ch14-statistical-modeling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistical modeling with statsmodel & patsy\n",
    "\n",
    "- __Intro__\n",
    "- __Intro to Patsy__\n",
    "- __Linear regression__\n",
    "- __Example datasets__\n",
    "- __Discrete regression__\n",
    "    - logistic regression\n",
    "    - poisson model\n",
    "- __Time series__\n",
    "\n",
    "* use case: for a set of response variables (Y), and independent variables (X), find a model that explains the relations between X & Y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.graphics.api as smg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "import patsy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using patsy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(123456789)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "y  = np.array([ 1,  2,  3,  4,  5])\n",
    "x1 = np.array([ 6,  7,  8,  9, 10])\n",
    "x2 = np.array([11, 12, 13, 14, 15])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   6.,  11.,  66.],\n",
       "       [  1.,   7.,  12.,  84.],\n",
       "       [  1.,   8.,  13., 104.],\n",
       "       [  1.,   9.,  14., 126.],\n",
       "       [  1.,  10.,  15., 150.]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# linear model: Y = b0 + b1x1 + b2x2 + b3x1x2\n",
    "X = np.vstack([np.ones(5), x1, x2, x1*x2]).T; X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5.55555556e-01,  1.88888889e+00, -8.88888889e-01, -1.11022302e-15])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use NumPy least-square-fit func to find beta coefficient vector\n",
    "beta, res, rank, sval = np.linalg.lstsq(X, y, rcond=None); beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Patsy syntax\n",
    "* basic structure: \"LHS ~ RHS\" (LHS contains response vars; RHS contains independent vars)\n",
    "* \"+\" & \"-\" signs in expressions are set union/difference ops, not math ops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# create a dictionary to map variable names to corresponding data arrays\n",
    "data = {\"y\": y, \"x1\": x1, \"x2\": x2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# define model\n",
    "y, X = patsy.dmatrices(\"y ~ 1 + x1 + x2 + x1*x2\", data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DesignMatrix with shape (5, 1)\n",
       "  y\n",
       "  1\n",
       "  2\n",
       "  3\n",
       "  4\n",
       "  5\n",
       "  Terms:\n",
       "    'y' (column 0)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# y, X are DesignMatrix instances = subclass of NumPy arrays\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DesignMatrix with shape (5, 4)\n",
       "  Intercept  x1  x2  x1:x2\n",
       "          1   6  11     66\n",
       "          1   7  12     84\n",
       "          1   8  13    104\n",
       "          1   9  14    126\n",
       "          1  10  15    150\n",
       "  Terms:\n",
       "    'Intercept' (column 0)\n",
       "    'x1' (column 1)\n",
       "    'x2' (column 2)\n",
       "    'x1:x2' (column 3)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.,   6.,  11.,  66.],\n",
       "       [  1.,   7.,  12.,  84.],\n",
       "       [  1.,   8.,  13., 104.],\n",
       "       [  1.,   9.,  14., 126.],\n",
       "       [  1.,  10.,  15., 150.]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# ordinary linear regression (OLS)\n",
    "model = sm.OLS(y, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5.55555556e-01,  1.88888889e+00, -8.88888889e-01, -7.77156117e-16])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = model.fit()\n",
    "result.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept   -5.555556e-01\n",
       "x1           1.888889e+00\n",
       "x2          -8.888889e-01\n",
       "x1:x2       -7.771561e-16\n",
       "dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using statsmodel API (imported as smf)\n",
    "# pass Patsy model formula & data dictionary\n",
    "model = smf.ols(\n",
    "    \"y ~ 1 + x1 + x2 + x1:x2\", \n",
    "    df_data)\n",
    "\n",
    "result = model.fit()\n",
    "result.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/bjpcjp/anaconda3/lib/python3.6/site-packages/statsmodels/stats/stattools.py:72: ValueWarning: omni_normtest is not valid with less than 8 observations; 5 samples were given.\n",
      "  \"samples were given.\" % int(n), ValueWarning)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   1.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>6.860e+27</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 19 May 2019</td> <th>  Prob (F-statistic):</th> <td>1.46e-28</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>09:19:27</td>     <th>  Log-Likelihood:    </th> <td>  151.41</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>     5</td>      <th>  AIC:               </th> <td>  -296.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>     2</td>      <th>  BIC:               </th> <td>  -298.0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   -0.5556</td> <td> 6.16e-14</td> <td>-9.02e+12</td> <td> 0.000</td> <td>   -0.556</td> <td>   -0.556</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>        <td>    1.8889</td> <td>  2.3e-13</td> <td> 8.22e+12</td> <td> 0.000</td> <td>    1.889</td> <td>    1.889</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>        <td>   -0.8889</td> <td> 7.82e-14</td> <td>-1.14e+13</td> <td> 0.000</td> <td>   -0.889</td> <td>   -0.889</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1:x2</th>     <td>-7.772e-16</td> <td> 7.22e-15</td> <td>   -0.108</td> <td> 0.924</td> <td>-3.18e-14</td> <td> 3.03e-14</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>   nan</td> <th>  Durbin-Watson:     </th> <td>   0.071</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td>   nan</td> <th>  Jarque-Bera (JB):  </th> <td>   0.399</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.401</td> <th>  Prob(JB):          </th> <td>   0.819</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 1.871</td> <th>  Cond. No.          </th> <td>6.86e+17</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The smallest eigenvalue is 1.31e-31. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       1.000\n",
       "Model:                            OLS   Adj. R-squared:                  1.000\n",
       "Method:                 Least Squares   F-statistic:                 6.860e+27\n",
       "Date:                Sun, 19 May 2019   Prob (F-statistic):           1.46e-28\n",
       "Time:                        09:19:27   Log-Likelihood:                 151.41\n",
       "No. Observations:                   5   AIC:                            -296.8\n",
       "Df Residuals:                       2   BIC:                            -298.0\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -0.5556   6.16e-14  -9.02e+12      0.000      -0.556      -0.556\n",
       "x1             1.8889    2.3e-13   8.22e+12      0.000       1.889       1.889\n",
       "x2            -0.8889   7.82e-14  -1.14e+13      0.000      -0.889      -0.889\n",
       "x1:x2      -7.772e-16   7.22e-15     -0.108      0.924   -3.18e-14    3.03e-14\n",
       "==============================================================================\n",
       "Omnibus:                          nan   Durbin-Watson:                   0.071\n",
       "Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.399\n",
       "Skew:                           0.401   Prob(JB):                        0.819\n",
       "Kurtosis:                       1.871   Cond. No.                     6.86e+17\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The smallest eigenvalue is 1.31e-31. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "from collections import defaultdict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "data = defaultdict(lambda: np.array([1,2,3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'a']"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# intercept & a correspond to a constant and a linear dependence on a.\n",
    "patsy.dmatrices(\"y ~ a\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'a', 'b']"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now we have 2nd independent variable, \"b\"\n",
    "patsy.dmatrices(\"y ~ 1 + a + b\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['a', 'b']"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# intercept can be removed\n",
    "patsy.dmatrices(\"y ~ -1 + a + b\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'a', 'b', 'a:b']"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# auto expansion\n",
    "patsy.dmatrices(\"y ~ a * b\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'a', 'b', 'a:b', 'c', 'a:c', 'b:c', 'a:b:c']"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# higher-order expansions\n",
    "patsy.dmatrices(\"y ~ a * b * c\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'a', 'b', 'a:b', 'c', 'a:c', 'b:c']"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# removing specific term (in this case, a:b:c)\n",
    "patsy.dmatrices(\"y ~ a * b * c - a:b:c\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* \"+\" and \"-\" operators are used in Patsy for set-like operations (not math)\n",
    "* Patsy also provides an identity function (I)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "data = {k: np.array([]) for k in [\"y\", \"a\", \"b\", \"c\"]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'a', 'b']"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patsy.dmatrices(\"y ~ a + b\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'I(a + b)']"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patsy.dmatrices(\"y ~ I(a + b)\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'a']"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patsy.dmatrices(\"y ~ a*a\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'I(a ** 2)']"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patsy.dmatrices(\"y ~ I(a**2)\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'np.log(a)', 'b']"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patsy.dmatrices(\"y ~ np.log(a) + b\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "z = lambda x1, x2: x1+x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Intercept', 'z(a, b)']"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patsy.dmatrices(\"y ~ z(a, b)\", data=data)[1].design_info.term_names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Categorical variables\n",
    "* When using categories in a linear model, we typically need to recode them with dummy variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "data = {\"y\": [1, 2, 3], \"a\": [1, 2, 3]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     a\n",
       "0  1.0\n",
       "1  2.0\n",
       "2  3.0"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patsy.dmatrices(\"y ~ - 1 + a\", data=data, return_type=\"dataframe\")[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C(a)[1]</th>\n",
       "      <th>C(a)[2]</th>\n",
       "      <th>C(a)[3]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   C(a)[1]  C(a)[2]  C(a)[3]\n",
       "0      1.0      0.0      0.0\n",
       "1      0.0      1.0      0.0\n",
       "2      0.0      0.0      1.0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patsy.dmatrices(\"y ~ - 1 + C(a)\", data=data, return_type=\"dataframe\")[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# variables with non-numerical values are auto-interpreted & treated as category data.\n",
    "data = {\"y\": [1, 2, 3], \"a\": [\"type A\", \"type B\", \"type C\"]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a[type A]</th>\n",
       "      <th>a[type B]</th>\n",
       "      <th>a[type C]</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   a[type A]  a[type B]  a[type C]\n",
       "0        1.0        0.0        0.0\n",
       "1        0.0        1.0        0.0\n",
       "2        0.0        0.0        1.0"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "patsy.dmatrices(\"y ~ - 1 + a\", data=data, return_type=\"dataframe\")[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C(a, Poly).Constant</th>\n",
       "      <th>C(a, Poly).Linear</th>\n",
       "      <th>C(a, Poly).Quadratic</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-7.071068e-01</td>\n",
       "      <td>0.408248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>-5.551115e-17</td>\n",
       "      <td>-0.816497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>7.071068e-01</td>\n",
       "      <td>0.408248</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   C(a, Poly).Constant  C(a, Poly).Linear  C(a, Poly).Quadratic\n",
       "0                  1.0      -7.071068e-01              0.408248\n",
