMf61bN7jBtLRAaqqrOxcRERGJA0qg+8oYmD4dqqv9jmTA7aisBGBcyKa9cSNHdpwbNNXV7nlOTh7c+xURERHphhLo/igqgvZ2v6OIGRNa2hHmWMy1tsLEiYN7nyIiIiI9UALdHyNGuK8hNpVwvFffHbravKuqqsuqdEw1N0NmptrXiYiISFxRAt0fxsCBB7opeUPI1MJCxo8axbOlpR3HGpubeXntWo479NDBC2TvXpg2zfXcFhEREV98b9lapl33NFOufYpp1z3N95at9Tsk36X4HUDCKyyENWv8jiJqtQ0NfLh1KwDt1rJl507e+vBDRuXmMmncOK487zx++OCDHDRpEp8oLubWP/2JnMxMvnDyyYMXpMo3REREfPW9ZWt5cPWWju/brO34/tazZ/kVlu+MDUx5SxAlJSW2NGhlNC4sX+6SvexsvyPpsGrDbh55vYyK2iYKctK5YHYxcw8c03H+xbfeYt6iRV2u9+UFC7j/2mux1nLTAw/w27//naqaGuYcfDB3X3klM6dOHZwH0NDgntMzznAr/SIiIjLopl33NG1hcsVkY/hoyWk+RDS4jDFrrLUlXY4rgR4AW7bAK6+41eg4sGrDbpau3ERz0KjxtORkLj1haqckOq5t3w5z5sABB/gdiYiIyLA15dqnuj23+bbTBzESf3SXQKu4dCBMmODGTDc3+x0JAI+8XtYpeQZobmvjkdfLfIooSm1trm2dyjdERER8ldzNb4G7Oz5cKIEeCCkpcPDBUFXldyQAVNSGH+7S3fG4U1kJM2a4DyUiIiLim8/PKY7q+HChBHqgTJniekLHQV/ogpz0qI7HFWvd9MHBqrUWERGRbt169iwuPGZSx4pzsjFceMykYb2BENSFY+BkZbl63a1bweuj7JcLZheHrYG+YHYCfFrct88NqBkxwu9IREREBJdED/eEOZRWoAfS9OlxMVRl7oFjuPSEqR0rzgU56YmzgbCuDg46yO8oRERERLqlFeiBNGqU21C4dy/k5fkaytwDxyRGwhysthZGj4axY/2ORERERKRbWoEeSMbAYYe5RDDB2gPGhb174cgj1fdZRERE4poS6IE2ejRMnhw3HTkSxt69bvV+TIKtmouIiMiwowQ6FmbNgsbGuOjIkRCsdbXPhx2m1WcRERGJe0qgYyEvz20o3LPH70gSQ1UVTJrkVu9FRERE4pwS6Fg55BA3US9kIqCEaGuDpia3ai8iIiKSAJRAx0pOjksKd+3yO5L4VlHhpjj63LVEREREJFJKoGNpxgyXSNfV+R1JfGpocOO6DznE70hEREREIqYEOpZSUmDOHKiu1obCUNZCZSUcfbRLokVEREQShBLoWBs71k3W273b70jiy549bvT5hAl+RyIiIiISFU0iHAyzZkF5OdTXQ1aW39H4r7HRtavT0BQRERHpxrI3t3L78vVsq25gQn4mixfM4Owji/wOC9AK9OBIS4Njj3Xt2oZ7V462Nrf6fOyxkJHhdzQiIiISh5a9uZXrHl/L1uoGLLC1uoHrHl/Lsje3+h0aoAR68IwdC5/8JGzfPrzHfO/c6VbkVbohIiIi3bh9+XoaWjovOja0tHH78vU+RdSZEujBNGMGTJs2fOuhKyqgqAhmzvQ7EhEREYlj26obojo+2JRADyZj3Cp0djbs3et3NIOrthZSU11XkiS97URERKR7E/Izozo+2JTJDLa0NPjUp9z0vcZGv6MZHM3NUFMDJ5ygumcRERHp1eIFM8hMTe50LDM1mcULZvgUUWdKoP0wYoRLoisrXSI9lDU3u5KVuXNh5Ei/oxEREZEEcPaRRSw5ZxZF+ZkYoCg/kyXnzIqbLhzGJtiGtpKSEltaWup3GANj61Z48UUYM2ZoDhNpaXGbBufOhSlT/I5GRGRYiOfWX4lKz+nwZYxZY60tCT2uFWg/FRW5lejdu91K7VDS2gq7drl2dUqeRUQGRby3/kpEek4lHCXQfps0CY4/3iWbLS1+RzMwWlthxw43pnvaNL+jEREZNuK99Vci0nMq4WgSYTyYMgXa22H1alcnnBkfO0z7pLHRtas7+mg48EC/oxERGVbivfVXItJzKuFoBTpeHHAAnHyya/dWXe13NH2zb59rzzd/PnziE35HIyIy7MR7669EpOdUwlECHU/GjoWFC12/5F27/I4mOhUV7s+FCzVlUETEJ/He+isRDbfndNmbWzn+thVMvfYpjr9thWq9u6ESjniTmwunnAKvvQZbtrikOjXV76i6F9gsOGECHHOM+jyLiPgo0BlCHSMGznB6TgMbJgM134ENk8CQfLz9oTZ28aq9HT76CNascS3uRo3yO6KuqqpczfORR7p65+Tk3q8jIiIicen421awNUxtd1F+Jq9cO9+HiPzXXRs7rUDHq6Qkl5QWFrokurwcCgogPd3vyPYPRykshJNOcoNhREREJKFpw2TklEDHu5wcNwJ7yxYoLXWrvqNG+TN4paXFTU80Bo47DiZPdom+iIiIJLwJ+ZlhV6C1YbKrmCbQxpjNQA3QBrSGLoEbYz4N/C+wyTv0uLX25ljGlJCMccnq+PGwaROsW+dWgUeOHJya4+ZmlzgnJ8OsWa5jiGqdRUREhpTFC2Z0qoGGob1hsj8GYwV6nrW2oofzL1trzxiEOBJfejocdJAbTlJWBmvXusQ2IwPy8ga2BrmtzbWla2hwfak/+UmXxA/FkeMiIiIyrDZM9pdKOBJRaqpbBZ482XXAKCuDjz92HTFSUlwnj/R0t3IdKWvdSnNNjSvVSE52UxInTXKdQFL0VhERERnqzj6ySAlzBGKdFVngn8YYC/zWWrs0zGWONca8DWwDvmutXRfjmIaO5GS3ka+w0K0QV1XBtm2wdatLrAMdVqzdnwAnJbnvrXWrzAHGuMR7+nQoKnJ11uqqISIiItJFrBPo462124wxY4FnjTHvW2tXBp1/A5hsra01xpwGLAO6zH82xlwKXAowadKkGIecoJKTXZeOggI47DDXBq+hAerr3VdDg1uhttYlyykprvQjO9uVaGRlaUOgiIiISAQGrQ+0MeZGoNZa+9MeLrMZKOmpZnrY9IEWEREREV911wc6ZkuOxphsY0xu4O/AqcC7IZcZb4wr1DXGHO3FsydWMYmIiIiI9FcsSzjGAU94+XEK8JC19hljzNcBrLW/Ac4DLjPGtAINwAU20UYjioiIiHRj2Ztb1dViCNIobxEREZEYWPbm1rB9lZecM0tJdILQKG8RERGRPujrKvLty9d3Sp4BGlrauH35eiXQCU4JtIiIiEg3QleRt1Y3cN3jawF6TYK3hRmL3dNxSRzqWyYiIiLSjZ5WkXszIT8zquOSOJRAi4iIiHSjP6vIixfMIDO181