       "1                  1.0      -5.551115e-17             -0.816497\n",
       "2                  1.0       7.071068e-01              0.408248"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Category data encoding is binary by default.\n",
    "# Encoding can be changed/extended.\n",
    "# Example: encoding categories with orthogonal polynomials instead of treatment indicators\n",
    "# using (C(a,Poly))\n",
    "\n",
    "patsy.dmatrices(\"y ~ - 1 + C(a, Poly)\", data=data, return_type=\"dataframe\")[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Linear regression\n",
    "* Basic workflow:\n",
    "    - Create instance of model class\n",
    "    - invoke fit method\n",
    "    - print summary stats\n",
    "    - post-process model fit results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "np.random.seed(123456789)\n",
    "N = 100\n",
    "x1 = np.random.randn(N)\n",
    "x2 = np.random.randn(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame({\"x1\": x1, \"x2\": x2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# true value: y = 1 + 2x1 + 3x2 + 4x12\n",
    "\n",
    "def y_true(x1, x2):\n",
    "    return 1 + 2*x1 + 3*x2 + 4*x1*x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    -0.198823\n",
       "1   -12.298805\n",
       "2   -15.420705\n",
       "3     2.313945\n",
       "4    -1.282107\n",
       "Name: y_true, dtype: float64"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# store true value of y in y_true column of the DataFrame.\n",
    "data[\"y_true\"] = y_true(x1, x2)\n",
    "data[\"y_true\"][0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.56463281,  0.56190437,  1.22155556, -1.08257084, -0.35554624])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# add normal-distributed noise to true values\n",
    "e = np.random.randn(N)\n",
    "e[0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y_true</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.212902</td>\n",
       "      <td>-0.474588</td>\n",
       "      <td>-0.198823</td>\n",
       "      <td>-0.763456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.128398</td>\n",
       "      <td>-1.524772</td>\n",
       "      <td>-12.298805</td>\n",
       "      <td>-11.736900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.841711</td>\n",
       "      <td>-1.939271</td>\n",
       "      <td>-15.420705</td>\n",
       "      <td>-14.199150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.082382</td>\n",
       "      <td>0.345148</td>\n",
       "      <td>2.313945</td>\n",
       "      <td>1.231374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.858964</td>\n",
       "      <td>-0.621523</td>\n",
       "      <td>-1.282107</td>\n",
       "      <td>-1.637653</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x1        x2     y_true          y\n",
       "0  2.212902 -0.474588  -0.198823  -0.763456\n",
       "1  2.128398 -1.524772 -12.298805 -11.736900\n",
       "2  1.841711 -1.939271 -15.420705 -14.199150\n",
       "3  0.082382  0.345148   2.313945   1.231374\n",
       "4  0.858964 -0.621523  -1.282107  -1.637653"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[\"y\"] = data[\"y_true\"] + e\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we have two explanatory values (x1,x2) and a response (y).\n",
    "# start with linear model\n",
    "model = smf.ols(\"y ~ x1 + x2\", data)\n",
    "result = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.376\n",
      "Model:                            OLS   Adj. R-squared:                  0.363\n",
      "Method:                 Least Squares   F-statistic:                     29.19\n",
      "Date:                Sun, 19 May 2019   Prob (F-statistic):           1.19e-10\n",
      "Time:                        09:41:05   Log-Likelihood:                -269.97\n",
      "No. Observations:                 100   AIC:                             545.9\n",
      "Df Residuals:                      97   BIC:                             553.8\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      1.0444      0.377      2.774      0.007       0.297       1.792\n",
      "x1             1.1313      0.385      2.940      0.004       0.368       1.895\n",
      "x2             2.9668      0.425      6.981      0.000       2.123       3.810\n",
      "==============================================================================\n",
      "Omnibus:                       16.990   Durbin-Watson:                   1.619\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               33.548\n",
      "Skew:                          -0.640   Prob(JB):                     5.19e-08\n",
      "Kurtosis:                       5.533   Cond. No.                         1.32\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3757287272091422"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# r-squared: how does data fit model? (1.0 = perfect)\n",
    "result.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    -2.903191\n",
       "1   -10.665331\n",
       "2   -11.573520\n",
       "3    -0.930212\n",
       "4    -1.809809\n",
       "dtype: float64"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# to investigate whether assumption of normal-distributed errors is justified\n",
    "# start with residuals\n",
    "result.resid.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.690964627386556"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check for normality\n",
    "z, p = stats.normaltest(result.fittedvalues.values)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    1.044399\n",
       "x1           1.131253\n",
       "x2           2.966821\n",
       "dtype: float64"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# extract coefficients\n",
    "result.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# QQ plot - compares sample quantiles with theoretical quantiles\n",
    "# should be similar to a straight line if sampled values are normally distributed.\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "smg.qqplot(result.resid, ax=ax)\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig(\"ch14-qqplot-model-1.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Above significant deviation == unlikely to be a sample from normal distribution. We need to refine the model.\n",
    "* Can add missing interaction to Patsy formula, then repeat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.950\n",
      "Model:                            OLS   Adj. R-squared:                  0.949\n",
      "Method:                 Least Squares   F-statistic:                     614.3\n",
      "Date:                Sun, 19 May 2019   Prob (F-statistic):           1.70e-62\n",
      "Time:                        09:46:58   Log-Likelihood:                -143.25\n",
      "No. Observations:                 100   AIC:                             294.5\n",
      "Df Residuals:                      96   BIC:                             304.9\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.9304      0.107      8.725      0.000       0.719       1.142\n",
      "x1             2.0025      0.112     17.877      0.000       1.780       2.225\n",
      "x2             2.8567      0.120     23.738      0.000       2.618       3.096\n",
      "x1:x2          3.8681      0.116     33.384      0.000       3.638       4.098\n",
      "==============================================================================\n",
      "Omnibus:                        2.046   Durbin-Watson:                   1.814\n",
      "Prob(Omnibus):                  0.359   Jarque-Bera (JB):                1.774\n",
      "Skew:                          -0.326   Prob(JB):                        0.412\n",
      "Kurtosis:                       3.011   Cond. No.                         1.38\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = smf.ols(\"y ~ x1 + x2 + x1*x2\", data)\n",
    "result = model.fit()\n",
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9504900208668222"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# r-squared stat: much better.\n",
    "result.rsquared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# repeat the QQ plot. (It's better.)\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "smg.qqplot(result.resid, ax=ax)\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    0.930429\n",
       "x1           2.002468\n",
       "x2           2.856701\n",
       "x1:x2        3.868131\n",
       "dtype: float64"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Predict values of new observations using __predict__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-1, 1, 50)\n",
    "X1, X2 = np.meshgrid(x, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "new_data = pd.DataFrame(\n",
    "    {\"x1\": X1.ravel(), \n",
    "     \"x2\": X2.ravel()})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2500,)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# predict y values\n",
    "y_pred = result.predict(new_data)\n",
    "y_pred.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# resize to square matrix for plotting purposes\n",
    "y_pred = y_pred.values.reshape(50, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# do contour plots - true model vs fitted (100 noisy obs) model\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(12, 5), sharey=True)\n",
    "\n",
    "def plot_y_contour(ax, Y, title):\n",
    "    c = ax.contourf(X1, X2, Y, 15, cmap=plt.cm.RdBu)\n",
    "    ax.set_xlabel(r\"$x_1$\", fontsize=20)\n",
    "    ax.set_ylabel(r\"$x_2$\", fontsize=20)\n",
    "    ax.set_title(title)\n",
    "    cb = fig.colorbar(c, ax=ax)\n",
    "    cb.set_label(r\"$y$\", fontsize=20)\n",
    "\n",
    "plot_y_contour(axes[0], y_true(X1, X2), \"true relation\")\n",
    "plot_y_contour(axes[1], y_pred, \"fitted model\")\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig(\"ch14-comparison-model-true.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Datasets from R\n",
    "\n",
    "* Datasets sourced from http://vincentarelbundock.github.io/Rdatasets/datasets.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Ice Cream Consumption'"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = sm.datasets.get_rdataset(\"Icecream\", \"Ecdat\")\n",
    "dataset.title"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 30 entries, 0 to 29\n",
      "Data columns (total 4 columns):\n",
      "cons      30 non-null float64\n",
      "income    30 non-null int64\n",
      "price     30 non-null float64\n",
      "temp      30 non-null int64\n",
      "dtypes: float64(2), int64(2)\n",
      "memory usage: 1.0 KB\n"
     ]
    }
   ],
   "source": [
    "dataset.data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# ordinary least squares regression\n",
    "model = smf.ols(\n",
    "    \"cons ~ -1 + price + temp\", \n",
    "    data=dataset.data)\n",
    "result = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>cons</td>       <th>  R-squared:         </th> <td>   0.986</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.985</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1001.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 19 May 2019</td> <th>  Prob (F-statistic):</th> <td>9.03e-27</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>09:52:26</td>     <th>  Log-Likelihood:    </th> <td>  51.903</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    30</td>      <th>  AIC:               </th> <td>  -99.81</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    28</td>      <th>  BIC:               </th> <td>  -97.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>price</th> <td>    0.7254</td> <td>    0.093</td> <td>    7.805</td> <td> 0.000</td> <td>    0.535</td> <td>    0.916</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>temp</th>  <td>    0.0032</td> <td>    0.000</td> <td>    6.549</td> <td> 0.000</td> <td>    0.002</td> <td>    0.004</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 5.350</td> <th>  Durbin-Watson:     </th> <td>   0.637</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.069</td> <th>  Jarque-Bera (JB):  </th> <td>   3.675</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.776</td> <th>  Prob(JB):          </th> <td>   0.159</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.729</td> <th>  Cond. No.          </th> <td>    593.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                   cons   R-squared:                       0.986\n",
       "Model:                            OLS   Adj. R-squared:                  0.985\n",
       "Method:                 Least Squares   F-statistic:                     1001.\n",
       "Date:                Sun, 19 May 2019   Prob (F-statistic):           9.03e-27\n",
       "Time:                        09:52:26   Log-Likelihood:                 51.903\n",
       "No. Observations:                  30   AIC:                            -99.81\n",
       "Df Residuals:                      28   BIC:                            -97.00\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "price          0.7254      0.093      7.805      0.000       0.535       0.916\n",
       "temp           0.0032      0.000      6.549      0.000       0.002       0.004\n",
       "==============================================================================\n",
       "Omnibus:                        5.350   Durbin-Watson:                   0.637\n",
       "Prob(Omnibus):                  0.069   Jarque-Bera (JB):                3.675\n",
       "Skew:                           0.776   Prob(JB):                        0.159\n",
       "Kurtosis:                       3.729   Cond. No.                         593.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# maybe ice cream consumption = linear corr to temp, no relation to price?\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "smg.plot_fit(result, 0, ax=ax1)\n",
    "smg.plot_fit(result, 1, ax=ax2)\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig(\"ch14-regressionplots.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/bjpcjp/anaconda3/lib/python3.6/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sure looks that way\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4))\n",
    "\n",
    "sns.regplot(\"price\", \"cons\", dataset.data, ax=ax1);\n",
    "sns.regplot(\"temp\", \"cons\", dataset.data, ax=ax2);\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig(\"ch14-regressionplots-seaborn.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discrete regression, logistic regression\n",
    "* Requires different techniques, because linear regression requires a normally distributed continuous variable.\n",
    "* statmodel discrete regression support: **Logit** (logistic regression), **Probit** (uses CMF of normal distribution, transforms linear predictor to [0,1], **MNLogit** (multinomial logistic regression), and **Poisson** classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 150 entries, 0 to 149\n",
      "Data columns (total 5 columns):\n",
      "Sepal.Length    150 non-null float64\n",
      "Sepal.Width     150 non-null float64\n",
      "Petal.Length    150 non-null float64\n",
      "Petal.Width     150 non-null float64\n",
      "Species         150 non-null object\n",
      "dtypes: float64(4), object(1)\n",
      "memory usage: 5.9+ KB\n"
     ]
    }
   ],
   "source": [
    "# Iris dataset\n",
    "df = sm.datasets.get_rdataset(\"iris\").data\n",
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['setosa', 'versicolor', 'virginica'], dtype=object)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3 unique species\n",
    "df.Species.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# let's use versicolor & virginica species as basis for binary variable\n",
    "df_subset = df[df.Species.isin([\"versicolor\", \"virginica\"])].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# map two species names into binary\n",
    "df_subset.Species = df_subset.Species.map(\n",
    "    {\"versicolor\": 1, \n",
    "     \"virginica\": 0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# clean up names so Python doesn't have problems (periods to underscores)\n",
    "df_subset.rename(\n",
    "    columns={\n",
    "        \"Sepal.Length\": \"Sepal_Length\", \n",
    "        \"Sepal.Width\": \"Sepal_Width\",\n",
    "        \"Petal.Length\": \"Petal_Length\", \n",
    "        \"Petal.Width\": \"Petal_Width\"}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sepal_Length</th>\n",
       "      <th>Sepal_Width</th>\n",
       "      <th>Petal_Length</th>\n",
       "      <th>Petal_Width</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>7.0</td>\n",
       "      <td>3.2</td>\n",
       "      <td>4.7</td>\n",
       "      <td>1.4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>6.4</td>\n",
       "      <td>3.2</td>\n",
       "      <td>4.5</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>6.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>4.9</td>\n",
       "      <td>1.5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Sepal_Length  Sepal_Width  Petal_Length  Petal_Width  Species\n",
       "50           7.0          3.2           4.7          1.4        1\n",
       "51           6.4          3.2           4.5          1.5        1\n",
       "52           6.9          3.1           4.9          1.5        1"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_subset.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# use Patsy to create a logit model \n",
    "model = smf.logit(\n",
    "    \"Species ~ Sepal_Length + Sepal_Width + Petal_Length + Petal_Width\", \n",
    "    data=df_subset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.059493\n",
      "         Iterations 12\n"
     ]
    }
   ],
   "source": [
    "result = model.fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:                Species   No. Observations:                  100\n",
      "Model:                          Logit   Df Residuals:                       95\n",
      "Method:                           MLE   Df Model:                            4\n",
      "Date:                Sun, 19 May 2019   Pseudo R-squ.:                  0.9142\n",
      "Time:                        10:06:06   Log-Likelihood:                -5.9493\n",
      "converged:                       True   LL-Null:                       -69.315\n",
      "                                        LLR p-value:                 1.947e-26\n",
      "================================================================================\n",
      "                   coef    std err          z      P>|z|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------\n",
      "Intercept       42.6378     25.708      1.659      0.097      -7.748      93.024\n",
      "Sepal_Length     2.4652      2.394      1.030      0.303      -2.228       7.158\n",
      "Sepal_Width      6.6809      4.480      1.491      0.136      -2.099      15.461\n",
      "Petal_Length    -9.4294      4.737     -1.990      0.047     -18.714      -0.145\n",
      "Petal_Width    -18.2861      9.743     -1.877      0.061     -37.381       0.809\n",
      "================================================================================\n",
      "\n",
      "Possibly complete quasi-separation: A fraction 0.60 of observations can be\n",
      "perfectly predicted. This might indicate that there is complete\n",
      "quasi-separation. In this case some parameters will not be identified.\n"
     ]
    }
   ],
   "source": [
    "print(result.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Logit Marginal Effects       \n",
      "=====================================\n",
      "Dep. Variable:                Species\n",
      "Method:                          dydx\n",
      "At:                           overall\n",
      "================================================================================\n",
      "                  dy/dx    std err          z      P>|z|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------\n",
      "Sepal_Length     0.0445      0.038      1.163      0.245      -0.031       0.120\n",
      "Sepal_Width      0.1207      0.064      1.891      0.059      -0.004       0.246\n",
      "Petal_Length    -0.1703      0.057     -2.965      0.003      -0.283      -0.058\n",
      "Petal_Width     -0.3303      0.110     -2.998      0.003      -0.546      -0.114\n",
      "================================================================================\n"
     ]
    }
   ],
   "source": [
    "# get_margeff = returns info on marginal effects of each explanatory variable.\n",
    "print(result.get_margeff().summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "# use fitted model to predict responses to new explanatory variable values.\n",
    "# TODO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson distribution\n",
    "* use case: response variable = #successes for many attempts - each with low probability of success."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# discoveries dataset\n",
    "dataset = sm.datasets.get_rdataset(\"discoveries\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>time</th>\n",
       "      <th>1860</th>\n",
       "      <th>1861</th>\n",
       "      <th>1862</th>\n",
       "      <th>1863</th>\n",
       "      <th>1864</th>\n",
       "      <th>1865</th>\n",
       "      <th>1866</th>\n",
       "      <th>1867</th>\n",
       "      <th>1868</th>\n",
       "      <th>1869</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>discoveries</th>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "time         1860  1861  1862  1863  1864  1865  1866  1867  1868  1869\n",
       "discoveries     5     3     0     2     0     3     2     3     6     1"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#dataset.data.head\n",
    "\n",
    "df = dataset.data.set_index(\"time\").rename(columns={\"value\" : \"discoveries\"})\n",
    "df.head(10).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABHgAAAEYCAYAAAAnPkG+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzt3Xu4JGV9L/rvywzIZeSijJeIw6DHGyIIDqiJioqiG3JAVDZ6ooIxwRONmuy4d8bkZOvx0YjRoO7t7ZCImkcN6kS8BBXYoNtrQEAQcUCUjDp44aJyUYkC7/mjCml6es2s7l49q2rN5/M89Uyv6u+q/lW/1dWrf1NdVWqtAQAAAKC/tlvsAgAAAACYjgYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD03PKt+WB77rlnXb169dZ8SAAAAIDeuvDCC6+rta7cUm6rNnhWr16dCy64YGs+JAAAAEBvlVK+N5+cr2gBAAAA9JwGDwAAAEDPafAAAAAA9NxWPQcPAAAA0B+/+c1vsnHjxtxyyy2LXcqSt+OOO2avvfbK9ttvP9Hva/AAAAAAI23cuDF3v/vds3r16pRSFrucJavWmuuvvz4bN27MPvvsM9EytvgVrVLKqaWUa0op3xyY96ZSyuWllG+UUk4vpew+0aMDAAAAnXXLLbfknve8p+bOjJVScs973nOqI6Xmcw6e9yV5+tC8s5PsV2vdP8m3k7xq4goAAACAztLc2TqmfZ632OCptX4hyU+H5p1Va721/fHfkuw1VRUAAAAATGwhzsHzh0k+PNedpZQTk5yYJKtWrVqAhwPY1Oq1Z2wyb8NJRy5CJQAAsHSN+rt7GuP+zf6a17wmK1asyI033pgnPOEJecpTnrKg9UzqiCOOyIc+9KHsvvvincFmqgZPKeWvk9ya5INzZWqtpyQ5JUnWrFlTp3k8AAAAgNe+9rWLXUKS5uTItdZ8+tOfXuxS5nUOnpFKKSck+f0kf1Br1bgBAAAAFtzrX//6PPjBD87jHve4XHHFFUmSE044IevWrUuSrF27Nvvuu2/233//vPKVr0yS/OQnP8kxxxyTAw44IAcccEC+8pWvJElOPvnk7Lffftlvv/3y1re+9be//453vOO3j/ea17wmb37zm5Mkb3rTm3LwwQdn//33z6tf/eokyYYNG/KQhzwkL3jBC7LffvvlBz/4QVavXp3rrrsuSfKBD3wghxxySB75yEfmxS9+cW677bbcdtttOeGEE7LffvvlEY94RN7ylrcs+PM00RE8pZSnJ/lvSQ6ttf5yYUsCAAAASC688MKcdtppufjii3PrrbfmoIMOyqMe9ajf3n/99dfn9NNPz+WXX55SSn7+858nSV7+8pfn0EMPzemnn57bbrstN998cy688MK8973vzXnnnZdaax796Efn0EMPzXHHHZc/+7M/y0tf+tIkyUc+8pGceeaZOeuss3LllVfm/PPPT601Rx11VL7whS9k1apVufLKK/P+978/j3nMY+5S7/r16/PhD384X/7yl7P99tvnJS95ST74wQ/m4Q9/eK6++up885vNBcrvqHMhzecy6f+c5KtJHlJK2VhKeVGStye5e5KzSykXl1LeveCVAQAAANu0L37xiznmmGOy8847Z9ddd81RRx11l/t322237LjjjnnRi16Uj33sY9l5552TJOeee27+5E/+JEmybNmy7LbbbvnSl76UY445JrvssktWrFiRZz7zmfniF7+YAw88MNdcc01++MMf5pJLLskee+yR+9///jnrrLNy1lln5cADD8xBBx2Uyy+/PFdeeWWSZO+9996kuZMk55xzTi688MIcfPDBeeQjH5lzzjknV111VR7wgAfkqquuyste9rJ89rOfza677rrgz9UWj+CptT53xOz3LHglAAAAAGNYvnx5zj///JxzzjlZt25d3v72t+fcc88deznHHnts1q1blx//+Mc57rjjkjTn13nVq16VF7/4xXfJbtiwIbvsssvI5dRac/zxx+cNb3jDJvddcsklOfPMM/Pud787H/nIR3LqqaeOXefmTHwOHgAAAIBZesITnpCPf/zj+dWvfpWbbropn/rUp+5y/80335wbbrghRxxxRN7ylrfkkksuSZIcdthhede73pUkue2223LDDTfk8Y9/fD7+8Y/nl7/8ZX7xi1/k9NNPz+Mf//gkyXHHHZfTTjst69aty7HHHpskedrTnpZTTz01N998c5Lk6quvzjXXXLPZeg877LCsW7fut7mf/vSn+d73vpfrrrsut99+e571rGflda97XS666KKFe5JaC3GZdAAAAGAbMO5lzad10EEH5bjjjssBBxyQe93rXjn44IPvcv9NN92Uo48+OrfccktqrTn55JOTJG9729ty4okn5j3veU+WLVuWd73rXXnsYx+bE044IYccckiS5I/+6I9y4IEHJkke/vCH56abbsr97ne/3Pe+902SHH744Vm/fn0e+9jHJklWrFiRD3zgA1m2bNmc9e6777553etel8MPPzy33357tt9++7zjHe/ITjvtlBe+8IW5/fbbk2TkET7TKlvzAlhr1qypF1xwwVZ7PGDbsXrtGZvM29pvPgAAsNSsX78+D3vYwxa7jG3GqOe7lHJhrXXNln7XV7QAAAAAek6DBwAAAKDnNHgAAACAOW3NU7tsy6Z9njV4AAAAgJF23HHHXH/99Zo8M1ZrzfXXX58dd9xx4mW4ihYAAAAw0l577ZWNGzfm2muvXexSlrwdd9wxe+2118S/r8EDAAAAjLT99ttnn332WewymAdf0QIAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7bYoOnlHJqKeWaUso3B+bdo5RydinlyvbfPWZbJgAAAABzmc8RPO9L8vSheWuTnFNrfVCSc9qfAQAAAFgEW2zw1Fq/kOSnQ7OPTvL+9vb7kzxjgesCAAAAYJ4mPQfPvWutP2pv/zjJvReoHgAAAADGtHzaBdRaaymlznV/KeXEJCcmyapVq6Z9OICtavXaMzaZt+GkIxehEgAAgLlNegTPT0op902S9t9r5grWWk+pta6pta5ZuXLlhA8HAAAAwFwmbfB8Msnx7e3jk3xiYcoBAAAAYFzzuUz6Pyf5apKHlFI2llJelOSkJE8tpVyZ5CntzwAAAAAsgi2eg6fW+tw57jpsgWsBAAAAYAKTfkULAAAAgI7Q4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoOQ0eAAAAgJ7T4AEAAADoueWLXQDAUrF67RmbzNtw0pGLUAkAALCtcQQPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9N1eAppfx5KeWyUso3Syn/XErZcaEKAwAAAGB+Jm7wlFLul+TlSdbUWvdLsizJcxaqMAAAAADmZ9qvaC1PslMpZXmSnZP8cPqSAAAAABjH8kl/sdZ6dSnlzUm+n+RXSc6qtZ41