CyzNRkFi+YMSCxiX9UwiEiIiLSjQn5mWwNkyxHsoocKPGIpH5a3ToSixJoERERkW4sXjAjbCeNSFeRzz6yqNdEuD911uIPlXCIiIiIdOPsI4tYcs4sivIzMUBRfuaAt6HrT521+CPhVqDrmlvZvreBcbkZJCUZv8MRERGRIS6SVeT+ULeOxJNwCfTG3XUcu2QFaclJFI3MZOLITCaOzKJ4VCbFI7MoHpXFxJGZjM5Ow5uCKCIiIhK3+lNnLf5IuAR6yuhsbjh7JmVV9ZRXNlBeVc/ybTuorGvudLmstGQmjnRJ9cSRmV5i7RLtiSOzyMtM9ekRiIiIiOzX3zprGXwJl0DnZqRw4TGTuxyvbWql3Euqy6rqKfP+LK9q4P82VVLT1Nrp8iMyUigeldUpwQ6sYheNzCQrLeGeGhEREUlA0XTrkPhgrLV+xxCVkpISW1paGtV1rLXsbWihzFuxDk2wy6vqaWxp73Sdgpw0b8U6q2MlO7B6XZSfSVqK9l+KiIiIDGXGmDXW2pLQ48NimdUYQ35WGvlZacyamNflvLWW3bVNHQl2eVUDZZUu0X6nvJp/rN1Oa7sNuj0YPyKjY/V64qgsijvKRDIpzMskWRscRURERIakYZFA98YYw9jcDMbmZvDJySO7nG9rt+zY10hZZefkuryqgdUb97D9ra0EL+SnJBkm5Ge6Fet8rzQkUIM9MpMxuena4CgiIiKSoJRARyA5yVCUn0lRN7thm1vb2Vbd4JLrqnovwXar2c+/v4uK2qZOl09PSQra2Li/e0hgRTs/K1UJtoiIiEicUgI9ANJSkphSkM2Uguyw5xua2/aXhgQS7MoGyqvreXNLNXsbWjpdPic9JXyC7dVg56TrZRMRERHxizKxQZCZlsyB43I5cFxu2PP7Gls6lYcE/tyyp55XPqygvrnzdKKRWamdVqyDa7CL8jPJSE0ejIclIiIiMixFnEAbY0YCE4AGYLO1tr2Xq0iERmSkcuiEPA6dEH6DY2Vdc0dJSFnl/lXsf2/fx7Pv7aS5rfNLMTY33Uuwuw6ZGZ+XQWqyOoiIiIgMtGVvbo1pK7pY375ErscE2hiTB3wT+DyQBuwGMoBxxpjVwD3W2hdiHuUwZoxhdE46o3PSOaI4v8v59nbLrpomb1Ojl2B7mxxLP67i7+9spy2og0hyknEdREYFhszs3+RYPDKLsbnpGpEuIiISpWVvbu00DGVrdQPXPb4WYECS3FjfvkSntxXovwJ/BD5lra0OPmGMKQEuNMYcYK29L1YBSs+Skgzj8zIYn5fB7CmjupxvaWtnx96gDiJBmxxXbtjNzn2dNzgGj0jvuskxk1EakS4iItLF7cvXd5okCNDQ0sbty9cPSIIb69uX6PSYQFtrT+nhXCkQ3UQTGXSpyUneBsSssOcbW9rYWt3QKcEOTHNc927PI9IDCXbwKvaIDI1IFxGR4WdbdUNUx+Pt9iU6EdVAG2Oet9ae1NsxSTwZqclMG5PDtDE5Yc8HRqR3THEMqsF+bVMltT2MSA90DQkuF8lM0wZHEREZeibkZ7I1TDI7oZsWuPF2+xKd3mqgM4AsoMDbRBj43f0I3IZCGeJy0lM4aPwIDho/osu54BHpnWqwq+rZsKuGF9bvoqm1+xHpoZscJ2hEuoiIJKjFC2Z0qlEGyExNZvGCGQlx+xKd3lagvwZciUuW17A/gd4H3B3DuCQB9GdE+ttlvYxI71i1zuwoQRk/IkMj0kVEJC4F6pBj1SUj1rcv0TE2eAZ1dxcy5lvW2rsGIZ5elZSU2NJSlV4PBcEj0sPVYO/Y19jtiPRwNdhjcjQiXURERAaOMWaNtbYk9HhENdDW2ruMMccBU4KvY63944BFKMNO8Ij0Yw4Y3eV8YER6WXANtreK/dy/ex6R3mn12kuw8zI1Il1ERET6L9JNhH8CpgFvAYHiG4trcScSE5GOSC8LLg/xVq/DjUjPTU+hKFyC7a1oZ2tEuoiIiEQg0oyhBDjERlLvITJIehuRvrehpVMHkUCS/fGeOlZtqOjST7PTiPRABxGNSBcREZEQkSbQ7wLjge0xjEVkQOVlppKX2fuI9NAhM+9FMCI9dMhMYV4GKRqRLiIiw8RwHyveWxu7v+NKNXKB94wx/wd0FJ5aa8+MbXgisRHNiPSOBNvrIPL65ir+9vY2ghqIdBmR3pFga0S6iIgMMRor3vsK9E8HJQqROBPNiPRONdhVDbz0wW521fQ8Ir3zJkeNSBcRkcShseK9j/J+abACEUkk0YxIL6vyarC9DY7vrt1OVX3nDY4akS4iIolCY8Uj78JRgyvlCLYXKAWustZuHOjARBJZNCPSQ2uww41Iz8tMDUqwO9dga0S6iIgMJo0Vj3wT4c+BbcBDuGmEF+A2Fa4Hfg98OhbBiQxV0YxID06wux+Rnt6pJCQ4wdaIdBERGUgaKx75JMLXrLVzQo6tttYeY4x521p7eMwiDKFJhDLchY5I77yC3cC26oZOI9KTvBHpE4NGpAdvctSIdBFJFMO980M8GS6vRb8mEQLtxpjPAX/1vj8v6Jx6Q4sMImMMY3MzGJubwScnj+xyvrWtnZ01TR0j0oNrsF/9aA9P7NvaaUR6arIbkd5dDbZGpItIPEiEzg/fW7aWh18ro81ako3h83OKufXsWX6HFRNnH1kUN8+7HyJNoL8I3Ancg0uYVwMXGmMygctjFJuI9EFKclKPI9KbWtvYXt3YsWId3EXkuX/vpKK2udPlM1KT3Op1cA22V3utEekiMljivfPD95at5cHVWzq+b7O24/uhmkQPZxEl0N4mwc92c3rVwIUjIrGWnpLc44j0+uZWtgaVhASXiLzxcRX7GjtvcMxNT2HiqDAJtkaki8gAivfODw+/VtbtcSXQQ09vg1Suttb+xBhzF2FKNay1345ZZCLii6y0lKhGpAcS7O5GpI/KTtvfMSSkBlsj0kUkUvHe+aGtmz1l3R2XxNbb0tC/vT/D7drTO0JkGIpmRHpZUKLd3Yj0cSPSQwbL7E+0NSJdRALivfNDsjFhk+VklbgNSb0NUvm79+cDoeeMMZpSKCKdRDIifWdN4/7JjR012N2PSC/My+icYAfVYGtEukjsxUu3hcB9xkMs4Xx+TnGnGujg4zL0RNTGLuwVjdlirZ00wPH0Sm3sRIaulrZ2tlc3utKQMJscu4xIT0liYn5mlxrsiSM1Il1kIIR2vgC36rvknFlxk7jGk+HUhWO46K6NXX8S6DJr7aB/rFICLTJ8Nba0Ue615SuraqA8ZIpjuBHpwavXoX9qRLpIz46/bUXYuuOi/ExeuXa+DxFJX8XLbxISTZ/6QBtjRnV3yvsSERk0GanJTB+bw/SxkY1ID1697m5EevGoTCbm7x+RHki4NSJdJP47X0hkEqGHdqLpbRPhGtxmwXDJcnOYYyIivultRHp1fUunFetAgt3TiPTgkpDgBFsj0mU4iPfOFxKZeO+hnYh620Q4dbACERGJJWMMI7PTGJmdxqyJXTuItLdbKmqbOiY3BjY5llfX83ZZNf9Yuz38iPRO9dcu0Z6oEekyRMR75wuJjH6TMPB6K+GYYq3d3MN5AxRZa8sHOjARkcGUlGQYOyKDsSO6H5G+Y19QB5GgGuyeRqR3V4OtEemSCOK984VERr9JGHg9biI0xjwKJAH/iyvn2A1kANOBecBJwA+stc/GPlRHmwhFJB41tbaxLdBBpHJ/mUhg02N3I9KLvXrr4pAhMxqRLiIDRd1U+q5PmwittecbYw4BvghcDBQCDbgBK08BP7TWNsYgXhGRhJKekszUgmym9jAivaODSMgmxzU9jEjvLsHWiHQRiZR+kzDw+tzGzi9agRaRoWhvQ0unFeuOMhEv4Q43Ij1Qbx1agz1BI9JFRAZEn1agg658TpjDe4G11tpd/Q1ORGS4y8tMJa8oj5lF4Uek76lr7kiwO41I37aPZ9d1PyK9OCjB1oh0EZGBEenvAP8bOBZ4wfv+08Bq4BPGmJutgIjljAAAHDZJREFUtX+KQWwiIoLrIFKQk05BTjpHTuq6wTEwIj2QVAfXYP/fpkr+962Gbkekd7TpCyoRGZOjEekSnzQMROJFpAl0O3CwtXYngDFmHPBrYA6wElACLSLik6QkQ2FeJoV5mRw9tev8q8CIdFdz3TnBfnH97h5HpIerwR6ZpQ2OMvg0DETiSaQJ9JRA8uzZBXzCWltpjGnp7koiIuK/1OQkJo3OYtLorLDnAyPSA5say70NjmWVDawtr+4yIj07LbkjqZ4Y1KYvsKKdqxHpEgMaBiLxJNIE+mVjzJPAo9735wErjTHZQHVMIhMRkUHR24j0msaWjv7XoTXYr360h7rmzklNYER6aA128ahMivI1Il36RsNA+qc/5S8qnekq0gT6m8A5wFzcWO8HgMesa+ExL0axiYhIHMjNSOXgwlQOLux+RHpwUh34+wc7a1jxfvcj0ovDrF4X5mlEuoSnYSB915/yF5XOhBdRAm2ttcaYVUAzYIH/s4nW/05ERAZc8Ij0wybmdzm/f0R6/f4pjl4N9ltl1Tzdw4j0zgm2+3OcRqQPWxor3nf9KX9R6Ux4kbax+xxwO/AibgX6LmPMYmvtX2MYm4iIJLjOI9K7ng+MSN+/er2/BvtfH1WwY19jtyPSw9VgF+SkaYPjEKVhIH3Xn/IXlc6EF2kJx/8AswM9n40xY4DnACXQIiLSZynJSV4SnAWM7nI+MCK9c/21S7SffW9njyPSi7sMmcliRGaKEuwEdvaRRUqY+6A/5S8qnQkv0gQ6KWRgyh5ARWoiIhJTkY5I70iwgzqI9DYiPTTB1oh0Gar6U/6i0pnwIv2X4hljzHLgYe/7/wSejk1IIiIikclKS+ET43L5xLjcsOf3j0gPTrAb2FRRx8sbKnockR5ag100MpP0FHUQke7Fa7eK/pS/qHQmPBPpXkBjzLnA8bga6JXW2idiGVh3SkpKbGlpqR93LSIiQ0jwiPSyqv1THMu9MpGt1Q20tHX+PzJ4RHpgyIxGpAt07VYBbqV2yTmzhn2ymciMMWustSVdjidaMw0l0CIiMhiCR6SH1mCXVzWwfW/PI9KLg5JrjUgf+o6/bUXYWuGi/ExeuXa+DxHJQOguge6xhMMYU4NrW9flFK67XdemoCIiIkNANCPSQxPsF9bvZncvI9JDa7A1Ij2xqVvF8NJjAm2tDV9UJiIiMsxFNSI9ZIrjO+XVVPcyIj10iqNGpMc3dasYXrTdWEREJAaiGZEeWoMdbkR6flZqSFu+zE4Jd0aqNjj6Sd0qhhcl0CIiIj6IZkS6m+To/r5+Zw3Pv7+L5pAR6WNy0zutWBd7/bWLR2UyIT+T1CG6wTFeOl+oW8Xwok2EIiIiCSZ4RHqXTY5V9WyrbqSthxHpHWUiCT4iXZ0vJNb6tIlQRERE4k80I9JDa7Bf+bCCnTVDY0T67cvXd+nl3dDSxu3L1yuBlpiKaQJtjNkM1ABtQGtoBm/cT+OdwGlAPXCRtfaNWMYkIiIy1AWPSD+2lxHpZSFDZv65bid76noekd55FTuLvCx/Njiq84X4ZTBWoOdZayu6OfcZ4EDvaw7wa+9PERERiZFoRqSHbnIs/biKmtAR6RkpXSY3ui4iLtHOSotNuqHOF+IXv0s4zgL+aF0h9mpjTL4xptBau93nuERERIatXkekexscyzttcnQj0ldu2E1jS+cNjqOz05gY0pYvsKLdnxHp6nwhfol1Am2BfxpjLPBba+3SkPNFQFnQ9+XesU4JtDHmUuBSgEmTJsUuWhEREelVXlYqeVl5zCzK63LOWktFbbNLrqv2b3Asr6pn3da9/HPdjk4j0o2BcbkZnVavg5Ptnkakx1vni3jpCCKxF9MuHMaYCdbabcaYscCzwLestSuDzj8FLLHWrvK+fx642lq7prvbVBcOERGRxNXWbtkVNCI9uAa7uxHpE/IzmJi/vz1fx5CZOBqRro4gQ5MvXTistdu8P3cZY54AjgZWBl2kHCgO+n4isC2WMYmIiIh/kqMckR6cYHc7In1kZpdNjoEEe7BGpKsjyPASswTaGJMNJFlra7y/nwrcHHKxvwGXG2MewW0e3Kv6ZxERkeEr2hHpwRscuxuRHlixnhhmiuNAjUhXR5DhJZYr0OOAJ7xPfSnAQ9baZ4wxXwew1v4GeBrXwu5DXBu7r8QwHhEREUlw0Y5ID67B7m5EemgHkYlBSXakI9LVEWR40SRCERERGRbs/2/v/oMjr+s7jr9elwvc9uAMYIRLTjltJVaKcBB/9dpqr52JINUT7ciodXTsOLbWYTrTgPlDndY/pJM6pdVBpEzHOnRqq6SpIpr+OMFfAzYhB4GesRQUbg/k8C6nByvmcu/+sbu5zd5usl8uu9/v7j4fMzck3/3u7pv9TO77um8+n/cnQoefWVzRPaRyF8f9hws1t0ivvGNdOQe7cot05kB3JnYiBAAAXc22zt58ms7efJpesa3vpMePHw8dPPrsiYBdMQd79rHD+urc4ydtkb71ebnl6SGvu6Bf9zzyEx1+ZlHnbjld1428jPDcobgDDQAA0IBjS8f1+JGf152DXWuL9MG+XN052FndIh0ncAcaAIAuQC/i5tnYs6EYgM+uv0V6/nBhOWBXbjJTa4v0XG/P8tzrkzeZSW+LdKyNAA0AQIeonoebXyhobGJOkgjRLXD6xh69pP8MvaS/9gLHp589trygsXqR43//8FDdLdIrd24sB/htZzVvi3SsjU8eAIAOQS/ibNt8+kYNnXemhs5rfIv0xw49o4cPPq27flB/i/RaixwH+jY95y3SsTYCNAAAHYJexO2tkS3SV+7cWAzaD+SPaKrOFunlUL1tuT1f8evVtkjH2gjQAAB0CHoRdy7b6j/zdPWfeboufdFZJz2+dDz045/+fEVbvvJd7HseOaTJvSu3SN+4wdrat+lED+zyAsfSdJGsbJGeVQRoAAA6xOjIUM1exKMjQylW1Vwsmizq2WAN9BV7U7+6xuO/OHZcjx8p6LFDpTnYpYC9//DqW6Sv3GTmRMBu1RbpWUWABgCgQ5SDY7cEShZNNu60jRt0/jmbdf45m2s+XtwivdSWr2qB432rbpG+chfH8gLH9doiPavoAw0AANrSzuv31JyyMtiX03c+vCuFijrXz36+WHH3+sQc7PJ87HpbpFd2EKmcg93oFulpow80AADoKCyabJ0zN/Xq5QO9evnAlpMeK2+RvnL+dTFof/+Jn+k/9z1Zd4v0lT2wiwF7a9+m5S3Ss4oADQAA2hKLJrOhcov0i19Yf4v05YB96MQc7HsfPazb76+/RfpJAfvsnF5w5ib1pLzAkQANAADaUjcummxHGzZY527ZpHO3bNLw9pMfL2+RXm7RVzkH+9v/+9QaW6SfPAf7nM3N3yKdAA0AANpSty2a7FSVW6TXUt4i/bHlXRxLW6Qfekb/fuCJVbdIr9xkZlvpLvbzcqe+wJFFhAAAABlDe77GlbdIX95cZnmaSPFu9s+erb9F+oo2fTW2SGcRIQAAQBugPV8yjW6RXr3I8f8a2CK9HgI0AABAhoxPza+Y1y1JhcUljU/NE6Cfg0a3SC8H7PI0kbn8kbqvSYAGAADIENrztc5aW6T72trPy3aTPQAAgC5Trw0f7fmygwANAACQIaMjQ8pV7dRHe75sYQoHAABAhtCeL/sI0AAAABmze8cggTnDmMIBAAAAJECABgAAABIgQAMAAAAJEKABAACABAjQAAAAQAIEaAAAACABAjQAAACQAAEaAAAASIAADQAAACRAgAYAAAASIEADAAAACRCgAQAAgAQI0AAAAEACBGgAAAAgAQI0AAAAkAABGgAAAEiAAA0AAAAkQIAGAAAAEiBAAwAAAAkQoAEAAIAECNAAAABAAgRoAAAAIIGNaRcAAACyYXI2r/GpeR1YKGigL6fRkSHt3jGYdlktxWeARhCgAWQGFy4gPZOzeY1NzKmwuCRJyi8UNDYxJ0ld83PIZ4BGMYUDQCaUL1z5hYJCJy5ck7P5tEsDusL41PxycCwrLC5pfGo+pYpaj88AjSJAA8gELlxAug4sFBId70R8BmgUARpAJnDhAtI10JdLdLwT8RmgUQRoAJnAhQtI1+jIkHK9PSuO5Xp7NDoylFJFrcdngEaxiBBAJoyODK1YvCNx4QJaqbxIrt0W8q7n4uN2/QzQeo6ItGtIZHh4OKanp9MuA0AT0IUDQBLVXTOk4j+8P3HVRfzdgXVheyYihquPcwcaQGbs3jHIRQ9Aw1ZbfMzfJWgm5kADAIC2xOJjpIUADQAA2hKLj5EWAjQAAGhLdM1AWpgDDQAA2lIzumawmBmNIEADAIC2tZ6Lj6u7euQXChqbmFt+H6CMKRwAAABavasHUIkADQAAILp6oHEEaAAAANHVA40jQAMAAIiuHmgciwgBAADUnK4e6EwEaAAAgJL17OqBzsUUDgAAACABAjQAAACQAAEaAAAASIAADQAAACTQ9ABtu8f2rO3bazz2ettHbO8t/flos+sBAAAATkUrunBcI2mfpC11Hv9WRFzZgjoAAABWNTmbp40d1tTUO9C2t0l6o6Rbmvk+AAAAp2pyNq+xiTnlFwoKSfmFgsYm5jQ5m0+7NGRMs6dw3CDpWknHVznntbbvs/012xc2uR4AAICaxqfmVVhcWnGssLik8an5lCpCVjUtQNu+UtKTETGzymn3Sjo/Ii6W9ClJk3Ve6/22p21PHzx4sAnVAgCAbndgoZDoOLpXM+9A75T0Jts/lPQFSbts31p5QkT8NCKOlr6+Q1Kv7edXv1BE3BwRwxEx3N/f38SSAQBAtxroyyU6ju7VtAAdEWMRsS0itku6WtKeiHhX5Tm2z7Pt0tevKtXzk2bVBAAAUM/oyJByvT0rjuV6ezQ6MpRSRciqVnThWMH2ByQpIm6S9DZJf2T7mKSCpKsjIlpdEwAAQLnbBl04sBa3W14dHh6O6enptMsAAABAh7M9ExHD1cfZiRAAAABIgAANAAAAJECABgAAABIgQAMAAAAJtLwLBwAAwHqZnM2va9eM9X49dCYCNAAAaEuTs3mNTcwtb7+dXyhobGJOkp5T6F3v10PnYgoHAABoS+NT88tht6ywuKTxqflMvB46FwEaAAC0pQMLhUTHW/166FwEaAAA0JYG+nKJjrf69dC5CNAAAKRocjavndfv0Ys//FXtvH6PJmfzaZfUNkZHhpTr7VlxLNfbo9GRoUy8HjoXiwgBAEhJ1hattVsHinJt61Xzer8eOpcjIu0aEhkeHo7p6em0ywAA4JTtvH6P8jXm1w725fSdD+9qaS3VYV4q3n39xFUXESDRtWzPRMRw9XGmcAAAkJIsLVqjAwXQOAI0AAApydKitSyFeSDrCNAAAKQkS4vWshTmgawjQAMAkJLdOwb1iasu0mBfTlZx7nNac46zFOaBrKMLBwAAKdq9Y/CkwJxGNww6UACNI0ADAJAhaba2qxXmAZyMKRwAAGQI3TCA7CNAAwCQIXTDALKPAA0AQIbQDQPIPgI0AAAZQjcMIPtYRAgAQIbQDQPIPgI0AAAZQzcMINuYwgEAAAAkQIAGAAAAEiBAAwAAAAkQoAEAAIAECNAAAABAAnThAAAAkqTJ2Tzt84AGEKABAIAmZ/Mam5hTYXFJkpRfKGhsYk6SCNFAFaZwAAAAjU/NL4fnssLiksan5lOqCMguAjQAANCBhUKi40A3I0ADAAAN9OUSHQe6GQEaAABodGRIud6eFcdyvT0aHRlKqSIguwjQAABAu3cM6q2XDarHliT12HrrZYMsIARqIEADAABNzuZ120xeSxGSpKUI3TaT1+RsPuXKgOwhQAMAALpwAAkQoAEAAF04gAQI0AAAgC4cQAIEaAAAQBcOIAG28gYAIGMmZ/Man5rXgYWCBvpyGh0Zano3jPLrt/p9syaNzx7thwANAECGTM7mNTYxt7ygL79Q0NjEnCS1JER3c1hM87NHe2EKBwAAGUI3jPTw2aNRBGgAADKEbhjp4bNHowjQAABkCN0w0sNnj0YRoAEAyBC6YaSHzx6NYhEhAAAZQjeM9PDZo1GO0p737WJ4eDimp6fTLgMAAAAdzvZMRAxXH2cKBwAAAJAAARoAAABIgAANAAAAJECABgAAABIgQAMAAAAJEKABAACABAjQAAAAQAIEaAAAACABAjQAAACQAAEaAAAASIAADQAAACRAgAYAAAAS2Jh2AQCA5pmczWt8al4HFgoa6MtpdGRIu3cMpl0WALQ1AjQAdKjJ2bzGJuZUWFySJOUXChqbmJMkQjQAnAKmcABAhxqfml8Oz2WFxSWNT82nVBEAdAYCNAB0qAMLhUTHAQCNIUADQIca6MslOg4AaAwBGgA61OjIkHK9PSuO5Xp7NDoylFJFANAZWEQIAB2qvFCQLhwAsL6aHqBt90ialpSPiCurHrOkv5F0haRnJL0nIu5tdk0A0C127xgkMAPAOmvFFI5rJO2r89jlkl5a+vN+SZ9pQT0AAADAc9bUAG17m6Q3SrqlzilvlvT5KLpbUp/trc2sCQAAADgVzb4DfYOkayUdr/P4oKTHKr7fXzoGAAAAZFLTArTtKyU9GREzq51W41jUeK332562PX3w4MF1qxEAAABIqpl3oHdKepPtH0r6gqRdtm+tOme/pBdWfL9N0oHqF4qImyNiOCKG+/v7m1UvAAAAsKamBeiIGIuIbRGxXdLVkvZExLuqTvuypHe76DWSjkTE482qCQAAADhVLe8DbfsDkhQRN0m6Q8UWdg+p2Mbuva2uBwAAAEiiJQE6Iu6UdGfp65sqjoekD7aiBgAAAGA9sJU3AAAAkABbeQMAkDGTs3m2YAcyjAANAECGTM7mNTYxp8LikiQpv1DQ2MScJBGigYxgCgcAABkyPjW/HJ7LCotLGp+aT6kiANUI0AAAZMiBhUKi4wBajwANAECGDPTlEh0H0HoEaAAAMmR0ZEi53p4Vx3K9PRodGUqpIgDVWEQIAECGlBcK0oUDyC4CNAAAGbN7xyCBGcgwpnAAAAAACRCgAQAAgAQI0AAAAEACBGgAAAAgAQI0AAAAkAABGgAAAEiAAA0AAAAkQIAGAAAAEiBAAwAAAAkQoAEAAIAECNAAAABAAgRoAAAAIAECNAAAAJAAARoAAABIgAANAAAAJOCISLuGRGwflPSjlN7++ZKeSum9sRJjkS2MR7YwHtnCeGQL45Ed7TAW50dEf/XBtgvQabI9HRHDadcBxiJrGI9sYTyyhfHIFsYjO9p5LJjCAQAAACRAgAYAAAASIEAnc3PaBWAZY5EtjEe2MB7ZwnhkC+ORHW07FsyBBgAAABLgDjQAAACQAAG6gu1Ntr9n+z7bD9r+81XOfaXtJdtva2WN3aTR8bD9ett7S+fc1eo6u0Uj42H7eba/UnHOe9OotVvY7rE9a/v2Go/Z9t/afsj2/bYvTaPGbrLGeLyzNA732/6u7YvTqLGbrDYeFedwLW+Rtcaj3a7lG9MuIGOelbQrIo7a7pX0bdtfi4i7K0+y3SPpLyVNpVFkF1lzPGz3SbpR0hsi4lHbL0ir2C7QyM/HByX9T0T8nu1+SfO2/zEifpFKxZ3vGkn7JG2p8djlkl5a+vNqSZ8p/RfNs9p4PCLpdRFx2PblKs79ZDyaa7Xx4FreenXHox2v5dyBrhBFR0vf9pb+1Jok/iFJt0l6slW1daMGx+MdkiYi4tHScxiTJmlwPELSmbYt6QxJhyQda12V3cP2NklvlHRLnVPeLOnzpXG7W1Kf7a0tK7DLrDUeEfHdiDhc+vZuSdtaVVs3auDnQ+Ja3jINjEfbXcsJ0FVKv2LYq+IP1H9ExD1Vjw9Keoukm9Kor9usNR6SLpB0lu07bc/Yfnfrq+weDYzHpyX9qqQDkuYkXRMRx1tcZre4QdK1kup9voOSHqv4fn/pGJpjrfGo9D5JX2tuOV1v1fHgWt5ya/18tN21nABdJSKWIuISFe8OvMr2r1WdcoOk6yJiqfXVdZ8GxmOjpMtU/JftiKSP2L6gxWV2jQbGY0TSXkkDki6R9GnbNX99iufO9pWSnoyImdVOq3GMtktN0OB4lM/9bRUD9HVNL6xLNTgeXMtbpMHxaLtrOXOg64iIBdt3SnqDpAcqHhqW9IXib6j1fElX2D4WEZOtr7J7rDIe+yU9FRFPS3ra9jclXSzpB62vsnusMh7vlXR9FPtjPmT7EUkvk/S91lfZ0XZKepPtKyRtkrTF9q0R8a6Kc/ZLemHF99tU/M0A1l8j4yHbr1DxV9iXR8RPUqizWzQyHlzLW6fRv6/a6lrOHegKtvtLE9llOyfpdyV9v/KciHhxRGyPiO2SviTpj/mBa45GxkPSv0n6Tdsbbf+Sioty9rW20u7Q4Hg8Kul3SuecK2lI0sOtrLMbRMRYRGwr/T10taQ91WFN0pclvbvUjeM1ko5ExOOtrrUbNDIetl8kaULSH0REZkNBJ2hkPLiWt06Df1+13bWcO9ArbZX0D6WVuRsk/UtE3G77A5IUEcyVaq01xyMi9tn+uqT7VZxbdUtEPFD/JXEKGvn5+Likz9meU3EKwXUR8VRqFXeZqrG4Q9IVkh6S9IyKvx1AC1WNx0clnSPpxtJdz2MRMZxieV2Ha3m2tPu1nJ0IAQAAgASYwgEAAAAkQIAGAAAAEiBAAwAAAAkQoAEAAIAECNAAAABAAgRoAMgA20dP8flfsv0S2/fY3mv7UdsHS1/vtb19fSpd8Z5/ZXvXer8uAGQdfaABoM3ZvlBST0Q8rOIGBLL9HknDEfEnTXzrT0n6O0l7mvgeAJA53IEGgAwp7Rw4bvsB23O23146vsH2jbYftH277Ttsv630tHequJNXvdf8Zdtftz1j+1u2X1Y6/jnbn7H9DdsP236d7b+3vc/25yqef9T2J23fa/u/bPdLUkT8SNI5ts9r1ucBAFlEgAaAbLlK0iWSLlZxu/Rx21tLx7dLukjSH0p6bcVzdkqaWeU1b5b0oYi4TNKfSbqx4rGzJO2S9KeSviLpryVdKOki25eUztks6d6IuFTSXZI+VvH8e0vvDwBdgykcAJAtvyHpnyJiSdKPbd8l6ZWl41+MiOOSnrD9jYrnbJV0sNaL2T5D0q9L+mJpC2lJOr3ilK9ERJS2X/9xRMyVnvegioF9r4pb6/5z6fxbJU1UPP9JSQPP8f8VANoSARoAssUJj0tSQdKmOo9tkLQQEZfUefzZ0n+PV3xd/r7eNSIqvt5Uen8A6BpM4QCAbPmmpLfb7inNNf4tSd+T9G1Jby3NhT5X0usrnrNP0q/UerGI+KmkR2z/vrQ8x/rihDVtkFSeb/2OUi1lF0h6IOHrAUBbI0ADQLb8q6T7Jd2nYneLayPiCUm3SdqvYlj9rKR7JB0pPeerWhmoq71T0vts3yfpQUlvTljT05IutD2j4nzpv5Ak270qBvfphK8HAG3NEbH2WQCA1Nk+IyKO2j5HxbvSOyPiCds5Sd8ofb/UhPc9GhFn1Dj+FkmXRsRH1vs9ASDLmAMNAO3jdtt9kk6T9PHSnWlFRMH2xyQNSnq0hfVslPTJFr4fAGQCd6ABAACABJgDDQAAACRAgAYAAAASIEADAAAACRCgAQAAgAQI0AAAAEACBGgAAAAggf8HkBjdCCytacEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = dta['log.light']\n",
    "X = sm.add_constant(dta['log.Te'], prepend=True)\n",
    "ols_model = sm.OLS(y, X).fit()\n",
    "abline_plot(model_results=ols_model, ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rlm_mod = sm.RLM(y, X, sm.robust.norms.TrimmedMean(.5)).fit()\n",
    "abline_plot(model_results=rlm_mod, ax=ax, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Why? Because M-estimators are not robust to leverage points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "infl = ols_model.get_influence()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10    0.194103\n",
       "19    0.194103\n",
       "29    0.198344\n",
       "33    0.194103\n",
       "Name: hat_diag, dtype: float64"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_bar = 2*(ols_model.df_model + 1 )/ols_model.nobs\n",
    "hat_diag = infl.summary_frame()['hat_diag']\n",
    "hat_diag.loc[hat_diag > h_bar]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    student_resid   unadj_p  sidak(p)\n",
      "16      -2.049393  0.046415  0.892872\n",
      "13      -2.035329  0.047868  0.900286\n",
      "33       1.905847  0.063216  0.953543\n",
      "18      -1.575505  0.122304  0.997826\n",
      "1        1.522185  0.135118  0.998911\n",
      "3        1.522185  0.135118  0.998911\n",
      "21      -1.450418  0.154034  0.999615\n",
      "17      -1.426675  0.160731  0.999735\n",
      "29       1.388520  0.171969  0.999859\n",
      "14      -1.374733  0.176175  0.999889\n",
      "35       1.346543  0.185023  0.999933\n",
      "34      -1.272159  0.209999  0.999985\n",
      "28      -1.186946  0.241618  0.999998\n",
      "20      -1.150621  0.256103  0.999999\n",
      "44       1.134779  0.262612  0.999999\n",
      "39       1.091886  0.280826  1.000000\n",
      "19       1.064878  0.292740  1.000000\n",
      "6       -1.026873  0.310093  1.000000\n",
      "30      -1.009096  0.318446  1.000000\n",
      "22      -0.979768  0.332557  1.000000\n",
      "8        0.961218  0.341695  1.000000\n",
      "5        0.913802  0.365801  1.000000\n",
      "11       0.871997  0.387943  1.000000\n",
      "12       0.856685  0.396261  1.000000\n",
      "46      -0.833923  0.408829  1.000000\n",
      "10       0.743920  0.460879  1.000000\n",
      "42       0.727179  0.470968  1.000000\n",
      "15      -0.689258  0.494280  1.000000\n",
      "43       0.688272  0.494895  1.000000\n",
      "7        0.655712  0.515424  1.000000\n",
      "40      -0.646396  0.521381  1.000000\n",
      "26      -0.640978  0.524862  1.000000\n",
      "25      -0.545561  0.588123  1.000000\n",
      "37       0.472819  0.638680  1.000000\n",
      "32       0.472819  0.638680  1.000000\n",
      "38       0.462187  0.646225  1.000000\n",
      "0        0.430686  0.668799  1.000000\n",
      "31       0.341726  0.734184  1.000000\n",
      "36       0.318911  0.751303  1.000000\n",
      "4        0.307890  0.759619  1.000000\n",
      "9        0.235114  0.815211  1.000000\n",
      "41       0.187732  0.851950  1.000000\n",
      "2       -0.182093  0.856346  1.000000\n",
      "23      -0.156014  0.876736  1.000000\n",