nCulnJjkxCRZtWrVpA8HALBNWb32jE3mbTjpyEWoBADog2m+orVHkqOT7JPkd5LsUkp53nCu1npKrXVNrXXNypUrJ68UAAAAgJGm+YrWU5L8e6312lrrb5J8LMnvLkxZAAAAAMzXNA2e7yd5TCll51JKSXJYkvULUxYAAAAA8zVxg6fWel6SdUkuSnJpu6xTFqguAAAAAOZp4pMsJ0mt9dVJXr1AtQAAAAAwgWkvkw4AAADAItPgAQAAAOg5DR4AAACAntPgAQAAAOg5DR4AAACAntPgAQAAAOg5DR4AAACAntPgAQAAAOg5DR4AAACAntPgAQAAAOg5DR4AAACAnlu+2AUAjLJ67Rkj52846citXEm/jHre5nrOPMcAzNI470kATM8RPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9N1WDp5SyeyllXSnl8lLK+lLKYxeqMAAAAADmZ/mUv/+2JJ+ttT67lLJDkp0XoCYAAAAAxjBxg6eUsluSJyQ5IUlqrb9O8uuFKQsAAACA+ZrmCJ59klyb5L2llAOSXJjkFbXWXwyGSiknJjkxSVatWjXFwzGO1WvPGDl/w0lHbuVKABaG/Rpd1MftclTNc9U7TnYp6+M4A7DtmeYcPMuTHJTkXbXWA5P8Isna4VCt9ZRa65pa65qVK1dO8XAAAAAAjDJNg2djko211vPan9elafgAAAAAsBVN3OCptf44yQ9KKQ9pZx2W5FsLUhUAAAAA8zbtVbReluSD7RW0rkrywulLAgAAAGAcUzV4aq0XJ1mzQLUAAAAAMIFpzsEDAAAAQAdo8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM8tX6wHXr32jE3mbTjpyEWoBGbP9g7bJq/98Y16zpKl8bwt5XUbl9cGw2wTANNzBA8AAABAz2nwAAAAAPScBg8AAABAz2nwAAAAAPScBg8AAABAz2nwAAAAAPScBg8AAABAz2nwAAAAAPScBg8AAABAz2nwAAAAAPScBg8AAABAz2nwAAAAAPScBg8AAABAz03d4CmlLCulfL2U8q8LURAAAAAA41mII3hekWT9AiwHAAAAgAlM1eAppeyV5Mgk/7gw5QAAAAAwrmmP4Hlrkv+W5PYFqAUAAACACSyf9BdLKb+f5Jpa64WllCduJndikhOTZNWqVZM+HDDC6rVnjJy/4aQjp8rCtmSpvzZGrd9CrNuslgvbkj6+j3vtL31d2daWsnFeR30bj77Vu9RMcwTP7yU5qpSyIclpSZ5cSvnAcKjWekqtdU2tdc3KlSuneDgAAAAARpm4wVNrfVWtda9a6+okz0lybq31eQtWGQAAAADzshBX0QIAAABgEU18Dp5BtdbPJ/n8QiwLAAAAgPE4ggcAAACg5zR4AAAAAHpOgwcAAACg5zR4AAAAAHpOgwcAAACg5zR4AAAAAHpOgwcAAACg5zR4AAAAAHpOgwcAAACg5zR4AAAAAHpOgwcAAACg5zR4AAAAAHpu+WIXMB+r156xybwNJx25CJXMz6h6k+lrntVyl7pxtp9ZZWl0ZRvu29gthXqT0TV3ZZsYR9/Gg4btkq2lj9tP3/h7bXy2y22DccYRPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9p8EDAAAA0HMaPAAAAAA9N3GDp5Ry/1LK50op3yqlXFZKecVCFgYAAADA/Cyf4ndvTfIXtdaLSil3T3JhKeXsWuu3Fqg2AAAAAOZh4iN4aq0/qrVe1N6+Kcn6JPdbqMIAAAAAmJ9pjuD5rVLK6iQHJjlvxH0nJjkxSVatWrUQD7dgVq89Y5N5G046ctFrWIw65muW9XZhPLrANrFt6Nv23rdx7lu9yXjbhO1ntsulW6Z9bcyVX8rbz7jr1rd9ShfMalvr23a51Le1vtU7jr5ta320GNvP1CdZLqWsSPIvSf6s1nrj8P211lNqrWtqrWtWrlw57cMBAAAAMGSqBk8pZfs0zZ0P1lo/tjAlAQAAADCOaa6iVZK8J8n6WuvJC1cSAAAAAOOY5gie30vy/CRPLqVc3E5HLFBdAAAAAMzTxCdZrrV+KUlZwFoAAAAAmMDUJ1kGAAAAYHFp8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM9p8AAAAAD0nAYPAAAAQM8tX+wCWHyr154xcv6Gk46cybK7vFwAAOiDWf4N3wXj/L0/q+w4lvLnk1lta+Msd9walvJ4bI4jeAAAAAB6ToMHAAAAoOc0eAAAAAB6ToMHAAAAoOc0eAAAAAB6ToMHAAAAoOc0eAAAAAB6ToMHAAAAoOc0eAAAAAB6ToMHAAAAoOc0eAAAAAB6ToMHAAAAoOc0eAAAAAB6bqoGTynl6aWUK0op3ymlrF2oogAAAACYv4kbPKWUZUnekeQ/Jdk3yXNLKfsuVGEAAAAAzM80R/AckuQ7tdaraq2/TnJakqMXpiwAAAAA5qvUWif7xVKeneTptdY/an9+fpJH11r/dCh3YpIT2x8fkuSKoUXtmeS6MR56nLys7KTZrtQhu/SzXalDdulnu1KH7NLPdqUO2aWf7Uodsks/25U6ZJd+dq783rXWlVv8zVrrRFOSZyf5x4Gfn5/k7RMs54JZ5WVlJ812pQ7ZpZ/tSh2ySz/blTpkl362K3XILv1sV+qQXfrZrtQhu/Szk+QHp2m+onV1kvsP/LxXOw8AAACArWiaBs/XkjyolLJPKWWHJM9J8smFKQsAAACA+Vo+6S/WWm8tpfxpkjOTLEtyaq31sgkWdcoM87Kyk2a7Uofs0s92pQ7ZpZ/tSh2ySz/blTpkl362K3XILv1sV+qQXfrZSfK/NfFJlgEAAADohmm+ogUAAABAB2jwAAAAAPScBg8AAABAz2nwAAAAAPScBg8AAABAz018mfRplFIemuToJPdrZ12d5JO11vVjLOOFtdb3jlju/ZKcV2u9eWD+02utnx3KHpKk1lq/VkrZN8nTk1xea/30PB77n2qtL5hH7nFJDknyzVrrWUP3PTrJ+lrrjaWUnZKsTXJQkm8l+dta6w0D2ZcnOb3W+oN5POYOSZ6T5Ie11v9VSvm/kvxukvVJTqm1/mYo/4Akz0xy/yS3Jfl2kg/VWm8csexFH7d2vrHL2GO3W5rnaXDszqy1/nxLdQ0s46m11rOH5u2aZGWt9btD8/evtX5jaN59kqTW+uNSysokj09yRa31snk89t/WWv9qHrl9khyY5Fu11suH7luV5Jpa6y2llJLkhNw5bv9Qa711KH9UkrNqrbds6XHb/BOS/KTWekUp5feSPDbNdnLGiOyKNOMxOHZn1VpvH5Fd9Ned19xv81t1f9kux9iNfsxZjt3Tkjwjdx27T4x6P5qFdv90bJKaZF2SJ6fZli5P8u5R+4mh3z+31vrkmRc6oVLKPZL8aZIfJnlPkr9Ku79Ms038bIplG7sZmeW4tcv3XtfP/eWij1s739jFe12XzHqfudnH3tqXSS+l/GWS5yY5LcnGdvZeaTbe02qtJ81zOd+vta4a+PnlSV6a5kl7ZJJX1Fo/0d53Ua31oIHsq5P8pzQNrrOTPDrJ55I8Nc2H3tcPZD85/NBJnpTk3CSptR41kD2/1npIe/uP23pOT3J4kk8Nrlsp5bIkB9Raby2lnJLkl2k27sPa+c8cyN6Q5BdJvpvkn5N8tNZ67RzPywfb9do5yc+TrEjysXa5pdZ6/NBz9vtJvpDkiCRfb3/nmCQvqbV+fiC76OPWzjN2GXvsXpDk1UnOSrPzTpqxe2qS/7fW+k+j6hlR3/DY/eckb01yTZLtk5xQa/1ae9/wa+7Fad7sSpI3pmmufDPJ45L8Xa31PQPZ/zH80Emen+SfkqTW+vKB7Mdrrc9obx/d1vP5NG9+b6i1vm8g+80kh9Raf1lKeWOSByb5eJo3lNRa/3BofX+VZuw+k2bszqy13jbHc/PWNG/6y5OcmWbMPpPk0CRfr7X+16Hn7ZVJvpFme/xKmqMpH5HkD2qtlw5kF/115zV3l+dsq+4v22UZu9HPy6zG7q1JHpxmfzM4di9IcmWt9RWj6hlR33+vtb52aN7T2mWdU2vdMDD/D2utpw78/M4k90qyQ5Ibk9wtySeTHJmmifyKgexdGulpxu3BSa5Iklrr/kM17FlrvW7g5+el/cCSptFdB+47Jsn/rrX+tDRN+b9P20BP8he11o0D2ZOT/Eut9cvzeG4+neTSJLsmeVh7+yNptssDaq1HD+WflORZuesHln+stX5nKLdkx66P49b+znzHzntderm/XPRxa+cZu4w9dvaXGW9/2eYX/b1uXmqtW3Vqi91+xPwd0mxQg/O+Mcd0aZL/GMpemmRFe3t1kgvS7BCS5gPWcHZZmhfLjUl2befvlOQbQ9mLknwgyRPTfFh7YpIftbcPHcp+feD219Ic2ZAkuyS5dCi7fvAxhu67eHi5aT4AHp6mA3htks8mOT7J3Yefs/bf5Ul+kmRZ+3MZsW6XDty/c5LPt7dXjXjOFn3cjN3EY3dFkt1HPJd7JPn20LxPzjF9Kskvhtc1yX3b24ek6bgfs5nX3M5J7pnk5iT3Gahh+Dn7QTtuL2ifp+Pb5+34JMdvZty+kmSf9vaeSS4Zyn5r4PaFSbYb+Pku2YGx2yPJHyc5px2Tdw9vO232snacdk7ysyQ7t/O3T/M/PcOvj50H6jyzvb1/kq907XUXr7mZ7i+NXffGbnh8Bpa7ydjNNSX5/tDPf5vmj+63pvmj/mWbeV4ubf/dPsn1SXYYWNfhdftkO24PTbJ3u038oL2994i6Lhq4/f+kaUgfn+SjSd4ylB3cZ344yZ+n+aP9hCRnD2WvbbfF7yX5uyQHbua5uXjgOb16C9vEG5K8N8nz0nxYelOaffLXkxy7rYxd38ZtkrGL97qkh/vLxR43Yzf52M3xOre/nGN/2WYW/b1uXuMy7i9MO6X5ELj3iPl7p/m6xuC8n6Tp3O49NK1Oc6jaYPayoZ9XtC+Wk0e9sEbdnuMJ364d7LOTPLKdd9Uc63ZJmg+E90xywVyP2f780SQvbG+/N8ma9vaDk3xtrg114IVwVJqu77VD930zzY51jyQ3JblHO3/HDOx87nhhJblbe3uPwZqz6YfSRR83Yzfx2H07yW4j1nm3bPoG/LM0nfNDh6Ynpumm36WGoZ/vm6Zx8vIR6z24sx1uvAw/v3dP88bwoSS/s4VxG1zu+VtY7plJntze/pc7tud2zEc1eIbX4T7tun01yQ+Gx25grH6WZKf252UZePMYGLs7jp7caWib7tzrLl5zM91fGrvOjd03khw8Yp0Pyab7vBvnmG5KcuuIGpa3t3dP8um0f2iOeM4Gx+2zmxu3dt4xaf6gPmpz4zZi2Rcl2WXguR5evysGbl+4he3n6wPj+jdpmt6Xpzl69MEjnuM90nzouCHJ6nb+PTNifzlwe3mSLw+M4zYzdn0btwnGzntd7eX+ctHHzdhNPHb2l3W8/eXgsrOI73XzmcYKL8SU5juR30nz9YVT2umz7bynD2Xfk+RxcyznQ0M/n5v2hTr0BP1TktuG5p+XO/8HffB/8XcbftEN3LdXmhfv2zPUrRzIbEhyVZJ/b/+94+iGFcMbSftY70vT3TwvyW/a3/nfaQ7bmnMnMnTfzkM//3m7nO+l+TB6TpJ/aF9wrx7KvqLd+P6h3Tjv2DGtTPKFro2bsZt47I5va31Xmu9//lWaI1G+m+ZrVYPZzyR50hz1Di/3K0keODRv17bu4f+NuTDt//Ik2Wtg/o4Z0Vxp73tUmkNsX5lkwxyZ23Lnm8yvB8Zth2za/b9/u7wvpDki6Wftz19PctiIZW9u7PYe+vmNSb6Y5n943tQu/6/TfC3u3SOyZ7b3fzHJX7Xz75FN/6hZ9NddvOZmur/s8Ni9Yxsdu4PaOr+V5vV7VpqvCfxbkkcNZb+f5N5z1DvcBB7+Q3xZO+4fzaav+8+k/d/rofn3yVAje+C+XdJ8+PlEko2beR4vT3P4+aOyabN9eOz+vySvTdOI/vvceYTmk9Ic0j6Y3WR7SnNU4huSfGdo/nPTfNj7SZrD0f9Xmg9bVyc5cSh7Se78QLMqyb8N3Df8vC3ZsevbuE0wdt7r7nys96U/+8tFHzdjN/HY2V/W8faX7fxFf6+bzzRWeKGmNN3Tx7Qr+6z29rIpl7lX2q99jLjv94Z+vtscuT2TPGILj3NkmhMjjVPbzmm/OjLivl2THNBuhHO9eB485uP9Tu488mH3JM9Oc+6RUdmHt/c/tOvjZuymGrs90nwn+i/a6TlJ9phy7A5I8qAR87dPcy6ZwXmrMvow3vslecpmHqOk+c7zB8asbfckj53jvoelOYnbs9J8T3u7OXJPHPMxH5vkMe3tB6ZpTP3nUctP893oVyZ56sC87UZt34v9uvOau0t2UfeXxm7rjF2bv09b66M283y/bjOP98ahn/81o7/e+bokt8+zpl2S3GsLmQOS/N+buf9zQ9MdH1hG/Q/19klek+aP++8nuT1NM/1DSVYNZef8wDJHHcty5//yLk+y5o5ahnLHpflgc3Zbw5Ht/JUZ+lC4lMeub+M2ydjFe93gfb3ZXy72uBm7yceuzdtfznN/2eY78163uWmrn2R5WCnl/0gzSOtrrd+S7Wa2lLJ7necVl2aV7Uodfcu2+eW1vUpUaa7g9NA0hzb+VHZ0tmN1rEzzB89tbe7mUTnZ7mRLKSXNoc6DV6c4v87xpjtOXna22bmUUh5ah67ON8bv7pQktdZfjbjvfrXWqzf9relqGDO7LM2HpF/Ocf9uaf5IvX6O+1ds7nUzX6NqLs2VSB6Q5n9Ht/i+V0rZvm56ZZm7nHRzzJrGHrtxapim3sUYtzHXbd5jV0rZLklqrbeX5spB+6U5enfUe6hsR7IjfvcltdZ3bik3y2xX6uhTtv1b9MFp/q6Z9+eLEcuZ+L1unBomqXfa/eUdjzvpe92Wah73vW6z6pgdoWmnNJ20Pdvbz097hug0h5q9TLaz2VvTHFr2oow4Ye/WyHaljh5mT0hz8rJvp7nKwFVpDvH8QZLnym6a7UpbmMieAAAKoUlEQVQdSfZtx/k7ab6Cdl6aQ4Xfl6HzKnU4e1UHatja9R6eOw9b/8d2uuOw9cNHbGvzzsvONruFfenIw/jnyM7rf08nyI5Tw7yzM655Vuv30KGfn5TmajDXpfm6weqB++b6msaoI0v3nDQ7Tg1dqHdW6zbBsp+R5msMP0pzhO15ad4XNyb5P2U7m/0vI6br7ri9hexfLER2AZY9q5q3+nMxZvadA7cfl+aokc+l+Vv0iLlez21+RZqveM3nc9uc2XFq6EK9s1y/aevY5Pcn+aVppgycKCjN+Sru2d7eOZueM0O2O9lL01x674NpPpx+Is3XfHYaMcYzyXaljp5m90yyT5rz1TywnX/vOcZ5m892pY4034V+SHv7kCTvb2//cZJ1sp3Nrs/Ah5+B+ftk6Pvp4+ZlZ579H3NM/zPJjcPLmGvKFI2YcWpYqHqnrXlW6zfmcr+W5OHt7WcnuTJ3fm12+OSeM2nEjFlDF+qdybpNsOyvp/mqyB3vi3fsa/fOiJPbynYme1OaKw/99zQnmX11mvMbvjqbnh9mJtmu1NHD7OBFSj6X5KD29gNGjPNMGjFj1rDo9c54/SZuBo2axgovxJRmx3G/gZXdsb29LJuefEm2O9nBjXSnNOcW+Via5sLwydFmku1KHT3MXjxwe/hKBcMNBdkO1ZFNTw43OO7DH0xlu5O9Mu13rofm75Chk/CNm5edefamJCemOTn98HTdUHYmjZgxa5h3dsY1z2r9xlnu8Gv04UmuSHNEwtZqxIxTQxfqncm6TbDszV1NcpNmkGxnsqvSnDz3jbnzJMdzXdloJtmu1NHD7ODfMMNXj9rclXA/l4VrxExaw6LUuxXXb4t1bGlanq3vz5OcVUr5lzSXFju3lHJmmm7Ve2U7my133KjN9yo/kuQj7fcVn7GVsl2po2/Z75dS3pDm8uOXl1L+Pk0z6ClpDsGV3TTblTq+W0r5mzRXlHhmkouT5hwIaU5sKNvN7KlJvlZKOS3N/74kzVXcnpPmahLDxsnLzjb7tTQfar4yND+llNcMzXphmkPg/2M4m+bqGZNmx6lhnOwsa57V+o2z3N+UUu5Ta/1xktRaLyulHJbmpJ8PHMruUGu9rM2tK6WsT/KxUspfJqlTZMepoQv1zmrdxl12Sinb1VpvT/KHA/OWpWnEynYwW2v9fpJjSylHJzm7lPKW4WXNOtuVOvqWTfLQUso30nyeWF1K2aPW+rPSnH9pk21iwK611ovax7uqzU+aHaeGLtQ7y/Wbpo5NjdsRWogpzaXk/iTJW9L8L8xfZo7vaMt2I5vklWOM70yyXamjh9ldk7wqydo03+l8dpo/yN6ZoTO5y3arjjRXS/i79v7XJ7l7O3+3tP8TKtu9bDt/33aM/2c7rU2y72Zep/POy84um+QeGbpM7WbG7NwkvzvHff8+RXacGuadnXHNs1q/cZb7lAxdjridv3uSvx6ad0GGrhiT5uTpFye5aYrsODV0od6ZrNsEyz447VHkQ/NXJ3mebDezQ/evSPKmDF2Oe2tmu1JHH7JpvnI3OO3Qzt8zyTOHsr9Mc/n1S9McgblHO3+7bHqU1zjZcWpY9HpnvH5j1bGladGvogUA0DelueLFLXWOK3JMmp2lWdU8q/Wb4XKfkuTaWuslQ/N3T/LSWuvrJ8nOyqzqneW6deF5A6ZXStl7aNaPaq2/LqXsmeQJtdaPTZLtY72zWr8FX+64HaFppzTXf/9ckg+kOUT67CQ/T3PI7oGyvcresDWzXaljiWS7sP10NtuVOjq8/chuPrsiyWvTfPX1hiTXpjlJ8wlzvC/OOy/bneyspr7VO8v168Jyjd3s6+3C61m2n9mu1LGUs13Yp3Sh3lmu34I/9iKs7PlpLg383DTfhX92O/+wJF+VlZ0r25U6ZJd+tit1yPY2+4kkJ6T5OsJ/SfI3SR6U5P1J/nbEtjbvvGynsrP6w3sm9c645lmtXxeWu+hj17dx69DzJrvEs12pY4lnF32f0oV6u/KeNJ9p7F+Ydspdz84+fInLzZ1VX3Ybz3alDtmln+1KHbK9zQ5fbeZr7b/bJbl8xLY277xsp7Kz+uN0JvXOuOZZrV8XlrvoY9e3cevQ8ya7xLNdqWOJZxd9n9KFeme8fmPVsaVp/LMyT++WUsrhpZRjk9RSyjOSpJRyaJLbZGU3k+1KHbJLP9uVOmT7mf1FKeVx7f1HJflpktTmqiQlmxonL9ud7Opa6/tqrRtrrScnOarWemWaKz89c4rsrOqdZc2zWr8uLLcLY9e3cevK8ya79LNdqWMpZ7uwT+lCvbNcv3Hr2LxxO0LTTkkOSHJmks8keWiSt6U5/8RlGbpSgqys7UfWtibbw+z+ab7S9bMkX0ry4Hb+yiQvH7GtzTsv26nsV5I8rr19VJIzB+67YorsTOqdcc2zWr8uLHfRx65v49ah5012iWe7UscSzy76PqUL9c54/caqY0vTWOFZT0leKCs7SbYrdcgu/WxX6pBd+tmu1CE7OjvmH29jfWCZ1brNquZZrV8XltuFsevbuHXleZPdtrNdqaPv2a7sU7pQ76zWb6GW+9vljfsLs5wydF4DWdn5ZrtSh+zSz3alDtmln+1KHbITZWf1h/cst7UufLCY1XO8ZMeub+PWoedNdolnu1LHEs8u+j6lC/XOeP3GqqPWmtL+4lZTSvnGXHel6VbdTVZ2VLYrdcgu/WxX6pBd+tmu1CE7fnZzSinfr7WumiS7GPVOW/M42Vk9x9vq2PVt3KZdtqys99Ctm90c+8u584tR8x2WjxNeIPdO8rQ0hyANKmm+fyYrO1e2K3XILv1sV+qQXfrZrtQhO2Z2C3+83XvS7KzqnWXNs1q/Liy3C2PXt3Gb8bJlZYd1oY4lm+3IPqUL9XbiPWk+FqPB869JVtRaLx6+o5TyeVnZzWS7Uofs0s92pQ7ZpZ/tSh2y42dn9Yf3LLe1Rf+wMGbNXVhuF8aub+M2y2XLyg7rQh1LOduFfUoX6h03P6uat6yO+Z0uk8lkMplMpm19SvKetFe9GHHfhybN9rHmWa1fF5bbhbHr27h15XkzmUzTT13Zp3Sh3i68J81n2urn4AEAAABgYW232AUAAAAAMB0NHgAAAICe0+ABAJakUsrupZSXtLd/p5SybrFrAgCYFefgAQCWpFLK6iT/Wmvdb5FLAQCYucW4TDoAwNZwUpIHllIuTnJlkofVWvcrpZyQ5BlJdknyoCRvTrJDkucn+Y8kR9Raf1pKeWCSdyRZmeSXSf641nr51l8NAIAt8xUtAGCpWpvku7XWRyb5r0P37ZfkmUkOTvL6JL+stR6Y5KtJXtBmTknyslrro5K8Msk7t0rVAAATcAQPALAt+lyt9aYkN5VSbkjyqXb+pUn2L6WsSPK7ST5aSrnjd+629csEAJgfDR4AYFv0HwO3bx/4+fY0fx9tl+Tn7dE/AACd5ytaAMBSdVOSu0/yi7XWG5P8eynl2CQpjQMWsjgAgIWkwQMALEm11uuTfLmU8s0kb5pgEX+Q5EWllEuSXJbk6IWsDwBgIblMOgAAAEDPOYIHAAAAoOc0eAAAAAB6ToMHAAAAoOc0eAAAAAB6ToMHAAAAoOc0eAAAAAB6ToMHAAAAoOf+f9yTi6PGIfurAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(16, 4))\n",
    "df.plot(kind='bar', ax=ax)\n",
    "fig.tight_layout()\n",
    "#fig.savefig(\"ch14-discoveries.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 2.168457\n",
      "         Iterations 1\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Poisson Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>    <td>discoveries</td>   <th>  No. Observations:  </th>  <td>   100</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>              <td>Poisson</td>     <th>  Df Residuals:      </th>  <td>    99</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>               <td>MLE</td>       <th>  Df Model:          </th>  <td>     0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>          <td>Sun, 19 May 2019</td> <th>  Pseudo R-squ.:     </th>  <td> 0.000</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>              <td>10:19:48</td>     <th>  Log-Likelihood:    </th> <td> -216.85</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>           <td>True</td>       <th>  LL-Null:           </th> <td> -216.85</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th> </th>                      <td> </td>        <th>  LLR p-value:       </th>  <td>   nan</td> \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>    1.1314</td> <td>    0.057</td> <td>   19.920</td> <td> 0.000</td> <td>    1.020</td> <td>    1.243</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                          Poisson Regression Results                          \n",
       "==============================================================================\n",
       "Dep. Variable:            discoveries   No. Observations:                  100\n",
       "Model:                        Poisson   Df Residuals:                       99\n",
       "Method:                           MLE   Df Model:                            0\n",
       "Date:                Sun, 19 May 2019   Pseudo R-squ.:                   0.000\n",
       "Time:                        10:19:48   Log-Likelihood:                -216.85\n",
       "converged:                       True   LL-Null:                       -216.85\n",
       "                                        LLR p-value:                       nan\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      1.1314      0.057     19.920      0.000       1.020       1.243\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# attempt to fit to a poisson process\n",
    "# patsy formula \"discoveries ~ 1\" == model discoveries variable with only intercept coeff.\n",
    "\n",
    "model = smf.poisson(\"discoveries ~ 1\", data=df)\n",
    "result = model.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# lambda param of poisson distribution via exponential function\n",
    "# use to compare histogram of observed counts vs theoretical results\n",
    "lmbda = np.exp(result.params) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "X = stats.poisson(lmbda)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>1.020084</td>\n",
       "      <td>1.242721</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  0         1\n",
       "Intercept  1.020084  1.242721"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# confidence intervals\n",
    "result.conf_int()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# create upper & lower confidence interval bounds\n",
    "X_ci_l = stats.poisson(np.exp(result.conf_int().values)[0, 0])\n",
    "X_ci_u = stats.poisson(np.exp(result.conf_int().values)[0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/bjpcjp/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: VisibleDeprecationWarning: Passing `normed=True` on non-uniform bins has always been broken, and computes neither the probability density function nor the probability mass function. The result is only correct if the bins are uniform, when density=True will produce the same result anyway. The argument will be removed in a future version of numpy.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "v, k = np.histogram(df.values, bins=12, range=(0, 12), normed=True)\n",
    "#v, k = np.histogram(df.values, bins=12, range=(0, 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(12, 4))\n",
    "ax.bar(\n",
    "    k[:-1], v, \n",
    "    color=\"steelblue\",  align='center', \n",
    "    label='Dicoveries per year') \n",
    "\n",
    "ax.bar(\n",
    "    k-0.125, X_ci_l.pmf(k), \n",
    "    color=\"red\", alpha=0.5, align='center', width=0.25, \n",
    "    label='Poisson fit (CI, lower)')\n",
    "\n",
    "ax.bar(\n",
    "    k, X.pmf(k), \n",
    "    color=\"green\",  align='center', width=0.5, \n",
    "    label='Poisson fit')\n",
    "\n",
    "ax.bar(\n",
    "    k+0.125, X_ci_u.pmf(k), \n",
    "    color=\"red\",  alpha=0.5, align='center', width=0.25, \n",
    "    label='Poisson fit (CI, upper)')\n",
    "\n",
    "ax.legend()\n",
    "fig.tight_layout()\n",
    "#fig.savefig(\"ch14-discoveries-per-year.pdf\")\n",
    "\n",
    "# conclusion:\n",
    "# dataset NOT well described by poisson process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time series\n",
    "* Not same as regular regression - time series samples can't be regarded as independent random samples.\n",
    "* example model type for time series = autoregressive (AR) model - future value depends on \"p\" earlier values. AR = special case of ARMA (autoregressive with moving average) model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# outdoor temp dataset\n",
    "df = pd.read_csv(\n",
    "    \"temperature_outdoor_2014.tsv\", \n",
    "    header=None, \n",
    "    delimiter=\"\\t\", \n",
    "    names=[\"time\", \"temp\"])\n",
    "\n",
    "df.time = pd.to_datetime(df.time, unit=\"s\")\n",
    "df      = df.set_index(\"time\").resample(\"H\").mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "# extract March & April data to new dataframes\n",
    "df_march = df[df.index.month == 3]\n",
    "df_april = df[df.index.month == 4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Attempt to model temp observations using AR model.\n",
    "* Important assumption: applied to \"stationary process\" (no autocorrelation or other trends other than those explained by model terms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x216 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 4, figsize=(12, 3))\n",
    "\n",
    "smg.tsa.plot_acf(df_march.temp,                               lags=72, ax=axes[0])\n",
    "smg.tsa.plot_acf(df_march.temp.diff().dropna(),               lags=72, ax=axes[1])\n",
    "smg.tsa.plot_acf(df_march.temp.diff().diff().dropna(),        lags=72, ax=axes[2])\n",
    "smg.tsa.plot_acf(df_march.temp.diff().diff().diff().dropna(), lags=72, ax=axes[3])\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig(\"ch14-timeseries-autocorrelation.pdf\")\n",
    "\n",
    "# below: clear correlation between successive values in left-most time series\n",
    "# also: decreasing correlation for increasing order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# create AR model using March data\n",
    "model = sm.tsa.AR(df_march.temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# set fit order to 72 hours\n",
    "result = model.fit(72)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.9985623006352973"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Durbin-Watson statistical test - for stationary behavior in a time series\n",
    "sm.stats.durbin_watson(result.resid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 3))\n",
    "smg.tsa.plot_acf(result.resid, lags=72, ax=ax)\n",
    "fig.tight_layout()\n",
    "#fig.savefig(\"ch14-timeseries-resid-acf.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAEYCAYAAABBWFftAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzs3Xl8lNX1+PHPM9n3PSGBrGwJISFAgMiioqCoCKgoKtalVSpYl7ZWrfZXv21tta3VikstFkQUQUUQRUVENoGwJCFAgJBA9n3fM0km8/z+GBJZEsgyk8kk5/168Qo8M8+9ZwjLnLnnnquoqooQQgghhBBCiN7TmDsAIYQQQgghhBgoJMESQgghhBBCCCORBEsIIYQQQgghjEQSLCGEEEIIIYQwEkmwhBBCCCGEEMJIJMESQgghhBBCCCORBEsIIYQQQgghjEQSLCGEEEIIIYQwEkmwhBBCCCGEEMJIrPtyMm9vbzUkJKQvpxRCCCGEEEKIXktMTCxTVdXnSs/r0wQrJCSEhISEvpxSCCGEEEIIIXpNUZTsrjxPSgSFEEIIIYQQwkgkwRJCCCGEEEIII5EESwghhBBCCCGMpE/3YAkhhBBCCNGftbS0kJeXh1arNXcowkzs7e0ZNmwYNjY2PbpfEiwhhBBCCCHOycvLw8XFhZCQEBRFMXc4oo+pqkp5eTl5eXmEhob2aAwpERRCCCGEEOIcrVaLl5eXJFeDlKIoeHl59WoFUxIsIYQQQgghziPJ1eDW2++/JFhCCCGEEEIIYSSSYIlO1Whb+P3GY7y05SQfHchm35ky8qsa0etVc4cmhBBCCDEgVVVV8c477/To3ptvvpmqqqoez+3s7HzZx3sT22AiTS5Ep/781Uk+T8rD1kpDk07fft3OWsM/FkYzP2aoGaMTQgghhBh42pKYZcuWXfKYTqfD2rrzt+/ffPONKUO7bGziJ5JgiQ59d6KIDYl5PH7dCH49axRFNVqyyurJLK/nnZ1n+eRwriRYQgghhBjQ/vTVCU4W1Bh1zDEBrrx4a2Snjz/33HOcPXuWmJgYZs+ezS233ML/+3//Dw8PD1JTU0lLS2PBggXk5uai1Wp58sknWbJkCQAhISEkJCRQV1fHTTfdxPTp09m/fz9Dhw5l8+bNODg4XDBXZmYm9957L3V1dcyfP7/9etuvKysraWlp4aWXXmL+/PmXxPbiiy92+LzBThIscYmyuiae33icyABXHr9uJBqNQoC7AwHuDkwd4U1uRSP/+zGDGm0LrvY9Ox9ACCGEEEJc6pVXXiElJYXk5GQAdu3aRVJSEikpKe1tw1etWoWnpyeNjY1MmjSJO+64Ay8vrwvGSU9PZ926dbz33nvcddddfP7559x3330XPOfJJ59k6dKl3H///bz99tvt1+3t7dm0aROurq6UlZURFxfHvHnzLolNp9N1+LzB3iREEixxAVVVee7z49Q26Vi3KAZb60u36V0f4cu7u8/yY1oZt0T7myFKIYQQQgjTu9xKU1+aPHnyBWcyLV++nE2bNgGQm5tLenr6JQlWaGgoMTExAEycOJGsrKxLxt23bx+ff/45AD/72c949tlnAcP7weeff549e/ag0WjIz8+nuLj4kvs7e96QIUOM8rotlSRY4gKfJeSx/VQxf7glglF+Lh0+Z3ygO+6ONvxwqlgSLCGEEEIIE3Nycmr/+a5du9i+fTvx8fE4Ojpy7bXXdnhmk52dXfvPraysaGxs7HDsjlab1q5dS2lpKYmJidjY2BASEtLhHF193mAjXQRFu9yKBv701QmmhHry82mdn1xtbaVh5mhfdp4uoVU6CgohhBBCGI2Liwu1tbWdPl5dXY2HhweOjo6kpqZy4MCBHs81bdo01q9fDxiSpfPn8PX1xcbGhp07d5Kdnd1hbJ09b7CTBEsA0KpX+e1nR1EUhX/dNQ6N5vK1s9eF+1LZ0EJybmUfRSiEEEIIMfB5eXkxbdo0xo4dy+9+97tLHp8zZw46nY6IiAiee+454uLiejzXG2+8wdtvv01UVBT5+fnt1xcvXkxCQgJRUVGsWbOG8PDwDmPr7HmDnaKqfbcCERsbqyYkJPTZfKLrNibl8ZtPj/KPhdHcFRt4xedXN7Yw8S/f88jVYTw7R/4yCSGEEGJgOHXqFBEREeYOQ5hZR38OFEVJVFU19kr3XnEFS1GUVYqilCiKktLBY79VFEVVFMW7WxGLfmdNfDbDfZy4c+KwLj3fzcGGSSGe7DhVYuLIhBBCCCGEsBxdKRFcDcy5+KKiKIHADUCOkWMSfSwlv5rk3CruiwvuVlvN6yN8OV1cS25FgwmjE0IIIYQQwnJcMcFSVXUPUNHBQ68DzwDS5cDCfXQgGwcbK26f0LXVqzbXR/gBsCNVVrGEEEIIIYSAHja5UBRlPpCvqurRLjx3iaIoCYqiJJSWlvZkOmFC1Y0tfJGcz/yYANwcundocKi3E2HeTvwgCZYQQgghhBBADxIsRVEcgeeBP3bl+aqqrlBVNVZV1VgfH5/uTidMbGNSHtoWPffFBffo/usjfDlwtpz6Jp2RIxNCCCGEEMLy9GQFazgQChxVFCULGAYkKYoyuI9stkCqqvLRgWxiAt0ZO9StR2NcF+5Hc6ueH9PLjBydEEIIIYQQlqfbCZaqqsdVVfVVVTVEVdUQIA+YoKpqkdGjEyYVn1HO2dJ6ftbD1SuA2BAPXOyt2ZFabMTIhBBCCCFEV+zatYv9+/f3agxnZ2ejxLJ69WoKCgqMMpYl60qb9nVAPDBaUZQ8RVF+YfqwRF/46EA27o423BLt3+MxbKw0XDvalx2ppej10u9ECCGEEKIvGSPBMhZJsAysr/QEVVXvucLjIUaLRvSZ4hot204U8/PpodjbWPVqrOvDffnqaAHH8quJCXQ3UoRCCCGEEGb27XNQdNy4Yw6JgpteuexTFixYQG5uLlqtlieffJIlS5YAsHXrVp5//nlaW1vx9vZm5cqVvPvuu1hZWfHRRx/x5ptvsnLlSubOncvChQsBw+pUXV0ddXV1zJ8/n8rKSlpaWnjppZeYP3/+ZeN47bXXWLVqFQAPP/wwTz31FFlZWcydO5eUFMMRua+++ip1dXWMHTuWhIQEFi9ejIODA/Hx8aSkpPDkk09SX1+PnZ0dP/zwAzY2NixdupSEhASsra157bXXmDlzJqtXr+aLL76gvr6e9PR0nn76aZqbm/nwww+xs7Pjm2++wdPTk7Nnz/LYY49RWlqKo6Mj7733HuHh4b39rhjVFRMsMTCtP5SLTq+yeEpQr8e6ZpQPGgV+OFUsCZYQQgghRC+tWrUKT09PGhsbmTRpEnfccQd6vZ5HHnmEPXv2EBoaSkVFBZ6enjz66KM4Ozvz9NNPA7By5coOx7S3t2fTpk24urpSVlZGXFwc8+bN6/QM1MTERN5//30OHjyIqqpMmTKFa665Bg8Pjw6fv3DhQt566y1effVVYmNjaW5uZtGiRXzyySdMmjSJmpoaHBwceOONN1AUhePHj5OamsoNN9xAWloaACkpKRw5cgStVsuIESP4+9//zpEjR/j1r3/NmjVreOqpp1iyZAnvvvsuI0eO5ODBgyxbtowdO3YY4XfdeCTBGoR0rXrWHcrh6lE+BHs59Xo8Dydbooa6kZBVaYTohBBCCCH6iSusNJnK8uXL2bRpEwC5ubmkp6dTWlrK1VdfTWhoKACenp7dGlNVVZ5//nn27NmDRqMhPz+f4uJihgzpuE/d3r17ue2223ByMrxXvP322/nxxx+ZN29el+Y7ffo0/v7+TJo0CQBXV9f2cR9//HEAwsPDCQ4Obk+wZs6ciYuLCy4uLri5uXHrrbcCEBUVxbFjx6irq2P//v3ceeed7fM0NTV16/ehL0iCNQhtP1VCUY2WvywYa7QxR/q5sDtNzjkTQgghhOiNXbt2sX37duLj43F0dOTaa69Fq9V2+X5ra2v0ej0Aer2e5uZmANauXUtpaSmJiYnY2NgQEhLSrXE7Gh/o0RidsbOza/+5RqNp/7VGo0Gn06HX63F3dyc5Odloc5pCjw4aFpbtk8M5DHG157pwX6ONOdLXmdLaJqobWow2phBCCCHEYFNdXY2HhweOjo6kpqZy4MABAOLi4tizZw+ZmZkAVFRUAODi4kJtbW37/SEhISQmJgLw5Zdf0tLS0j6ur68vNjY27Ny5k+zs7MvGMWPGDL744gsaGhqor69n06ZNzJgxAz8/P0pKSigvL6epqYktW7a033N+LKNHj6awsJDDhw8DUFtbi06nY8aMGaxduxaAtLQ0cnJyGD16dJd+b1xdXQkNDeWzzz4DDKtyR48e7dK9fUkSrEGmpEbL7rRS7pg4FCtNxzW3PTHC19De80xp7RWeKYQQQgghOjNnzhx0Oh0RERE899xzxMXFAeDj48OKFSu4/fbbGTduHIsWLQLg1ltvZdOmTcTExPDjjz/yyCOPsHv3bsaNG0d8fHx7id/ixYtJSEggKiqKNWvWXLExxIQJE3jwwQeZPHkyU6ZM4eGHH2b8+PHY2Njwxz/+kcmTJzN79uwLxnnwwQd59NFHiYmJobW1lU8++YTHH3+ccePGMXv2bLRaLcuWLUOv1xMVFcWiRYtYvXr1BStXV7J27VpWrlzJuHHjiIyMZPPmzd39LTY5RVX7rrV2bGysmpCQ0GfziUu9u/ssr3ybyo7fXkOYj3HOPADIKW/g6n/u5O93RLFoUu8bZwghhBBCmMOpU6eIiIgwdxjCzDr6c6AoSqKqqrFXuldWsAYRVVXZkJhHbLCHUZMrgKEeDthZa0gvrjPquEIIIYQQQlgSSbAGkeTcKs6U1LFw4jCjj22lUQjzceZMqSRYQgghhBBi8JIEaxDZkJiHvY2GW6L9TTL+SF9nzpRIgiWEEEIIIQYvSbAGCW1LK18eLeCmsf642NuYZI4Rvs7kVTbS0KwzyfhCCCGEEEL0d5JgDRLbThZTq9WZpDywzchznQQzSutNNocQQgghhBD9mSRYg8SGxDyGujtwVZiXyeZoa9WeXiKt2oUQQgghxOAkCdYgUFjdyI/ppdwxYSgaI559dbFgLyesNYrswxJCCCGE6EecnQ0fghcUFLBw4cLLPvff//43DQ0N3Rp/165dzJ07t8fxne9vf/ubUcYxJ0mwBoGNSfmoKtxhwvJAAFtrDcFejpJgCSGEEEKYWGtra7fvCQgIYMOGDZd9Tk8SLGMaCAmWtbkDEKbVdvbV5FBPgr2cTD7fCF9n0iXBEkIIIcQA8PdDfye1ItWoY4Z7hvPs5Gc7fTwrK4s5c+YwceJEkpKSiIyMZM2aNTg6OhISEsKiRYv4/vvveeaZZ5g0aRKPPfYYpaWlODo68t577xEeHk5mZib33nsvdXV1zJ8//4Kx586dS0pKCq2trTz77LNs3boVjUbDI488gqqqFBQUMHPmTLy9vdm5cyfbtm3jxRdfpKmpieHDh/P+++/j7OzM1q1beeqpp3B0dGT69OkdvhatVsvSpUtJSEjA2tqa1157jZkzZ7J69WoSEhJ46623AJg7dy5PP/00W7dupbGxkZiYGCIjI1m7di1r1qzh1VdfRVEUoqOj+fDDD8nKyuLnP/85ZWVl+Pj48P777xMUFMSDDz6Ig4MDR44coaSkhFWrVrFmzRri4+OZMmUKq1evBuj0NRmLrGANcEk5lWSW1Zu0ucX5Rvq6kF3eQLNO3yfzCSGEEEIMNKdPn2bZsmWcOnUKV1dX3nnnnfbHvLy8SEpK4u6772bJkiW8+eabJCYm8uqrr7Js2TIAnnzySZYuXcrx48fx9+/4eJ4VK1aQlZVFcnIyx44dY/HixTzxxBMEBASwc+dOdu7cSVlZGS+99BLbt28nKSmJ2NhYXnvtNbRaLY888ghfffUViYmJFBUVdTjH22+/jaIoHD9+nHXr1vHAAw+g1Wo7fd2vvPIKDg4OJCcns3btWk6cOMFLL73Ejh07OHr0KG+88QYAjz/+OA888MAFcbeprKwkPj6e119/nXnz5vHrX/+aEydOcPz4cZKTkzt9TcYkK1gD3OdJ+TjaWnFLlGnOvrrYCF9nWvUqWeX1jPJz6ZM5hRBCCCFM4XIrTaYUGBjItGnTALjvvvtYvnw5Tz/9NACLFi0CoK6ujv3793PnnXe239fU1ATAvn37+PzzzwH42c9+xrPPXvo6tm/fzqOPPoq1tSEd8PT0vOQ5Bw4c4OTJk+2xNDc3c9VVV5GamkpoaCgjR45sj3HFihWX3L93714ef/xxAMLDwwkODiYtLa3Lvw87duzgzjvvxNvb+4IY4+Pj2bhxY/vre+aZZ9rvufXWW1EUhaioKPz8/IiKigIgMjKSrKws8vLyOnxNxiQJ1gC3N72MaSO8cbLrm291WyfBMyV1kmAJIYQQQvSAoiid/trJybDlQ6/X4+7uTnJycpfG6AlVVZk9ezbr1q274Hpnc3aVtbU1ev1P1U6XW9XqLjs7OwA0Gk37z9t+rdPpsLKy6vA1GZOUCA5ghdWN5FQ0MCX00k8kTGW4jzOKAunFsg9LCCGEEKIncnJyiI+PB+Djjz/ucI+Tq6sroaGhfPbZZ4AhGTp69CgA06ZNY/369QCsXbu2wzlmz57Nf//7X3Q6HQAVFRUAuLi4UFtrOHInLi6Offv2cebMGQDq6+tJS0sjPDycrKwszp49C9BpsjJjxoz2+dPS0sjJyWH06NGEhISQnJyMXq8nNzeXQ4cOtd9jY2NDS0sLANdddx2fffYZ5eXlF8Q4derUC17fjBkzLvfbeYHOXpMxSYI1gB3KNPwhnBJqurOvLuZga8VQdwfOlEqCJYQQQgjRE6NHj+btt98mIiKCyspKli5d2uHz1q5dy8qVKxk3bhyRkZFs3rwZgDfeeIO3336bqKgo8vPzO7z34YcfJigoiOjoaMaNG8fHH38MwJIlS5gzZw4zZ87Ex8eH1atXc8899xAdHd1eHmhvb8+KFSu45ZZbmDBhAr6+vh3OsWzZMvR6PVFRUSxatIjVq1djZ2fHtGnTCA0NZcyYMTzxxBNMmDCh/Z4lS5YQHR3N4sWLiYyM5IUXXuCaa65h3Lhx/OY3vwHgzTff5P33329vetG2N6srOntNxqSoqnr5JyjKKmAuUKKq6thz1/4J3Ao0A2eBh1RVrbrSZLGxsWpCQkKvgxZd88Km42xOLiD5j7Oxtuq7XPqh9w9RVNPEt092/dMEIYQQQoj+4NSpU0RERJht/vM7/Qnz6ejPgaIoiaqqxl7p3q68614NzLno2vfAWFVVo4E04PddC1X0pcNZFUwM9ujT5AoM+7DOltbRqr988i6EEEIIIcRAc8V33qqq7gEqLrq2TVVV3blfHgD6pge46LKK+mbSiuuY3If7r9qM9HWhWacnr9J8h9SJn5TVNfGfXWcprjHeBlIhhBBCmEZISIisXlk4Yyxt/Bz4trMHFUVZoihKgqIoCaWlpUaYTnTF4ay2/Vd9n2ANP9dJUBpd9A/v7cng71tTufofO/nr1ycpr2syd0hCCCFEv3alLTRiYOvt979XCZaiKC8AOqDj9iSAqqorVFWNVVU11sfHpzfTiW44lFmBnbWGqGFufT53e6t2aXRhdqqq8m1KEROC3JkbHcDKvZlc/Y+d/GvbaaobDR169HqVWm0LhdWNZJTWoWuVQ6KFEEIMXvb29pSXl0uSNUipqkp5eTn29vY9HqPHhyMpivIghuYX16vyJ7DfOZRZQUygO3bWVn0+t5uDDb4udpwpkQTL3E4W1pBT0cDSa4dzz+Qgll4bxuvb03lzxxne+zEDG42GumYd5/8NDvV24rGZI1gQE9Dn+/eEEEIIcxs2bBh5eXlI5dXgZW9vz7BhPd8B1aMES1GUOcAzwDWqqspGm36mVtvCiYJqfjVzhNliGOHrTLokWGa3NaUIjQI3jPEDYISvC2/fO4Fl11bzWUIeGkXB2d4aFztrnO0N/xx8GJ/N058dZfkP6fxq5ghumzAUG0m0hBBCDBI2NjaEhoaaOwxhwa6YYCmKsg64FvBWFCUPeBFD10A74Ptzp0QfUFX1URPGKbohMbsSvQqT+/D8q4uN9HXm86R8VFU1ykniome+TSlicqgnXs52F1yPDHAjcl7H5aN3Twpk+6kS3vghjWc+P8byHen8c+E4rhpuvj9PQgghhBCWoitdBO9RVdVfVVUbVVWHqaq6UlXVEaqqBqqqGnPuhyRX/cihzAqsNQoTgt3NFsMIX2fqmnQUSec6szlTUsuZkjrmRA7p1n2KojB7jB9f/Wo6qx6MRVXhT1+dkFp0IYQQQogukLqfAehwVgVjh7rhaNvjLXa9NsLXBUD2YZnR1pQiAOaM9e/R/YqicF24H8tmDie1qJbk3CueJS6EEEIIMehJgjXAaFtaOZpbbZb27Odr7yQoCZbZfJtSxPggd4a49bwLDsC8cQE42FjxyeFcI0UmhBBCCDFwSYI1wCTnVtHcqjfLAcPn83a2xc3BRhpdmElOeQMnCmq4aWz3ygM74mJvw63j/PnyaAF1Tbor3yCEEEIIMYhJgjXAHMqsQFEgNti8CZaiKIz0deaMHDZsFltPFAJwUw/LAy929+QgGppb+epogVHGE0IIIYQYqCTBGmAOZVYQPsQVN0cbc4fCSD8XThfXSnMEM/g2pYjIAFcCPR2NMt74QHdG+7mw/lCOUcYTQgghhBioJMEaQFpa9SRmVzI5xMPcoQAQGeBKdWML+VWN5g5lUCmsbuRITpVRygPbKIrCokmBHM2r5mRBjdHGFUIIIYQYaCTBGkBS8qtpbGk16/lX5xsT4Aogb8j72He97B7YmdsnDMXWWsP6w7KKJYQQQgjRGUmwBpDDWRUATArtHytYEUNc0ShwQhKsPvVtShEjfZ3bOzkai7ujLTeNHcKmI/k0NrcadWwhhBBCiIFCEqwB5FBmBWHeTvi69K4tt7E42FoR6u3EyUJJsPpKWV0Th7MqjFoeeL67JwVRq9XxzfFCk4wvhBBCCGHpJMEaIFRVJSG7kth+sv+qTWSAm5QI9qFtJ4rRq8YvD2wTF+ZJqLeTlAkKIYQQQnRCEqwBIqOsnqqGFiYG968Ea0yAK/lVjVTWN5s7lEFhy7ECQrwcifB3Mcn4bc0uDmdVcqak1iRzCCGEEEJYMkmwBoik7EoAJgT1rwQr8lyji1NSJmhyRdVa4jPKmR8zFEVRTDbPHROGYa1RWH8o12RzCCGEEEJYKkmwBoiknCpc7a0Z7mPcxga9NcbfkGBJowvT+/JoPqoKC8YPNek8Pi52XD3Khx2pJSadRwghhBDCEkmCNUAcyakkJsgDjcZ0Kxc94eVsxxBXe2l00Qc2HSlgXKA7od5OJp8repgbmeX1NDTrTD6XEEIIIYQlkQRrAKjVtnC6uJYJQe7mDqVDYwJcOVFQbe4wBrTTRbWcKqxhQUxAn8wX4e+KqhrmFUIIIYQQP5EEawA4mluNqva//VdtIgNcOVtaj7ZFzk4ylS+S87HSKMyN7psEq630M1USLCGEEEKIC0iCNQAk5VSiKBDTX1ew/F1p1auy2mEier3Kl8kFTB/hjY+LXZ/MOdTdAWc7a2leIoQQQghxEUmwBoCknEpG+jrjam9j7lA6FBngBiD7sEzkcFYF+VWN3Gbi5hbn02gUwoe4SIIlhBBCCHERSbAsnF6vciSnqt+WBwIM83DAxc5a9mGZyBfJBTjYWDF7jF+fzhvh70pqYS2qqvbpvEIIIYQQ/ZkkWBYuo6ye6saWfp1gaTQKEQGunJRW7UbXpGvl62MF3Bjph5OddZ/OHeHvSm2TjrzKxj6dVwghhBCiP7tigqUoyipFUUoURUk575qnoijfK4qSfu5r/313P8Al5Zw7YDi4f+6/ajPG35VThbW06mW1w5h2nS6lRqtjfh+WB7aJ8HcBpPRTCCGEEOJ8XVnBWg3Muejac8APqqqOBH4492thBkdyKnG1tybMu38dMHyxyABXGltaySyrN3coA8oXR/LxcrJlxgjvPp979BAXFAXZhyWEEEIIcZ4rJliqqu4BKi66PB/44NzPPwAWGDku0UVJ2VWM74cHDF9sTIChrbesdhhPdWMLP6SWcOu4AKyt+r7a19HWmlAvJ0mwhBBCCCHO09N3ZX6qqhae+3kR0OnuekVRliiKkqAoSkJpaWkPpxMdqdG2kFZS26/3X7UZ6euCjZUijS6MaGtKIc06PQvMUB7YJuJc6acQQgghhDDo9cfeqqGFWKcba1RVXaGqaqyqqrE+Pj69nU6c52huleGA4X6+/wrA1lrDSF8XaXRhRJ8n5RPi5ci4YW5miyHC34WcigZqtS1mi0EIIYQQoj/paYJVrCiKP8C5ryXGC0l0VVJ2leGA4cD+n2CBYR/WyYIaaettBGdL6ziUWcGdsYEoivnKQyP8DaWfcoi0EEIIIYRBTxOsL4EHzv38AWCzccIR3ZGUU8koXxdc+ukBwxcbE+BKeX0zJbVN5g7F4q0/lIO1RuHO2GFmjSP8XIJ1ShIsIYQQQgiga23a1wHxwGhFUfIURfkF8AowW1GUdGDWuV+LPmQ4YLjSIsoD20QGGErZZB9W7zTpWtmQmMfsMX74utibNZYAN3tc7a2l0YUQQgghxDlXPJlUVdV7OnnoeiPHIroho6yOGq2O8RbQ4KJN+7lJBTVcF95pXxRxBd+dKKayoYV7JgeZOxQURTnX6EISLCGEEEIIMEKTC2EeSdlVABbRQbCNi70NwV6OnJBGF72y7mAOgZ4OTDfD2VcdifB35XRRLXo5RFoIIYQQQhIsS5WUU4mbgw1h3k7mDqVbxvi7SoLVCxmldcRnlHP3pKB+c/bZGH9XGppbya5oMHcoQgghAJrq4LsXDD9apcurEH1NEiwLlZRTyfgg937zJrurxg51I6eigcr6ZnOHYpHWH87tF80tztfWSVDKBAeGFzen8Pr3aeYOQwjRU5k/wn+mQvxbhh/r7oHmenNHJcSgIgmWBdK2tJJeUse4YZbT4KLNpBBPAA5nVZg5EsvT1txiVoT5m1ucb6SfM1YaRRKsAWD7yWI+iM/mowPZcpyCEJamqQ6++R18MBcUDTz4Ddz6Bpz9AVbPhfoyc0coxKAhCZbVfk1KAAAgAElEQVQFKqhqRFUhyNPR3KF0W/QwN2ytNRzMlASru7adKKaivpl7ppi/ucX57G2sCPN2kgTLwjU063jxyxPYWCmU1zdzpqTO3CEJIboq54Bh1erQCpjyKCzdByHTYOKDsGgtlJyElbOhItPckQoxKEiCZYEKqrQABLg7mDmS7rO3sWJ8oDsHM8vNHYrFWXcoh2EeDszoJ80tzmfoJChnYVmyf29PJ7+qkX8sjAYgPkP+jgphEVp1sP5ew88f/AZu+jvYnrc/O/xmuP9LaKw0JFkFR8wTpxCDiCRYFqiguhGAAPf+UybWHVPCvDhZUEONVjbedlVmWT37z5Zzz+T+09zifOH+LuRXNVLdIN9TS3SioJqVezO5Z3IgC2KGEuBmzwFJsISwDHmHoKEcbviLYdWqI0FT4OfbwNoePrpDGl8IYWKSYFmgwnMrWEPcLDTBCvVEr0JiVqW5Q7EY6w/nYKVRuHNi/2lucb72RhdFUiZoaVr1Ks9vSsHD0YZn54SjKApxYV4cyKiQfVhCWILT34LGBsJmXv55PqNgziuGZCwnvm9iE2KQkgTLAhVWN+LtbIudtZW5Q+mRCUEe2FgpHJAywS5RVZWNSflcH+6Lr2v/TKrHnEuwUmUflsX5+GA2R3Or+MMtY3B3tAUgbrgXFfXNpMs+LCH6v7TvDCtX9q5Xfm7YtWBla7hHCGEykmBZoIJqLf5ulrf/qo2DrRXRw9w5JI0uuiS9pI7S2iZmjfEzdyid8nWxw9PJVvZhWZjiGi3/2Hqa6SO8mR8T0H79qjAvAOLPyocgQvRrFRlQdhpG3dS159s5Q/A0SN9m2riEGOQkwbJAhVWN+FtoeWCbKaGeHM+rpqFZZ+5Q+r22vTBtb3r7I0VRiPB3kRJBC9Kka+WFTSk0tep5acFYFOWnvX3DPBwY6u4g+7CE6O/aVqJG3dD1e0bdCGVp0lFQCBOSBMsCFVZrLbKD4Pkmh3qi06skZVeZO5R+L/5sOUPdHQjs5235xwa4kVpYS1WDHCLd350qrGH+W/vYfqqYZ24cTYi30wWPt+3DOphZgV4v+7CE6LfStoL3aPAM6/o9I88lY+nfmyYmIYQkWJamRttCXZPO4lewYkM8sdIo0q79CvR6lYOZFcT149WrNvNjhtLcqmdDYp65QxGdaNWrrNhzlvlv7aOsrplVD8by8IyO35jFhXlSUd9MWomUfQphNpdrNKOtgax9MHpO98b0Gg6ewyFd9mEJYSqSYFmYtg6C/ha+guVsZ83YAFcOZsg+rMtJK6mlor6Zq4b3/wRrTIArE4Lc+fhgjnSf64fyKhu4970D/O2bVK4d7cN3T83guvDO9/W1JfUHZB+WEOZRehpeHgYZuzp+/OwO0LfAqG4mWGAoE8z8EZrrexWi6Oeq8wxlpPJ/cp+TBMvCtJ2BNdRCz8A63+RQT5Jzq9C2tJo7lH6r7c1tXJinmSPpmvvigsk4d2aX6D/K6pq4ZfleThTU8M+F0fz3ZxPxcra77D2Bno7n9mHJhyBCmMXpb6C5Dr591nCY8MXSvgN7dxg2ucPbG1oaaNQ1djz2yBugtQky9xgxYNFvVGbBl0/AGzHw8V2wf7m5Ixp0JMGyMO0rWBbcRbDNlFAvmlv1JOfKPqzOxGeUE+jpwDCP/r3/qs3NUf54ONrw0YFsc4cizrMxKY/qxhbWL4njztjACxpaXM5Vw704mFku+7AGiKbWJnR6aSxkMTJ2gY0TlKZC4vsXPqZvNZT4jbwBrKwveKhSW8kbSW8w89OZzPpsFt9ldVAKGDwNbJ2lXftAU34WvlgGyyfA0XUw8QEYMx++/yMc32Du6AYV6ys/RfQnhdWNaBRDW2xLNynEE0WBgxmWsceor7Xtv5od0X/bs1/M3saKO2MDWbk3k+IaLX799NyuwURVVT45nMuEIHfGDnXr1r1xYV5sSMzjdHFt+2HSwrKoqsqJ8hN8evpTtmZtxcXGhV9E/YI7Rt2BnZXl/z8yYLU0QnY8TPoFFB2HnX+DqIXg4GF4PD/RcGDwqBvbbylrLGPNiTWsP70erU7LjSE3kl+Xz9O7n2ZP3h5+P/n3ONs6G55sbWs4Eyt9m6F8rIsfuoh+SK+HrD2QsApOfWU452zyEpj2BLgGgK4J6sth06Pg7AuhV5s74kFBVrAsTH5VI36u9lhbWf63zs3RhvAhrhzKknKyjqQW1VLV0GJxyee9k4No1Rve1AvzS8qp5GxpPYsmBXb73rbSVGnXbnnqW+r5LO0zFm1ZxD1f38PWrK3MCZnDMJdhvHzoZW7eeDPrU9fT3CpdP/ul3IOGEr6wmTDnZWishN3//Onx09+CYgUjrken17E8aTk3fX4TH5z8gOuDrueL+V/wz2v+yQc3fcDScUvZkrGFhV8tJLE48acxRt0INflQfKLvX5/ovfpy2Lcc3poIa+Yb9tRNfRyeOg43vWJIrgCs7eDujwzNTdbfB8UnzRv3ICErWBamsEpr8R0Ezzcl1JP1h3No1umxtbb8pNGY4s+9qY2zgAYX5wvxdmLGSG/WHcph2bXDB8SHAZbsk8O5ONpacUt0wJWffJFhHo4EehrOw3poWqgJohOmUFBXwOJvFlPWWMYoj1G8MOUFbgm7BRdbF1RV5WDRQd5Jfoe/HvwrK1NW8sykZ5gdPNvcYYvzZewCjTUETzUcDjzhfjj0X4j9OXiPMJT2BU+lxsqK3/3wGPsL9jM3bC6PjnuUYNfg9mFsNDYsi1nG1ICpPL/3eR7a+hCPxTzGL8f9Ekac+56nfwdDxprndYorS/0G8g5DUw001Rq6R2qrIT8BWpsh6Cq49vcQMQ9sOnl/6OABizfA/2bB2oXw8PafEjBhEvLOx8IUVjdafAfB88WFeaJt0XM8X/ZhXexARjlB5xoNWJr74oIprNayI7XE3KEManVNOrYcK2RutD/Odj37PC0uVM7DsiSNukae2vkUTbom3r/xfTbcuoG7w+/GxdYFOHfGmX8cH8z5gBWzV+Bm68YLe1+gvkW6yfUrGbsMzSvszpX0XfcHsHaAbX+AqhwoOUFOSBz3fXMfh4oO8eepf+blGS9fkFydL8Y3hg23bmBW8CzeSn6L4vpicPWHIdFyHlZ/lvkjrL/H0KQiZaNhZbMmz1DSOfEhWBoPP98K0Xd1nly1cQ+ExZ8ZkrO1d0JzQ9+8hkGqVwmWoii/VhTlhKIoKYqirFMUZeAsrfRDqqoaDhkeQCtYk0IMJUgHM6VT2fla9SoHM8q5ysLKA9tcH+7LEFd7PjqYY+5QBrWvjxXQ0Nzao/LANnFhXlQ1tJBaJOdh9XeqqvKn+D+RWpHKK1e/QuyQ2E4bmiiKwlUBV/GHuD/QqGtkW9a2Po5WdKqhAgqSDXuk2jj7wtVPQ9q38N3zHLK3496Cr6nUVrJi9gpuG3nbFYd1tHHk8fGPA7A9Z7vh4qgbDW/aG+T/4H6nuR6+/JXhEOnncuHZTHjyKDy6Fx76Bm7+B/iN6d6Y/tGw4B0oToGMnaaJWwC9SLAURRkKPAHEqqo6FrAC7jZWYOJSFfXNNOn0A6KDYBsvZztG+jrLeVgXOVVYQ41WR9xwy2jPfjFrKw13Tw5kT1op2eXyybi5fHI4l+E+TkwI8ujxGG0lqrIPq//76NRHfJ3xNY/FPMbVw7q2kX2czzhC3ULZdGaTiaMTXZb1I6BemGABxC0FjxA+z93BL4f44eXoy8c3f8ykIZO6PHSoWygj3Efwffa5VauRN4KqN5ypJfqXHS8Z2q3PewtsjdhJePh1hq+yF8ukelsiaA04KIpiDTgCBb0PSXSmsNrQoj1gAJyBdb4pYZ4kZleia9WbO5R+o+3NrKU1uDjf3ZOCsNIofCyrWGZxpqSWpJwqFk3qelv2jgx1dyDI01ESrH7uUOEh/pXwL64Pup5Hoh/p8n2KonDbiNs4UnKEzOpME0YouixjF9i6wNAJF163tuPwlJ/zfz5eTLHz4aObPyLQtfur07ODZ5NUnERZY5lhDkcvadfe3+QcgAP/gUmPQMg0445t5wIeIVAizU1MqccJlqqq+cCrQA5QCFSrqnpJjYGiKEsURUlQFCWhtLS055EKCqoMBwYOpBUsMJyHVdek41h+tblD6TcOZJQT4uVo0d/rIW72zI7w49OEXGq1LeYOZ9D55HAu1hqF2ycM6/VYU0I9OZRVgarKPqz+qKCugKd3P02wazB/nf5XNEr3/mu/dfitWClWfHHmCxNFKLolYxeETAcrmwsuN7c285eiHxhq48brc1a176vrrtnBs1FR2ZGzAzRWhmYXZ7YbztYS5tfSCJsfA7dAmPV/ppnDN1K6R5pYb0oEPYD5QCgQADgpinLfxc9TVXWFqqqxqqrG+vj49DxScd4KluW+6e7IjJHeWGkUfjhVbO5Q+oXWc+dfXWVh3QM7suSaMGq0OpatTaJFVij7TEurno1J+Vwf4Yu3c+/POpoY7EFVQwuZZVLu2d80tzbz1M6n0Ol1vDHzDZxsnLo9hreDNzOGzeDLs1/KQcTmVpUDFRkQds0lD61KWUVmdSYvXP0yDh4hPZ5ihPsIQlxD2JZ97jPx4ddBYwWUnOrxmMKIdr0M5Wdg3vKfmpxcQUNLA68nvs5vd/2WkoYuNJfyG2M4lLhF28tgRWd6UyI4C8hUVbVUVdUWYCMw1ThhiY4UVDdia6XBy8nW3KEYlbujLZNDPPn+pCRYACcLaqjV6iy6PLDNhCAPXr49ih/Ty3h+43FZAekjP5wqoby+uVfNLc43/tweriM50u2zv9mQtoFTFaf4y/S/EOIW0uNxbhtxG2WNZezL32e84ET3Zew2fA279oLLWdVZvHfsPeaEzGHGsBm9mkJRFGYHzyahKIFKbSUMiTI8IAmW+eUnwv43DW35h8/s0i07cnYwf/N8VqWsYlfuLu748g525lyhgYVfJKitUHbaCEGLjvQmwcoB4hRFcVQMBf7XA/K304QKq7QMcbNHoxl4J67PHuNHWnGdNEQA4jPKAMvef3W+u2IDefL6kXyWmMcbP6SbO5xB4dOEXPxc7bh6pHGqBkb6OuNiZ82R3EqjjCeMQ6vTsvL4Sib6TeS6wOt6NdaMYTPwtPeUZhfmlrELnP3AJ7z9kqqqvHTgJeys7Hhm0jNGmeaGkBtoVVvZmbsTvEYYztwqkaYHZlWQDJuWgvMQuOGlKz+9roDHf3icJ3c+iYutC2tuWsNn8z5jiNMQntj5BC8deAmtrpMVKt9Iw1cpEzSZ3uzBOghsAJKA4+fGWmGkuEQHCqsbB9Qhw+ebPcYPQFaxgAMZFYR5O+HnOnC+10/NGsnCicP49/Z0Pk3INXc4A1pRtZZdp0tYOHGY0Q551mgUxgW6ywpWP7MhbQMljSU8FvNYrxqZgOFA2nnD57E7dzfljdLQxCz0ekOCFXat4Zyjc7ZkbOFg0UGemvgUPo7G+dBktMdohjkPM5QJWtuC10hZwTIHfSuc+grevxlWXAM1+TD/LbB3u+xt61PXs2DzAg4WHeTp2Kf5ZO4njPcdT5hbGGtvXsv9Y+7nk9OfcM/X95BWmXbpAJ5hYGUnCZYJ9ep/X1VVX1RVNVxV1bGqqv5MVdUmYwUmLlVQpR1w+6/aBHo6Ej7EZdAnWLpWPYczK9pbYw8UiqLw8u1RzBjpzfMbj7MnTRremMqa+CxUYFFskFHHHR/kTmpRLQ3NskenP2jUNbIyZSWTh0zuVpvuy1kwYgE6VceWjC1GGU90U8lJaCi7oDywSlvFPw//k2ifaBaOWmi0qRRFYXbIbA4WHKS6qRp8I2QFqy+1tkD8O7A8Bj65D6py4Ya/wm9OwojrL3vre8fe468H/8pEv4lsnr+ZByIfwEbzU0MUWytbfjfpd7w7610qtZXc9819lDZc9H+ulTX4jJbvuQkZ5+NNYXKtepWiGu2AXcECwyrW4awKKuubzR2K2SRkV1LbpGP6CG9zh2J0NlYa3lk8gZF+Liz9KJHEbCk3M7ZabQsfHsjmprFDCPIy4rkpGBKsVr3K8Tzp9tkffHr6U8oay1gWs8xoYw53H060TzSb0jfJfklzyNhl+Br6U4OL15Nep6a5hj/G/bHb3SGv5IbgG9CpOnbl7gLfMVCVDU1yoLjJtbbAhofgu9+D61C460N44ghM/dUVV67+c/Q/LD+ynLlhc3nzujfxd/bv9LnThk7j/Tnv06hrZEPahkuf4DdWzsIyIUmwLERpbROtehX/AbqCBTArwg+9CjtPd6EDzgD13YkibK01XDNqYHbcdLG34f0HJ+HjYsfi/x1gZ+rg/V6bwvpDudRqdfzy6uFGHzsm0NDoIknKBM2uoaWBVSmriPOPY6LfRKOOfduI2zhbfZaUshSjjiu6IGMXeI8Ct6EAnK44zcb0jdwfeT+jPUcbfbpIr0j8nfzZnr3dsIIFUCpND0yqVQefP2woC7zxZfj5Vhgzz7CidBmqqvLWkbd4J/kd5g+fz0vTXsJac/l7wHCw9LSh0/g07VNaWi86LsVvDNQVQb2UBJuCJFgWoqDacAZWwABewYoa6oafq92gLRNUVZVtJ4qZMcIbJ7sr/8NpqYa42bNh6VRG+Drz8JoEPk/MM3dIA0KzTs/KvZlcFebFuEB3o4/v6WRLiJcjR3Jk5dHcPjn9CRXaCh6LeczoY88JmYO9lT0bz2w0+tjiMnTNkL3vgvLA7Tnb0SgaHop8yCRTKorCrOBZ7CvYR51niOGilIyZjr4VNv0STn5haGJxVddWn1VVZfmR5fz32H+5Y+Qd/Hnan7HSWHV52nvD76WssYztOdsvfMB3jOGrHDhsEpJgWYjCKkMnGEs+ePZKNBqFWRF+7E4rRdsy+A48PFFQQ35VIzdE+pk7FJPzdrZj3SNxxIV58tvPjrJiz1lzh2TxNifnU1Sj5ZfXhJlsjvFBHhzJrZLyMTNqaGng/ZT3mRYwjRjfGKOP72zrzA0hN/Bt5reXfuItTCfvMLQ0XJBg7crdRYxPDB72Hiab9obgG2jRt7C7LgusHaTRhanoW+GLZZCywXB48NTHu3zr8iPL+d/x/3HXqLv441XdLxWdPnQ6gS6BrEtdd+EDfmMNX6VM0CQkwbIQhedWsIYO4BJBgFlj/GhobiU+Y/AtWW87UYRGMZRKDgYu9jasenASt0T787dvUvnbN6fQ6+WNe0/o9Sor9mQQPsTFpOWlE4LcKa1tIr+q0WRziMv7OPVjKpsqjbr36mLXBV1HfUs9x8qOmWwOcZHUr8HKFkKmA1BYV0hqRSozA7t2FlJPRftE4+vgy/c528E3XFawTEGvhy+fgGPrYeYfYPqvu3zryfKT/O/4/7hj5B38Ie4PPdqHp1E03D36bo6UHOFU+XkJtLMvOHrJCpaJSIJlIQqqtDjaWuHqMHBLxwCmDvfCydZqUJYJbjtZTGyIJ17OduYOpc/YWVux/O7x3H9VMCv2ZPDilydkdaQHdp4uIb2kjkevGd7rdt2XIwcOm1ddcx2rT6xmxtAZRPtEGy7WFMCbsfD3UHg5EF4aAn/2gv9zhw9uhfTvoZt/p2L9YtEoGg4WHjTBqxCX0LfCiY0wYnZ7k4NdebsAuDbwWpNOrVE0zAqexd78vTT4jJYVLFM48DYkfwTXPAfX/K5bt7555E3c7Nz4bexve/Vv+4KRC3CwdrhwFUtRDGWC0qrdJCTBshBtZ2CZ8s1Tf2BnbcXVo3z44VTxoFrNyC6vJ7Wolhsjh5g7lD5npVH407xIfnl1GB8eyOa17zs4s0Nc1ru7zzLU3YFbojvvKGUMo4e4YG+jkQTLTDaf3Ux1UzVLxy396eKB/0DFWYhcADGLYfLDMPUJQ0eysjOwdiG8cxUc+Qh0XTtJxc3OjQjPCEmw+kr2fqgthKg72i/tyt1FiGsIIW4hJp9+ZtBMmlqbOOzkAnXF0vTAmJobYO+/Yfh1cO1z3br1SMkR9ubv5aHIh3CxdelVGK62rswNm8s3md9QpT3v32+/SChJNayyCaOSBMtCFFQP3DOwLjZ7jB/FNU0czx887aC/O1EEwA1jBkd54MUUReG5m8K5e1Igb+44w8q9meYOyWIkZldwOKuSX0wPxcZIBwt3xsZKQ/RQd47kSqMLc9hydgujPUYT5RNluKCtgcTVMGYBzH0dbnrFsHl+1ouGr08ehdv+Cxor2PwY/DvKkJC1Xvkssyn+UzhWeoyGlgbTvihh2Jdj4wSjbgKgtrmWQ0WHTF4e2GaC7wQcrB3YR73hgpQJGk/SGsPZZlf/7oLDo69EVVWWJy3Hy96Le8LvMUood4ffTVNr04UNbPwioaUeqrKMMof4iSRYFqKwqnFAn4F1vuvCfbHSKIOqTHDbiWLG+LsS6Gncs4ssiaIo/PW2KG6OGsJftpxkg3QX7JL/7s7A3dGGuycH9sl844PcOZFfQ5Nu8DWiMafM6kxSylOYGzb3p4tHPoSmms43zFvbwri74dG98LNNhoNFtz4H710LeQmXnW+K/xR0qo7E4kTjvQhxKV0znNwM4TeDreHf/30F+9DpdcwM6psEy9bKlli/WPbXnPtgS8oEjUPXBPvegOBpEDy1W7fGF8aTUJzAI9GP4GhjnPcFozxGMWnIJD5J/YRW/bl/v30jDV+lTNDoJMGyAM06PaV1TQO6g+D53B1tiQ32YPupwZFgldY2kZhTOSjLAy9mpVF4fVEMM0Z68+znx9h2bmVPdOxMSR3fnyrm/rhgHG37Zn/m+CB3mlv1nCio6ZP5hMHXGV+joHBz2M2GC60thtWo4GkwdMLlb1YUQ4nS/V/CXWugvgz+Nwu2/BoaO16NHO87HhuNjZQJmlrGTsP3YOzC9ku7cnfhYedBtHd0n4Uxbeg0suvzyXPykBUsYzm6DmoL4Oqnu3Wbqqq8mfQm/k7+3DnqTqOGdE/4PRTUF7A7b7fhgm84oEgnQROQBMsCFNdoUVUIcB8cK1hgKBNMLaolt2Lgl6d8f7IYVYUbxw7O8sCL2Vlb8e59E4ka6sav1h0h/qzsB+jMyr0Z2FppuH9qSJ/NKY0u+p6qqmzJ2MIU/yn4OvoaLp7cDNW53Wr3jKLAmPnwq8MQt9RQXvjWJDi15ZKnOlg7EOMbw6GiQ8Z5EaJjxzeAvbshAQZa9C3sydvD1cOu7tZZR701NcCwwrLfO1BWsIyhVQc/vgZDJ0JY91Yid+XuIqU8hUfHPYqtla1Rw5oZOBM/Rz8+Tv3YcMHWCTxDpZOgCUiCZQEKqwf+GVgXa1vN+fJogZkjMb1tJ4sI8nRktF/vNrEOJE521qx+aBJBno48sf4IlfXN5g6p3ymva2JjUj63TxiGdx92nvRztWeou4McONyHjpYeJb8u/6fyQFWF/cvBaySMvLH7A9q5wJyXYckucBkCG5dAQ8UlT5s8ZDKpFakXbooXxtPcYGjPPma+oZwTSC5Jpra5ts/2X7UJcQ0hwCmA/fa2hgRLurn2TsoGqMqGGU93a++VXtXzVvJbBLsGM2/4PKOHZa2xZtHoRRwsPEhGdYbhou8YWcEyAUmwLEDBuTNnBtMKVqCnI3Fhnqw/nDOguwnWalvYf6acGyP9BnyHyO5yd7Rl+d3jqWpo5g9fpEj79ousPZhDk07PL6aH9PncMUHusoLVh746+xX2VvbMCp5luJD1IxQeNXQK1PTiv3H/cYYmGC31kPj+JQ/H+cehosoqlqmkbTX83kf9VB64M3cnthpbrgq4qk9DURSFqwKu4qCuipamakP7f9Ezej38+C/DQb6j5nTr1u+yviOtMo1l45ZhrTFN2feCEQtQUPgu6zvDBb9IQyfSFjnf0JgkwbIABecOGR5MK1gA904JJreikR/PlJk7FJPZebqU5la97L/qxJgAV56aNYqvjxcOitXMrmrStbImPptrR/swwrfvVz7HB7qTX9VISY22z+cebFpaW9iatZWZQTNxsnEyXNz/Fjj5QPTdvZ/ALxKGXw8H/3tJG/dI70gcrR1lH5appHwOzkMM++gwlILuzNnJFP8pRmts0B3Thk6jTt/McTs7KRPsjVNfQlkazPhttz4A0el1vJP8DiPcRzAntHuJWXf4OPoQ4xvD9uzthgt+kaDqoTTVZHMORpJgWYDCKi1uDjY42Q3sQ4YvdmOkH55Otnx8MNvcoZjMthNFeDvbtu9rEZf65dVhjA9y54+bT1Asb+gB+DK5gLK6Jn4xPdQs87fvw8qVVSxT+zH/R2qaa34qDyxJhfTvYPISsDFSVcPUxw3nHx3/7ILLNhobYofEcrBIEiyja6yC9G0w9nZDG33gbNVZ8uryTH64cGem+E/BSrFin4O97MnpKVWFH181lO+Omd+tW/fl7yOrJotHxz2KRjHt2/NZQbNIq0wjpybnvE6CUiZoTJJgWYC2Q4YHGztrK+6cOIztp0oG5BvrJl0ru06XMnuMH1YaKQ/sjLWVhtfuiqFJ18ozG44N+lJBVVVZuTeT0X4uTB/hbZYYIgNcsbFSpEywD2zJ2IKnvedPJWPxb4G1A8T+wniThF0LflGw/81L9t5MGTKF7Jpsiuqlo6dRpW6B1uYLuwfm7QLgmmHXmCUkV1tXoryj2O/sIitYPZW+DYqOw4zftCfOXbXpzCY87T25Lug6EwX3k7Zy4++zvzc0ubB2kO6RRiYJlgUoqBo8hwxf7J7JQbTqVT49nGvuUIxu/5ly6pp03CDlgVcU6u3E8zdHsDutlI8P5Zg7HLPad6ac1KJafjEj1Gz79uxtrBgT4CaNLkysprmG3bm7uSn0Jmw0NlBbDMc+gZh7wcnLeBMpimEVqzQVzmy/4KEp/lMApEzQ2I5vAI/QC1rs78zdSaRXJH5O5usoO3XoVE7YaKgsSTFbDBbtyEfg4g9R3WuvXtZYxu7c3dwadqvh77qJBTgHEOkVyQ85PxgSQZ/RUCzfc2OSBMsCDNYVLIAQbyemjfBi/eFcWgdYs4uvj0P1u9AAACAASURBVBfiYm/NtOHmWYWwNPdNCWb6CG/++vUpssvrzR2O2azcm4G3sy3zxgWYNY7xge4cy6tG16o3axwD2fdZ39Osb/6pPPDQCsP5V1c9ZvzJxt4OLgGG7oTnGekxEk97T0mwjKmuFDJ3w9g72jvMlTWWcbz0eJ93D7zYtIBpqMDBuhzQy2Hi3ZaXACHTwap7SdLXGV+jU3XcNvI2EwV2qVnBszhedtywOu03VkoEjUwSrH6usbmVyoaWQbuCBXDv5GDyqxrZk1Zq7lCMplmnZ9uJImaP8cPWWv4adoVGo/CPhdFYaRSeWHeEuiaduUPqc2dKatl5upSfxYVgb9N3Z+R0ZFKIJ40trRzNqzZrHAPZlowthLiGEOkVCc31kLASwm8Br+HGn8zKxnA2VuYeKEhuv6xRNEwaMomDhQcHfXmu0Zz8wtBU4LzugTtydqCimm3/VZtIr0hcrezZZ2cFlVlmjcXiVOcbDhYeNqlbt6mqysb0jUT7RDPc3QR/tzsxK8hQJrg9ezv4jYH6EsMh5MIo5J1dP1fY3kFwcK5ggeHQYW9nW9YeHDilYfEZ5dRoddw81t/coViUAHcH/nXnOFIKanj4g8M0Ng+uT1hX7cvC1lrD4rggc4fC1OFeKArsTZf/kE2hsK6QhOIEbgm7xVAKmvwxNFbC1CdMN+nEB8DWxbDP6zxT/KdQ0lhCZk2m6eYeTLL2gnsw+Ea0X9qYvpER7iMY5THKjIGBlcaKOK+o/8/efYdHVab/H3+fmUx6I70npBBIIAGkQ+gdAUFAXbvL2l11Xdvq1762dXX1Z1372hWlSe8l9BIICSQhIZDeG+nJnN8fh6BIQtpkzkzmeV3XXtlr5szMJxLCPPPcz32zx84WuUA0uuiUnEPKV/9hnXrY8eLjZFRksDB8YQ+EaluISwjhruHKOSyvKOVG8WduMN1aYEmS5CpJ0jJJkk5JknRSkiTjDm6wADkXZ2BZ7g6WtZWGxcMC2Xqq4OKC09ytPZ6Ho40Vcf1EeWBnTY/24c0lsew/U8pdXx+mvskyFlml1Q38fDibhUP8jTpYuC19HKwZ5O/CrrTes7NsStacWQPAnNA5SqnW3neVT8aDRvbci9q6KIusE79A+W/nXkf5jALEOSyDyT+uzCC74FTpKZJKkljUb5FJzEMcGzKNQisrTmfvVTuKeck+BFpr8BnYqYctT1uOnZUdM0K6MDS8m6YFT+No4VGKXS6UnItzWAbT3R2st4H1siz3B2IB0XbGwLLLlAVFoJvxZ2KYkhuGB6GX4Yde0OyisVnPhuR8pg7wwsZK3TIvczV/sD+vLYxhZ2oR9397lMZeeg6orLqB3WnFfLA9nXu+Pkx9k547VGrN3ppx4R4czSqnqq5R7Si9iizLrEpfxRCvIQQ6BSod58oylUYUPW3UPcq5oP0fXrwpwCkAPwc/DuSJgcPdVl8FpRngE3Pxpp9Tf8ZaY/3bWTuVjQlSzoHtKTqqchIzk31IWThbdfwDsJrGGtadWcf04Ok4Wjv2YLjWTQ2eiozM1pJjSnOOvONGz9BbdXmBJUmSCzAe+BRAluUGWZZFz14Dyy6rwUoj4e2k/ifWagpytycuwoMfDmaZ/aH6/RmllNc0MmuQKA/sjiXDA3lhfjSbkgt4+IeEXtEE5Xx9E78ez+Wv3x1l7KtbGfLiJm76dD+vrT9FbkUtD02NoJ+38QcLtyUuwpNmvcy+jFK1o/QqJ4pPcKbiDPPC5ik37HkX+oRAfyO8AXcJgOiFcPhLpaEGIEkSI31HciD/AM2i8UH3tJRg+SoLrNqmWtZkrGFq8FRcbFxUDPYbHwcfwiQb4uvy1I5iPpqbIC+h0+WBG89upKapxqjNLX4vwjWCYOdgpUzQNxbyjqmSozfqzuTavkAR8LkkSbHAYeBBWZYvae8lSdKdwJ0AQUHqnxswN9lltfi62mKlFcfl/jQiiHu+OcL2lCKmRqnXxra71iTm4WCtZUI/T7WjmL1bRodQ19jMy2tPYW+t5bVrY0yixKYzyqob2JRcwIakfHadLqahSY+bgzVjwty5ZXQwA/1diPZzxtXeWu2olxka7IqdTsvuNGWem2AYq9JXYaO1UUqGzu2H7AMw+41Oz9Xpsn4zIPFHKE5TDr+jnMNafno5J0pOEOsZ284TCG3KT1S++gwClAYDVY1VLOq36AoPMr7RDkH8WJVKbV0FdramsfAzaYXJ0FgDAZ1bYC1PW06wczBDvYa2f3EPkCSJqUFT+SLpC8r95uOathEaasDasqumDKE779qtgKHAB7IsDwGqgSf+eJEsy/+VZXmYLMvDPD3FG8rOyi6rJcBV/KADTI3yxs/Flre3pKE3092Kpmale+DkAd6qd4HrLe4cH8b9k8L58VA2m08Wqh2nU2oampj59k4e+/k4p/KruHFkEN/fOYoD/5jCu38ayl0Twhgb7mGSiytQhoGPDHVj12nR6MJQGpobWJe5jsmBk3GydlLaptv1UWZfGUsrB97jAuKw0lixKXOT8XL0RnnHwN5dKccClqUuI8gpiGHenXtj3tPGeo+gQZI4mLZK7SjmIfug8tX/qg4/JLMikyOFR7gm/BpVPxicFjyNZrmZbTYapbulaHRhEN1ZYGUD2bIst5x6XYay4BIMKLushoA+ltvg4vd0Wg2PzexPYk4Fy45kqx2nSw5kllJS3cDsgWK4sCE9ODWCft6OPLcqyaw6Cy4/mkNBZT0f3XwVux+fxLNzoxkV6m5WO9bjwj3IKKq+2JBH6J5d2buoqK9gbthcKEmHU2tg2J/B2sF4ITwiQKO75MC7s7UzY/3GsuHsBvSyeZdpqyo/Udm9kiQyKjI4UniEhRELTW7nfUTYHJya9Ww4s1btKOYh5zDYeyilvB204vQKNJLmt1JglUS5R+Hn4Mfm6gudmvMSrvwAoUO6/K+4LMv5QJYkSZEXbpoCiCllBlTf1ExBZT0BfcQOVov5g/0YEuTKvzakmOUcpLWJedjptEyM9FI7Sq+i02p4Yf5Acspr+WD7abXjdIgsy3y5J5OB/s5Mj/I2uTdYHRUXoVQm7BbdBA1iZfpKPOw8GO03Gva9r8ynGnGncUNodeDZXyl7+p0ZITPIr87neJE4CN8lzY1QePJieeDytOVYSVbMD5+vcrDLWXtHM6W+ia3lJ6lvrlc7junLPqSUB3bw93iTvolV6auI84/Dy17d9wOSJDEleAp7i45y3sFdnMMykO5+TPoA8I0kSceBwcDL3Y8ktMgtrwMQO1i/I0kSz1wdRVFVPe9vM4830i2a9TLrTxQwub8XdtaiPNDQRoW6c81gPz7ckUFmcXX7D1DZ3vQSUgvOc9uYvma7uALo5+2Il5MNu8Q8rG4rrStlV/Yu5vSdg1VtBRz9BmKuAycVzrd5R11WKjQpcBLWGms2ZG4wfp7eoDgNmuvBJ5bG5kZWpa9iQuAEPOxMcFyHRsMshxDOy83sztmtdhrTVlsOxSmdanCxJ3cPRbVFLAhXp7nFH00NmkqjvpHt3qFigWUg3VpgybKccOF8VYwsy9fIslxmqGCCUh4IYoH1R0OC+rBgiD+f7D5DVmmN2nE67FBmKcXn65k1SJQH9pR/zB6AtZWG51YnIcumfU7v8z2ZuDlYc3WMeXeTlCSJcREexJ8uNtuzkaZi3Zl1NMlNzPMeAT//GZpqYfT96oTxjobKHKj5rUOko7UjY/3HsvHsRlEm2BX5F3b+fAaxNWsrpXWlXBtxrbqZrmBEQBx9mptZn75a7SimLfeI8rUTDS5+zfgVFxsXxgeM76FQnTPYazC+Dr78ao2yy9rUoHYks2c+hf4WqGUGVoCFz8BqzeMz+6OVJF5ZZz6j19Ym5mFjpWGSKA/sMV7Otjw0NYLtKUVsSi5QO06bskpr2HyygD+NCOoVzU7iIjwoq2kkKbdS7ShmbdXpVQyw8aTf1zdA1n6Y8yZ49VcnjHe08rWVMsHCmkKOFYlPuTstPxGsbME9nF/SfsHHwYcxfmPUTtUmq8BRTK+uYXv2TmoazefDTKPLPgxI4N+xNgQ1jTVsz9rO9ODp6LS6ns3WQRpJw9ywueytL6RA0kOR+by3MlVigWXCxAystvm42HLPxDDWJuazL6NE7Tjt0utl1p3IZ1KkFw423ZmOILTn1jEhRHo78fzqZJNtePHVvrNoJImbRgWrHcUgxoYrJU67TotzWF11OmMzyaXJzM1NhcARcO8+GP5n9QJ5D1S+Fly6wJoYOBFrjTXrz6xXIZSZyz8OXlHk1BawN3cvC8IXoDVW6/2uCLiKWedrqNM3sj1ru9ppTFf2QfDoBx1sZ781ayu1TbXM7ju7h4N1zvyw+eiR+dXRXpQJGoBYYJkwMQPryu4cH4q/qx0vrE42+SGzR86VUVglygONQWl4EU1OeS3vm2DDi5qGJr4/cI6ZA33wcbFVO45BeDnZ0t/Hid3iHFbXHPuBVWv+glaWmR33HNz0C/RRefHt6A12bpd0EgRw0DkQFxDHprObxNDhzpDlix0El6ctBzCZ8zdtsuvDEKcgvLBiXeY6tdOYJlmGnEOdKg9cm7EWHwcfhnqbVuPtIOcghngOZqWTM3Ku6CTYXeKduwkTM7CuzFan5YlZ/UnOq+SdLWkm3VVw9bFcbKw0TO4vygONYeSFhhcf7chgT7ppvelfcTSXyrombh8TonYUg4qL8OBQZpnJ7hqasubdb7LGyYlxvqNxH760w53IepQkKWWCrczEmRkyk6LaIo4WHlUhmJmqyIbaMvQ+g1iVvorRfqPxdTT985eagJHMrK5ld85uKuor1I5jesoyoaakwwus0rpS9uTuYXbf2Wgk03sLPj/8Gs7otCQWHFY7itkzvT9d4SIxA6t9V8f4Mr6fJ29vSWPYS5u479sjbEzKp77JdN7kNTbr+fV4HlMHeONkaxr11pbg6aujCHa357bPD7IxKV/tOIDSmv2LPWeI9nPmquA+ascxqHERnjQ06zmQWdr+xcJvzhey/3wmhZLMvMjFaqe5lPdA5cC7/tKGFuMDxmOrtRXdBDsjPxGAQ7Y25FXnqT77qMMChjGrvIQmfRNbz21VO43pyT6kfO1gB8ENmRtolptNrjywxfSQ6diiYWVdDjSb7ofW5kAssEyUmIHVMZIk8cVtw/np7tEsuiqAvekl3PnVYYa/tJn3TKSN++7TxZRUNzB/sJ/aUSyKh6MNP941mgE+TtzzzRF+MYHh1HszWlqzh5h1a/bWjAhxw1qrYVeqOIfVKWd2strRAScreyYGTlQ7zaW8o6GxGsozL7nZXmcvygQ7Kz8RkFhZloSDzoHJQZPVTtQxgSOIbmggwNqVdWdEmeBlcg6Bzh68ojp0+dqMtYS7hhPpFtn+xSpwsnZiSp8o1tnZUF94+e610HFigWWixAysjtNoJIaHuPHSNYPY/48pfH77cAYFuPDGxhRyy2vVjseqhFycba2YEOmpdhSL08fBmm/+MoqRfd3424/H+CL+jKp5vohXWrPPje19i207ay3DQvqw+7RplWSauoaM7Wy3t2dq8DSstdZqx7mU94U3ja2UCc4ImUFJXQmHRSlRx+Qfp8Y9lE3Z25gRMgM7KzP5t92zP5K1E7O0fdifv5+SWtNvKmVU2YfAbwho229elV2VTUJRAnNC5xghWNfNC7+GKq2GbSk/qx3FrIkFlolqmYEVKFq0d4pOq7RBf3nBIGQZ1Xctahqa2JCUz5wYX2ysTLhbVC/maGPFZ7cNZ1qUN8+tTuadLWmqzMhqac1+w4jAXtGavTVxEZ6cyq+isKpO7ShmY1/2Ls5rJKaGTFc7yuU8BwBSqwusOP847KzsRJlgR+UfZ7OHP7VNteZTHgig0YL/UGaVFaOX9Ww6u0ntRKajqV7pDOl/VYcub9kBNNXywBYj+y3Au6mZlXliwHR3iAWWibo4A0vsYHVJsLsDo0Ld+OlwtqoDZzclF1DT0Mz8wf6qZRCUhigf3DiUhUP9eXNTKos+3MuutCKj/mx8Fn8GjSRx86gQo72msU3qr+zSrj2ep3ISM1F+ji1yJY4aa0b5jlI7zeWs7cE97LJOgqCUCU4ImMDmc5tp0ouzGldUWw7l51ilqSfAMYChXqbVPa5dgSOIyD9FuEuoKBP8vfxEaG7oUIMLWZZZk7GGoV5D8XM07QoGrZU18yRn9tQXUVQjSr67SiywTNTFGVjOvaONsxqWDAvkbEkNB86od+h+VUIuvi62jAhxUy2DoLDSanhjUSwvXTOQ3PJabv70gNEWWhU1jfxwMIt5g/16TWv21vT3cWaQvwvfH8xS9YMNc9GUsYOt9naM9x5ueuWBLbyjL5uF1WJGyAxK60o5kH/AyKHMTMEJ8rRaDtTlMy9snvmdvwwYAXIzM/tEc6TwCPnVptE0SHUtDS4Chrd7aUpZCukV6SZfHthinscQ9BL8mr5a7ShmSyywTFRWaS1+rnZoNWb2i9iEzBroi6ONFT8dVqdMsLS6gR2pRcyL9UMj/hxNgkajDPfd/uhEXrpmIHkXFlrXfrCHlPyqHnvdbw6cpaahmaXjQnvsNUzFdcMDOZVfRWKOaOncniOn11Cu1TI1YqHaUdrmFQ2lGdBQfdld4/zH4aRz4tf0X1UIZkbyE/nV0QEZmblhc9VO03kXdmhmNSsfAvyaIf68AaXBhZMfOLe/I7U2Yy1WkhXTgqcZIVj3hQSMJraunpWpy8SHZV0kFlgmSrRo7z47ay1zY31ZczxPlRlZaxLzaNLLojzQBNlYablpVDDbLiy0zpXWcstn+8mrMHxTlIYmPV/EZxIX4UGUn7PBn9/UzBvsh61Ow/cHs9SOYtpkmU2lidgiMTZgnNpp2uYdDchQeOqyu2ytbJnZdyabzm7ifMN542czE3LuMVY5O3OV91UEOAWoHafz7N3APZygghRG+Izgu1Pf0djcqHYqdckynNvXofJAvaxn7Zm1jPUfSx9bMxnP4RvL/PPnST+fRVKJ6CbYFWKBZaKyy2rFAssAFg8LpLaxmTXHc43+2iuP5hDh5cgAXyejv7bQMS0LrW+WjqS6vpk7vjhk8MX4qmO5FFbVszSu9+9eATjb6pg9yJdVCbnUNIizOW3RF6exVadnrFMY9joTbmbkHa18beUcFsD88PnUNdeJ5gdXcLwogUwrDfPD5qsdpesCRkD2QW6NupXCmkLWZ65XO5G6yjKhIgv6jm/30sMFhymoKTCb8kAAPAcwo6YRGzT8nCa6CXaFWGCZoLrGZgqrxAwsQxgS6EqYpwM/HTJumWBWaQ2HzpZxzRB/86u3t0CRPk68d+NQUguqeODbIzQ169t/UAfIsswnuzKI9HZifISHQZ7THFw/PIjz9U2sEc0u2nQ8+QcKrayYauolY67BYO0Iha2fw4rxiCHEOYQVp1cYOZiZaGpgVWMhtpLWbMrDWhUwDKqLGGfvT5hLGF8mfWnZpWNndipfO7DAWnF6BQ46B9Obc3clVtY4ew3gahxYdXoVxbVi/EZniQWWCWqZ3SR2sLpPkiSWDAvk0Nky0ouMV8Ky6piyYzavF8476q0m9PPkhfnRbEsp4oVfkw3y5mFXWjGn8qtYGtfXohbaw0P6EOrhwI+HRJlgW7Zkb8dKlhnf/1q1o1yZRgNeA1pt1Q7K79j54fM5UniEc5XnjBzO9NXnH2edvR1T+kThaO2odpyuCxwBgCbnCLdG30pKWQr78vapHEpFmbvA0Rs8+l3xsor6CjZkbuDq0KvNZ/ZZC99Ybi3Kp1HfyLcnv1U7jdkRCywT9FuLdrGDZQgLhvqj1UhG28WSZZmVCTkMC+4j5piZmRtHBvOXuL78b+9ZPo/P7PbzfbwrAy8nG+YNtqyFtiRJXDc8kIOZZZwuFGdz/khubmZTXT6jdG4427ioHad93tFKiWAbHzrMDZ2LRtKwKn2VkYOZvu1pK6jSapgXvkDtKN3jFQU6B8g+wJzQObjbuvNl0pdqp1KHLCs7WCFx0M4HZ6vTV1PfXM/ifouNFM6AfGPpe76Eyb6j+T7le2oaa9ROZFbEAssEiRlYhuXlZMukSE9+OZJtsNKvKzmZV0VqwXnmW9ib6t7iyVkDmBHtzYtrknl+dRJvbUrl3a1pfLA9nU92ZbA9pbBDu1sn8yrZlVbMrWNCLHLI9MKhAVhpJLGL1YqU9HXkWGmY5jNa7Sgd4z0QasugqvWST28Hb0b7jmZV+ir0cs//jjUnv+bvxaupmZERZnz+Ci4OHCbrANZaa24ccCPxufGklaWpncz4itPgfAH0jbviZbIs81PqT8R4xBDpFmmkcAbkOxiAO/rEUtVQJc5idZJYYJkgMQPL8BYPC6Swqp6daT0/NO+Hg+ew0kjMiRELLHOk0Uj857ohjA5158s9mby9JY03Nqby2vpTvLTmJLd9fpAbPt7HiXbakH+8KwN7ay03jgwyUnLT4ulkw5QBXvx8OJuGJvGm+/c2pSxDI8tMHHiz2lE6xitK+drGPCxQml3kVedxMP+gkUKZvobmBvbXFzFFckRrZaJzzjojcISyk9lQw5LIJdhZ2VnmLtaZHcrXds5fHSk8QkZFBov6LTJCqB7gHQ2SlpjKEq7yvor/Jf+PRr2Fd4/sBLHAMkHZZWIGlqFN7u+Fh6N1j5cJnsip4Kt9Z1k8LAA3h17wD6qFsrPW8u1fRpHxyhwyXp5N6kuzOPnCTI49O50XrxlIasF55r67m7//dIyCyrqLj2ts1nMip4Kv951l9bFclgwLxNXecn8Orh8eREl1A1tOFqgdxaRsKT3BsGYNbt4D1Y7SMd4tC6zWOwkCTAqchJPOiZWnVxoplOk7UniEWklmrHOY2lEMI2A46JsgLwEXGxeuCb+GNWfWUFhTqHYy48rcBc4B0KfvFS/7KfUnnHROzOw700jBDExnpzQ3SVnHHQPvIL86n/VnLLx7ZCeIBZYJEjOwDE+n1bBgiD8bkwv4YHs6zXrDdz9qatbz5C+JuDnY8MTMAQZ/fkEdGo2EtZUGO2stLnY6bh4VzLa/T+TOuFBWJeQy8V/befiHBK55L57oZzdw9f/bzdMrTuDpaMPSuCv/A9zbje/niY+zLT+IMsGLMkrTSKeeKc4RakfpOLs+yhvKNhpdgJiJ1Zo9mVuwkmWG+wxXO4phBFz4Ps7GA3DzgJvRy3rLaoCg18OZXcru1RXOX5XVlbExcyNXh5lhc4vfG7QYCpMYp3Ul3DWcz5M+t+zukZ3Q7QWWJElaSZKOSpIkRnsbiJiB1TMemBLBjGhvXlt/iuv/u5esUsMe2PxiTyaJORU8Ny8KF3udQZ9bMC0udjqenD2ATX8bz6T+nmw9VYi1lYZbRwfzzg1D2PHoROKfmGzxjWq0GoklwwLYkVp0sTuqpduS/A0AU8KuVjlJJ3lHX3GBBWIm1h/tztnFVXX12HsPUjuKYTh4KIusZGWXMtA5kClBU/gx9UeqG6tVDmckhclQW9ru+atV6ato1DeaZ3OL34teCBorNCeWcfvA20krS2N3zm61U5kFQ+xgPQicNMDzCIgZWD3J2VbHe38ayptLYjmVV8XM/+zkx0NZBvk0Jqu0hn9vTGVyfy/mDPI1QFrBHAS7O/D+jVdx7Nnp/HjXaJ6aE8W8WD+C3R0sqi37lSweFogswy9HjDuLzlRtzd5BTF093v3MaOgoKGWCxanQ1NDmJWIm1m8KawpJq85hTG0teJphg4O2RC+E/EQoPg3AbdG3UdVQxfK05SoHM5KW+VchbS+wZFlmWeoyBnsOJqKPGe1Ut8bBHcKnQuIyZgXNwNvem8+TPlc7lVno1gJLkqQAYA7wiWHiCGIGVs+SJImFQwNY//B4BgW48Niy49z11WGKz9d3+TllWeaZlSeQJHhhfrR4Yy0IvxPoZs/wkD6sTMi1+NKSuqY6TtYXM1LjCI5easfpHO+BoG+EorY/TxUzsX4Tn6OU0Y1tRCmv7C2irwEkSPoFgBjPGIZ6DbWcBgiZu5SzV66BbV5yMP8gmZWZLIlcYsRgPWjQYqjMQZd9gJujbuZg/kESixLVTmXyuruD9R/gMaDNFlGSJN0pSdIhSZIOFRX1fAc3cydmYBmHv6sd3y4dxdNzBrA9tYjpb+1kbWLrLYjbsyYxj20pRTwyPVL8uQlCK+YN9iet8Dyn8qvUjqKqlMJjNAPRnrFqR+m8oAst5c/suuJlLTOxlp+2kB2NNuzJ3YMnWvq5hCrDmnsLZz/lZ+HELxdvun3g7eRV57Ehc4OKwYxA3wyZ8e12D/wp9SecrZ2ZFjzNSMF6WORssHaE4z+wqN8inKydeP/Y+xb/gVl7uvy3XpKkq4FCWZYPX+k6WZb/K8vyMFmWh3l6enb15SyGmIFlPBqNxNK4UNY8MI6APnbc+80R/vrdUcqq2y6B+aOKmkaeW5VMTIALt40J6bmwgmDGZg/0QauRWHUsV+0oqkpKVc6uREea4UwkF3/w6AcZ2694mbeDN5MDJ/NDyg8WO5i0Wd/Mntw9jKlrRPLsr3Ycwxu4UNnJvNC2f3zAeMJcwvj8RC9vgJB3DOorrrjAKqktYfO5zcwLm4etVS8ZtWNtDwPmQvIqHNByT+w97M7ZzTcnv1E7mUnrzscqY4F5kiRlAt8DkyVJ+togqSyYmIFlfBHeTvx8zxgemdaPtYl5TP/Pzg61lW5o0vOP5YmU1TTw8oJBoq2+ILTB3dGGuAgPVll4mWBS7gHcm/V