      "27      -0.147406  0.883485  1.000000\n",
      "24       0.065195  0.948314  1.000000\n",
      "45       0.045675  0.963776  1.000000\n"
     ]
    }
   ],
   "source": [
    "sidak2 = ols_model.outlier_test('sidak')\n",
    "sidak2.sort_values('unadj_p', inplace=True)\n",
    "print(sidak2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    student_resid   unadj_p  fdr_bh(p)\n",
      "16      -2.049393  0.046415   0.764747\n",
      "13      -2.035329  0.047868   0.764747\n",
      "33       1.905847  0.063216   0.764747\n",
      "18      -1.575505  0.122304   0.764747\n",
      "1        1.522185  0.135118   0.764747\n",
      "3        1.522185  0.135118   0.764747\n",
      "21      -1.450418  0.154034   0.764747\n",
      "17      -1.426675  0.160731   0.764747\n",
      "29       1.388520  0.171969   0.764747\n",
      "14      -1.374733  0.176175   0.764747\n",
      "35       1.346543  0.185023   0.764747\n",
      "34      -1.272159  0.209999   0.764747\n",
      "28      -1.186946  0.241618   0.764747\n",
      "20      -1.150621  0.256103   0.764747\n",
      "44       1.134779  0.262612   0.764747\n",
      "39       1.091886  0.280826   0.764747\n",
      "19       1.064878  0.292740   0.764747\n",
      "6       -1.026873  0.310093   0.764747\n",
      "30      -1.009096  0.318446   0.764747\n",
      "22      -0.979768  0.332557   0.764747\n",
      "8        0.961218  0.341695   0.764747\n",
      "5        0.913802  0.365801   0.768599\n",
      "11       0.871997  0.387943   0.768599\n",
      "12       0.856685  0.396261   0.768599\n",
      "46      -0.833923  0.408829   0.768599\n",
      "10       0.743920  0.460879   0.770890\n",
      "42       0.727179  0.470968   0.770890\n",
      "15      -0.689258  0.494280   0.770890\n",
      "43       0.688272  0.494895   0.770890\n",
      "7        0.655712  0.515424   0.770890\n",
      "40      -0.646396  0.521381   0.770890\n",
      "26      -0.640978  0.524862   0.770890\n",
      "25      -0.545561  0.588123   0.837630\n",
      "37       0.472819  0.638680   0.843682\n",
      "32       0.472819  0.638680   0.843682\n",
      "38       0.462187  0.646225   0.843682\n",
      "0        0.430686  0.668799   0.849556\n",
      "31       0.341726  0.734184   0.892552\n",
      "36       0.318911  0.751303   0.892552\n",
      "4        0.307890  0.759619   0.892552\n",
      "9        0.235114  0.815211   0.922751\n",
      "41       0.187732  0.851950   0.922751\n",
      "2       -0.182093  0.856346   0.922751\n",
      "23      -0.156014  0.876736   0.922751\n",
      "27      -0.147406  0.883485   0.922751\n",
      "24       0.065195  0.948314   0.963776\n",
      "45       0.045675  0.963776   0.963776\n"
     ]
    }
   ],
   "source": [
    "fdr2 = ols_model.outlier_test('fdr_bh')\n",
    "fdr2.sort_values('unadj_p', inplace=True)\n",
    "print(fdr2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Let's delete that line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "l =  ax.lines[-1]\n",
    "l.remove()\n",
    "del l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights = np.ones(len(X))\n",
    "weights[X[X['log.Te'] < 3.8].index.values - 1] = 0\n",
    "wls_model = sm.WLS(y, X, weights=weights).fit()\n",
    "abline_plot(model_results=wls_model, ax=ax, color='green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* MM estimators are good for this type of problem, unfortunately, we do not yet have these yet. \n",
    "* It's being worked on, but it gives a good excuse to look at the R cell magics in the notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "yy = y.values[:,None]\n",
    "xx = X['log.Te'].values[:,None]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: The R code and the results in this notebook has been converted to markdown so that R is not required to build the documents. The R results in the notebook were computed using R 3.5.1 and robustbase 0.93."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "```ipython\n",
    "%load_ext rpy2.ipython\n",
    "\n",
    "%R library(robustbase)\n",
    "%Rpush yy xx\n",
    "%R mod <- lmrob(yy ~ xx);\n",
    "%R params <- mod$coefficients;\n",
    "%Rpull params\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "```ipython\n",
    "%R print(mod)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```\n",
    "Call:\n",
    "lmrob(formula = yy ~ xx)\n",
    " \\--> method = \"MM\"\n",
    "Coefficients:\n",
    "(Intercept)           xx  \n",
    "     -4.969        2.253  \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-4.969387980288108 2.2531613477892365\n"
     ]
    }
   ],
   "source": [
    "params = [-4.969387980288108, 2.2531613477892365]  # Computed using R\n",
    "print(params[0], params[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abline_plot(intercept=params[0], slope=params[1], ax=ax, color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: Breakdown points of M-estimator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(12345)\n",
    "nobs = 200\n",
    "beta_true = np.array([3, 1, 2.5, 3, -4])\n",
    "X = np.random.uniform(-20,20, size=(nobs, len(beta_true)-1))\n",
    "# stack a constant in front\n",
    "X = sm.add_constant(X, prepend=True) # np.c_[np.ones(nobs), X]\n",
    "mc_iter = 500\n",
    "contaminate = .25 # percentage of response variables to contaminate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_betas = []\n",
    "for i in range(mc_iter):\n",
    "    y = np.dot(X, beta_true) + np.random.normal(size=200)\n",
    "    random_idx = np.random.randint(0, nobs, size=int(contaminate * nobs))\n",
    "    y[random_idx] = np.random.uniform(-750, 750)\n",
    "    beta_hat = sm.RLM(y, X).fit().params\n",
    "    all_betas.append(beta_hat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_betas = np.asarray(all_betas)\n",
    "se_loss = lambda x : np.linalg.norm(x, ord=2)**2\n",
    "se_beta = lmap(se_loss, all_betas - beta_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Squared error loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4450294873068618"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(se_beta).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.99711706,  0.99898147,  2.49909344,  2.99712918, -3.99626521])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_betas.mean(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3. ,  1. ,  2.5,  3. , -4. ])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.236091328675419e-05"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "se_loss(all_betas.mean(0) - beta_true)"
   ]
  }
 ],
 "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",
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