4R8xWO0rXhE5UOshd4RwWKDsaljyYNKkkicqGSsZWlvau81ctouaDpLlYJqiRNNw28DZSy1KJz41XOVwP6sD5q1Xpq2jSN5l/c4s/GrRYWVymbeSmATcxMXAi/z78b1EqeAVdXmDJsvykLMsBsiyHANcDW2VZvslgySyUmIGlDp1WwwNTIlh5/1jcHaz585eHeOTHY1TUtl5TXlRVz58+3seaxDz+Pj2Sgf4uRk4srkx4+QAAIABJREFUCOZlXqwfOeW1HDlXpnYUdej1JNfmEaXrg2SuQ2dDJ0JjDWRfeZhwjGeMRQ8mjc+JR0JidG0d9MYdLEcvZZFx4he48IHJnL5z8LL34rMTn6kcrgdl7gKPSHDybvOSdWfWEesZS6hrqBGDGUHfCeDoDcd/QJIkXhr7El52Xvx9x9+pqK9QO51J6kWFwb2DmIGlrmg/F1bdP477J4WzIiGHGW/tZHvKpUMUE7MrmPfubk7kVvDODUO4Z2IvGSIpCD1oerQPNlYaViZYZplgTdZeMrQS0V4xakfpupBxys5FO2WCgEUPJo3PjWegnQ+uer3yhrw3GrgQStMh/zgAOq2OW6Ju6b0NEJob4ezeK5YHZldlc7L0ZO85e/V7WisYeC2kbYTaMlxsXHhjwhsU1hbyf/H/Z9GVCW0xyAJLluXtsiyb2VAP0yRmYKnP2krD32dEsvzeMTjZWnHb5wd5fNlxKusaWZmQw6IP96CRJJbdPYZ5sX5qxxUEs+BoY8XUKG/WHM+jqbnNvki9VkrSj+glieiwWWpH6TpbF/C/qkMLrHH+4yxyMGlFfQWJxYmM0TqD1hr6hKgdqWcMmAcaq0uaXbQ0QOiVbbxzjkBj9RXnX205twWAKUFTjJXKuGKWQHPDxTlogzwH8ber/sa2rG18lfyVyuFMj9jBMiFiBpZpiQlwZfUD47hnYhg/Hc5iwuvbePD7BGIDXFl5/1hRFigInTQv1o+S6gbi00vUjmJ0SRfadkf5jVQ5STeFToScw1B35bIgjaS5OJi0V5/L+YN9efvQy3rG1daDe7jyyX9vZO+m/Cwk/VYm6KBz4PrI69l8djOZFZlqpjO8Dpy/2nJuCwPcBhDg1Iva8v+e72Bwj4DjP1286aYBNzE5cDJvHX6LY0XHVAxnesQCy4SIGVimx1an5fGZ/fn5njEEutlz25gQvl46Eg9HG7WjCYLZmRjpiZOtFSsTctSOYlzl50hqKMVLa4+XvZnNv/qj0IkgX2hX3Y5ZIbOUwaQneuGORhvic+Jx0jkxsORs72xw8XvRC6H8nLLgvuBPA/6ETqPjy+QvVQzWAzJ3gvcgZWHZiqKaIhIKE3rv7hWAJEHMdXB2N5RnXbhJ4oWxL+Dt4M2jOx6lvK5c5ZCmQyywTIiYgWW6hgT1YdX943huXjTWVuKvjSB0hY2VllkDfdiYVEBdY7PacYwnZT1J1tZEeUSrnaT7AoaDzr5DZYI6rY6bo27mQP4BThSf6PlsKpNlmfjceEb5DMeq7FzvbHDxe/3nKGWQvysT9LDzYH74fFadXkVxbbGK4QyooQbO7b/i+attWduQkZkaPNWIwVQwaJHy9cSyize52Ljw7wn/pri2mCd3P4letrwS8NaId4omJLOkGoAgN7HAEgShd5o/2J/z9U1sPVXY/sW9RHXKGjJ1OqJ8h6sdpfusbCB4TIcWWHDhXI7OySJ2sdLL0ymsKWSsUyggK3PDejM7VwibAknLQf/bm+pbo2+lUd/I18m9ZHLPmZ3QXA8RbS+eNp/dTIhzCKEuvax74B+59YXAkZeUCQJEe0Tz+PDH2Z2zm08SP1EpnGkRCywTkpJfhbOtFd7OovxMEITeaVSoO55ONqyylG6C9VWczD+ILEG0ey/YwQKlTLA4BSrb/zN00DlwXf/r2HxuM+cqz/V4NDW1nDUbKzkoN/T2HSxQuglW5ULW/os3BTsHMyNkBl+f/JozFWdUDGcgaRvA2hGCx7Z6d0V9BQfzDzI1eCqSZAEjdgYugsIkKDx1yc1LIpcwu+9s3kt4j315+1QKZzrEAsuEpORXEenjZBl/QQVBsEhajcTVMb5sTSmkss4CZiSlbyXpQllxlHuUymEMJHSi8jVjR4cuv3HAjWglbe+ekYRy/irMJQyfynylnb27BYzwiJwFVrZw/PtLbn50+KPYaG14evfTNOmbVApnALIMqRuUn3mr1j/83pG9gya5ialBvbw8sMUfBk23kCSJZ0c/S4hzCI/vfJyC6gKVApoGscAyEbIsk1KgLLAEQRB6s3mxfjQ06VmfmK92lJ6Xsp4ke0d87H3wsPNQO41heEWDvUeHywQ97DxYErmE5aeXc7LkZM9mU8n5hvMcKjjEWP+xUHQK3ELbfEPeq9g4Qez1cPQbKM24eLOXvRdPj3qa48XH+SLpC/XydVdBElTmQL+ZbV6y+exmfBx8es8HKO1x8r4waPrnix0kW9jr7Hlr4lvUNtXy2M7HLHLQeAuxwDIReRV1VNU1EektFliCIPRugwNd6e/jxCvrTpJZXK12nJ6jb4a0DSTbOxHdGxpctNBoIHSCssDq4Iyrewffi6uNK//c/89eeQh+Z/ZOGvWNSpODolTLKA9sMeEJZSbWlhcvuXlmyEymB0/nvYT3SClNUSlcN6VeGJQdMb3Vu2saa9iTu4epQRZSHthi4LVQcvrioOnfC3UN5dnRz3Kk8AjvHHlHhXCmQSywTERKQRUAkT7OKicRBEHoWZIk8eFNVwFwxxcHKa9pUDlRD8k+SGVdKWflut5z/qpF6EQ4nw9FHXvj7GztzMNXPcyxomOsSl/Vo9HUsPncZjzsPIjtMwBK03t/g4vfc/aF0fcpJWM5Ry7eLEkST496GmdrZ57a/RSNzWa4m5G2EfyGKLs2rdiVs4v65vre3Z69NQPmXhg0/XOrd88JncN1kdfxRdIX7MzeaeRwpkEssExESv6FBZbYwRIEwQKEeDjw31uGkV1Wy11fHaahqfftapCyjpO2ylzDXlc+FDpR+drBMkGAeWHziPWM5a3Db1HZUNkTqVRR11TH7pzdTA6cjKYsE/RNlrWDBTD2QbB3h83PXrKr2ce2D8+Nfo6UshQ+PP6higG7oLoEsg5csTxwy9ktuNm6McRriBGDmQB7NwibrLTob2MX+9HhjxLZJ5Kndz9NUU2RkQOqTyywTERKfhU+zra42OvUjiIIgmAUw0Pc+NfiGPafKeWJX44jd7DczGykrifJOwLohQss1yDlnFEnFlgaScNTI5+ivL6c946+13PZjCw+N57aplqmBE9RuisCeFrQDhaArTOMf0xpaX56yyV3TQqaxLyweXya+CmJRYkqBeyC05sBuc3ywPrmenZk72BS4CS0Gq1xs5mCgddCRRZkH2z1bhutDa+Pf53aplqe2v1UrywNvhKxwDIRLR0EBUEQLMn8wf48PLUfvxzJ4d2tp9WOYzhZB6HoFMlOHvg7+tPHto/aiQwvdCJk7oZOlH4NcB/A4n6L+T7le06Vnmr/AWZgy9ktOFs7M9xn+G8lk5ZUIthi2B3QJ0TZxdJfOkj8iRFP4GnvyVPxT1HXVKdOvs5KXQ+O3uA7uNW79+ftp6appvcPF25L5GzQ2rRZJgjKeazHRjzG3ry9/C/pf0YMpz6xwDIBTc16ThedFwssQRAs0l+nhLNwiD//3pTK5/FnqG9qbv9Bpm73W2DXhyR9Te/bvWoROhEaqiD7UKce9sCQB3CxduHl/S+b/a5lY3Mj27O3MzFwIjqNTllguQaBtYPa0YzPyhom/x8UnIDjP15yl5O1E8+PeZ4zFWd4P+F9lQJ2QnMjpG+BiGlKU5dWbD67GUedIyN9Rho5nImwdYZ+0y8Mmm77d/aiiEVMDZrK20ffJqkkyYgB1SUWWCYgs6SGhia9OH8lCIJFkiSJV64dxNhwd55fncyYV7by6rpTZJXWqB2tawpPQcoaKq66jezqnN7X4KJF3wmgtYaTqzv1MBcbFx6+6mGOFh5ldUbnHmtqDuYfpKqh6rcZSEUp4BGpbig1RS9Udny2/RMaL92pGuM3hkX9FvFl8pccKzqmUsAOytoPdRVtnr+qbqxm49mNTA6ajE5rwUc7Bl4L5wvgbHybl0iSxHNjnsPN1o3Hdz5OTaOZ/l7vJLHAMgEXG1yIHSxBECyUjZWWr+4YyZd3jGBocB/+uzOd8f/axm2fH2BfRona8Ton/m3Q2ZMUOhqgd7Vo/z07V+V8yoll0Ny5YbLzw+cT4xnDawdeI708vYcC9rzN5zZjZ2XHaL/Ryqf4JWngacELLI0Gpr2gnM058N/L7n7kqkfwtvfm6d1Pm3apYOoG0Oh+a+byB6vTV1PdWM11kdcZNZbJiZgBOocrlgmC8qHKq3Gvcq7yHK8ceMVI4dQlFlgmIKWgCo0E4V6OakcRBEFQjUYjMaGfJx/fMozdj0/mgUnhJOVWcvOn+0kvOq92vI4pz4LEH2HorSRXZwEwwG2AyqF6UMx1yifYZ7Z36mEaScNrca9hrbXmrk13kV9tfkOnm/XNbDm3hTj/OGytbKH8LDTVWfYCC5QZaWFTIP4/l+1iOVo78vyY58mszOS9BBNudJK6AULGKYOU/0CWZb479R3R7tEM8hikQjgTYm0P/WdD8sp2z2IO9xnO0kFLWXF6BWsz1hopoHrEAssEpORXEuLhgK3OArvQCIIgtMLP1Y6/TY9kzV/HYWul5fnVyeZxXmfvhTeNY+4nqTiJQKdAXGxc1M3Uk/rNAFuXy87cdESAUwAfTP2A6sZq7t50NxX1FT0QsOckFCVQWlfKtOBpyg0tDS4srUV7a8Y+CDUlyu7mH4z2G83ifov5MulLEgoTVAjXjtIzSjfIfjNavXt//n4yKjK4of8NljVcuC0Dr4Xasg51FL1n8D0M9hzM83uf52zl2Z7PpiKxwDIBKflV4vyVIAhCK7ycbHloWj92phaxKblA7ThXVl0CR75UdnVcAkgqSeq9569aWNlA9ALlHFZ953cZ+7v1553J73Cu6hz3b7mf2qbaHgjZMzaf3YxOoyMuIE65wZI7CP5R3/HgFQX7Pmh1TtIjwx7B18GX/4v/P9MrFUzbqHxtY4H13cnv6GPTh5l9256PZVHCJisfsrRTJgig0+h4ffzrWGmseHTHozQ099Ih84gFlupqG5o5W1ojzl8JgiC04ZbRwfTzduSFX5OpazThDoMHPoLGGhj7ILnnc8mrzrOMEqKY65Tv+9SaLj18uM9wXhv/GseKjvHojkdp1He87btaZFlmy7ktjPEbg4PuQsfAohRw9FHOplk6SYKRdysdBTN3X3a3g86B58cqpYLvHn1XhYBXkLoB3COUOW9/kHs+l+3Z27m237XYaG1UCGeCrGxgwFw4+Ss01bd7ua+jLy+NfYmTpSf596F/GyGgOsQCS2VphVXIMmIHSxAEoQ06rYbn5kWTXVbLhztMtCFC/XnY/xH0vxo8I9mWtQ2ACYETVA5mBIGjlNbkx3/o8lNMC57G06OeZkf2Dl7Y+4LJl4MmlySTV53HlKApv91YnCLOX/1ezBKwc4P9H7Z69yjfUSzpt4T/Jf+PIwVHjByuDbXlkLmrzd2rH1KUn/El/ZYYM5Xp6z9XGdmQuatDl08KmsTNUTfz7alv2XJ2S/sPMENdXmBJkhQoSdI2SZKSJUlKkiTpQUMGsxSig6AgCEL7xoR5cHWMLx9sTzfN9u1HvoS6chj7EABbz20l3DWcYOdglYMZgUYDg5ZAxjao6noZ55LIJdwdezcrTq9gxekVBgxoeJvPbUYraZkUOEm5obkRCk+CVy9uaNJZOjsYdruys1l6ptVLHhn2CP6O/vxj9z+obqw2csBWrH9C6QYZc3l3wLqmOn5J+4XJgZPxdfRVIZwJC50AOns41fHmFQ8PfZho92j+b8//kXM+pwfDqaM7O1hNwCOyLEcBo4D7JEnqpdMUe05KfhU2VhqC3S1wKKEgCEInPDVnABpJ4sVfk9WOcqmmBtjzLoTEQeBwyuvKOVxw+Lc335Yg5jqQ9a02NeiMe2LvYaTPSF458IrJHoKXZZnNZzczzGcYrrYXygHzE5UyycAR6oYzNcOXgkYLBz5u9W57nT3/HPdPcs/n8sahN4wc7g+SVsCx72D838E35rK7151ZR3l9OTf0v0GFcCZOZ6ecxUpZ1+qZu1YfotXxrwn/QpZlHtvxGI3tdCE0N11eYMmynCfL8pEL/78KOAn4GyqYMexJL+aVtSdVLUVIKagiwtsRrUZ0ohEEQbgSXxc7HpgSzsbkAranFKod5zfHf4CqXBin7F7tzNlJs9zM5KDJKgczIs9+4DekW2WCoLRvf2ncS+g0Op7Y+YRJnsf67tR3ZFZmMjPkd00Ozu1TvgaOUieUqXL2g6hr4OhXUF/V6iVDvYdy28DbWJa6jJ3ZO40c8ILKPPj1IfAbCuMfvezultbs4a7hDPcZrkJAM9B/jvJ7MPdohx8S6BTI82Oe53jxce7fej8ltWY28/AKDHIGS5KkEGAIsL+V++6UJOmQJEmHioqKDPFyBhN/upiPdmbwgYo1/Sn5VfQT568EQRA65M/j+tLXw4HnVydT32QCDS/0zbD7LfCNVWb/oJQHetl7EeVuYUUdMddB3jEoPNWtp/Fx8OHZ0c9youQEHx5r/fyOWuJz4nnt4GtMDJzIgvAFv92RtU85h+ZiVp8zG8eoe6C+EhK+bfOS+wffT0SfCJ6Jf4ayujIjhgP0elh5rzKza+HHoNVddsmxomOcLD0pWrNfScQMkDSQ0rkZV9NDpvPs6Gc5XHCYRasXsS9vXw8FNK5uL7AkSXIEfgYekmW58o/3y7L8X1mWh8myPMzT07O7L2dQj0yLZF6sH6+vT2H50Wyjv35ZdQOFVfX0F+evBEEQOsTGSsuzc5WFS165CbR3Tl4JpekQ9whIErVNtcTnxDMpcBIaycL6SA28FiRtt3exQHnTdU34NXyS+AmHCw4bIFz3pZen8/cdfyfcNZzX4l5Dq7kwu1KWlR0ssXvVuoBh4D9MaQKj17d6ibXWmlfGvUJFQwUv7nvRuJVFBz+G9K0w4yXwCG/1km9PfYujzpGrQ682Xi5z4+AOQaM7dQ6rxaJ+i/h2zrc4WTtx58Y7eefIOzTpm3ogpPF067e/JEk6lMXVN7Is/2KYSMaj0Uj8a3EMo0LdeGzZceJPFxv19VMKWhpcOBv1dQVBEMzZxEgvNj48nhAPlc+uyjLselOZe9R/LgD7cvdR11xnWeWBLRy9lHMYiT+1+Ua6M54Y8YTSAGHXP6hqaL28zFjK6sq4f8v92GhteHfyu9jr7H935xk4XwBBYoHVplH3KB9EnN7U5iWRbpHcN/g+Np3dxJozXWv532lFKbDpGYiYDsP+3OolW89tZUPmBhZELLj0z124XP85UJgEZZmdfmi/Pv34fs73zA+fz8eJH/PnDX8mvzrf8BmNpDtdBCXgU+CkLMtvGi6ScdlYafno5mH09XDg7q8OczLvsk24HnOxg6AoERQEQegUndYEdofSNkFBIox7WOmkB2zN2oqTzonh3hZ6TiP2eqjIgnN7u/1UDjoHXol7hYKaAv65/58GCNc1Dc0NPLTtIQprCnl78tuXd5BrOX8VNNr44cxF1Hxw8oN971/xstujb2ew52Be3vdyzzc5qciGX/6idL+b964yu+sPEgoTeGznY0S7R3P/4Pt7Nk9vEDlb+dqFXSxQmp68OPZFXol7hVOlp3j94OsGDGdc3fkXaixwMzBZkqSEC/+bbaBcRuVip+OL20dgb6Pl9s8PkldhnEnyKQVVuNjp8HYWw+oEQRDMiizDrjfAJRAGLQagWd/MjqwdxAXEoWvlHIdFiJwN1k5w6DODPF2sZyx3xd7Fmow1vHX4LaM3pdLLel7c9yJHCo/w4tgXifWMvfyic/vA1gU8+xs1m1nR6mDknZCxHbIOtn2ZRsvL415Go9Fw09qbDFceqtcrzRf2fQg/3Q5vRsFb0cqZwXnvgJP3ZQ/JrMjkga0P4G3vzbtT3hW7Vx3h1he8ojp9DuuPrg69mh/n/siTI540UDDj604Xwd2yLEuyLMfIsjz4wv+6919URX6udnxx+wjO1zdx22cHqajp+c5FKflVRHo7iQOTgiAIatA3Kw0ZEr6DtY91blFwdg9k7YexD148FJ9QlEBZfZlllge2sLaH4XdA0i9QmmGQp7xz0J0s6beEz058xtPxTxuls2BDcwPL05azYOUCVpxewd2xdzM7tI3PkFvOX2lMYFfVlA3/Czh4wpbnr9jKO9A5kG9nf4urjStLNy5l5emV3XvdknT4Yg78dyKsf1z5exs4Ema9DvfshQFzL3tIcW0xd2++G42k4cOpH+Jm69a9DJYkcrby+7GmtFtPE+wcjKe9afVu6AwrtQOYkgG+znx081Xc/vlBbv38AF8vHYmjTc/8J5JlmdT8Kq4ZIjoOCYIgGNXBT+HEz8qn1w3nldskrTLHyS1MGZrZnl3/Vt4sDrnp4k1bz21Fp9Exzn9cDwU3E6PuU3YK4t+GuW93++m0Gi1Pj3oaD3sP3k94n7K6Mt6Y8EaP7ChU1FfwU+pPfHPyG4pri4nsE8krca8wp++c1h9QXQLFKRB7+WBa4Q9sHCHu78oiJ2Obcl6vDUHOQXw9+2se2fEIT8c/TWZlJg8MeaBzjWP0ejjwEWx+HrTWMPsNiJwFLgFXfFh1YzX3br6X0rpSPpvxGYHOgR1/TQH6z1Z299M2KiXDFkp83PIHY8M9ePdPQ0jMqWDplwepa+yZNsC5FXVU1TfRT3QQFARBMJ7UjbDmb1BbDrE3wDUfwL374Ymz4B4GK+6B2nbaROcehfQtMOpeZcAmyodmW89tZZTvKBx0Fj443skbht6stOWuzDXIU0qSxD2x9/DM6GeIz43nLxv/YtB23npZz5dJXzJ92XTePvI2Ea4RfDTtI36a+xNXh17ddqVJ1oXpNOL8VccMux1cgmDLC+0OpHWxceGDqR+wqN8iPkn8hEe2P0JFfUXHXqckHb6YDeufgL5xcN8+GPGXKy6uyurK2JW9iwe3PkhqWSpvTHiDgR4DO/PdCQC+Q8DJF04ZqVGJiRI7WK2YHu3Dm0tieeiHBO75+jAf3TwMayvDrkVTLzS4EC3aBUEQjKSmFFbdr5wRuHMbWP3h/OvCj+HTafDr32DRZ60eegeUzoE2LjD8t65jaeVpZJ/P5s+DWu9EZnHG/BUOfQ5734MZhmtQsbjfYtxs3Xhsx2Pcsu4WPpj6AQFOV96RaE9+dT5P736a/fn7mRAwgQeGPECkW2THHpy1T9kd8RvarQwWw8oGJj6hzJ06uUppfnEFOo2OZ0Y9Q1/nvrxx6A22Zm0lxiOGsf5jGec/jij3qN92tZqblAVv6jo48Iny53LNB8oHKb/7uyzLMkW1RaSXp3O6/DSJxYmcKD5BVlWWElGy4pnRzzA+YHyP/Wfo1TQaZafw2A/KbDGdrdqJVCEWWG2YP9if6vpm/rE8kYd/SODt6wdjZcCuVSfzlW6FYsiwIAiCEcgy/Pqwssi6cdnliysA/6HKm7+tLylvEGKWXH7N2b1wcrUy98rW5eLNW89tRUJiYuDEnvsezEmfYOW/36HPYNzflBk5BjIlaAofT/+YB7Y+wPVrrueNCW8wyrdrLdLXn1nPC/teoEnfxPNjnmdB+ILOnYs+tw/8hljsm8guib1eKR/d+hJEzgHtld+KSpLELdG3MMJ3BFvObSE+J573E97nvYT36GPjwjBbXwbWVDEoP4XoqjLsJS1EzkKe+RqFVlak5+4lrTyN9PJ00ivSOVN+hqrG39r+e9t7M8hjENdGXEuMZwxR7lFiF7q7Iucof/fP7IR+09VOowqxwLqCP40MoqahiZfWnMTOWsvr18ag0RimIcX6E/n093HCxc5CO00JgiAYUHlxKk/+eiMPjXqKyP7XXH7BiZ8heQVMeQZ8Y9p+onF/g7TNsOYRZa6Ra5Bye0M1bP0n7P8AnP2VuT6/s/XcVmI9Y/Gw8zDgd2Xmxj0Mx76H/R/C5KcM+tRDvYfy3ZzveHDbg9y96W4eGfYINw24qcOLo5LaEt449Aa/ZvxKjGcMr457tfNnbRprIefIZT8LQjs0Wpj8NPx4Mxz//pJzjFfS360//d36c9/g+ygtP8ve3S8Tn7WNo7piNul04O6Ixt2JUJe+ONloOL128SXz09xs3QhzDWN26GxCXUIJcw0jzDVM/J3tCX3jlG6iKWvEAkto3dK4UM7XN/GfzWnUNTbzxuJYbHXabj1ncm4lx7MreG5ulIFSCoIgWLazhcdIlmu5ft/T3H7qR+6a/TE21hc+ha7MVc5dBYyAMQ9e+Yk0Wlj4EXwwDpbfDbeuVg7k//owlJ+DYXfA1Ocu2b3KqMjgZOlJHr7q4R77/sySZyQMuFppNDDmAbB1NujTtzRCeGr3U7x+8HVOlpzkmdHPYGt1+W6SLMuklKWwM3snO7N3crzoOBpJw32D72PpoKVYabrwdij3KOgbxfmrrhgwV9n52/6qMuagtR3l1jTVw8FPcdv1BnNqSpgTNR/G/JUyt76cKE0msTiR48XHqW2sZVbILML7hBPuGk6Ya5joBGhMVjYQPgVS1sGctyyyw6ZYYHXAg1MisNVpeXXdKQoq6/j4lmG42lt3+fl+PJSFtZVGdBAUBEEwkNioxazyG8Hra27l44pENn87lhfGvczgsFmw8j5oboQFH7ZbjgRAnxCY/S9YcTd8PEnpNujRD25fB8FjLrm0Ud/IU7uewtnambmhl7d7tnjj/qaUVB76DMY9ZPCnd9A58ObEN/n4+Me8m/Au6RXpLAhfQGVDJZX1lVQ1VlFZX0licSIFNQUARLtHc0/sPUwPmU6Ya1jXX7xlwHDgSAN8JxZGkpTd5K8WKGf1Rt195etlGRJ/UppjVGRB6ETl8f5XAdAHiLOPIy4grqeTCx01YK5SNZC5q2OdWXsZyZhD+4YNGyYfOnTIaK9naKuP5fLIj8cIcLPji9tGEOTe+RaxdY3NjPjnZiZGevHODUN6IKUgCIJli9/9Cs+nfE2+VuIGa18eTDuI/ax/KV3EOkqWYdkdF85b/U05c9XKp+xvH3mbTxI/4c2JbzIteJoBv4te5KsFkH8CHjp+setiT9ietZ0ndz3J+Ual9b4vMcGSAAARGUlEQVSt1hZna2ecrJ0IcQlhQsAE4gLiDFcS9s0SKMuE+w8Y5vksjSzDl3Oh8CTcsQE8wlu/rqle2YE++rWy6zXlWQibZNysQuc11sG/IyFiGlz7idppDEaSpMOyLA9r9zqxwOqcA2dK+cv/DmGlkfj0tuEMDnTt1ONXJuTw4PcJfLt0JGPCRd2vIAhCT6guSuGdNbfzHZUESta8OvsLBnle4exVa5qblJbtjq0PuzyQd4ClG5eyMGIhz415rvuhe6vM3cqg19lvdG6R2wU1jTXUNNXgbO2MtbbrlSbt0uvh9RClC968/9dzr9Pb5R1TFllN9cqO1Mi7lTLdFpV5ylmt7IMw/lGY+A+LLDczW2sfhcNfwiOnwL53lGh2dIElfko7aURfN365dwz2Nlqu/+9etqcUdurx3x/IIsjNnlGhhuuoJAiCIFzKwTOSJ2/ZzWdRd9Fo78bN627hw2Mf0qRv6viTaK3aXFxV1Ffw5O4nCXYO5rHhjxkodS8VPFY5/7bn/4G+Z2ZLtrDX2eNh59GziyuAolNQVyHOX3WXb6wyhy50Imz4B3w+W5lhBZB1EP47EQqSYcn/lMYYYnFlXobeAs31SnmnhRE/qV0Q5unI8nvHEubpyF1fHWZvekmHHne2pJq9GSVcNzzQYN0IBUEQhDZoNAwb8QDL5v/CjJAZvJfwHrevv/3ivJuukmWZ5/Y8R2ldKa+OfxV7XefLxS2KJClNLsrPKiWXvUHWhfNXQV1rDy/8jrMv3PA9LPgIik7CB2Nh9UPKoGCdLSzd3O68LMFE+QxSyjqP/K/dwdK9jVhgdZGHow3/u2MEgW72LP3yIAlZ5e0+5sdDWWgkuHZo94YiCoIgCB3nbO3Ma+Nf49W4V0kvT2fx6sX8lPoTelnfpef7Je0XNp/bzF+H/JVo92gDp+2l+s+BPn2VXaze8Ebr3D5w9Fa+J6H7JEmZj3XvfqUhwuHPlZ3Pv2wDb9Fx2awNuRkKTihdNy2IWGB1g7ujDd8sHYm7ow23fnaAk3mVbV7b1Kznp0PZTIr0wsdFDCQUBEEwtjmhc1g2bxlR7lG8sPcFblp7E0klSR1+fFFNET+m/MhrB19jpO9Ibo2+tQfT9jIaLYy+D3IOQdZ+tdN037m9yu5VZ4YSC+1r2c26O14ZCN5Lzu1YtEGLwMpO2cWyIGKB1U3ezrZ8s3QkdjotN3+6n4yi861etz2liMKqeq4b3slBhoIgCILB+Dn68en0T3l53Mvkns/lhl9v4KV9L1FRX3HZtbIsk1mRyWcnPuPGtTcy+afJvLjvRfwd/fnn2H+ikcQ/oZ0y+Eaw66PsYpmzknRlJpo4f9UzJAl8BnZspIJg+mxdIPoaZdh7Q7XaaYxG/PQaQKCbPV8vHcl1H+3lpk/2878/jyDcy+mSa74/mIWnkw2T+nuplFIQBEEAkCSJuWFzmRA4gfcT3ue7U9+x6ewmpgRNoby+nOLaYopqiiipK6G2qRaAKPcoHhjyAJMDJxPmGoYkdi46z9oehi+FnW8oixT3bsygUtPxHwBJnAsShI4aegsc+w6SV8LgP6mdxihEm3YDSsqt4Ib/7qOyrokhQa7Mj/VjTowfsiwz+tWt3Dk+lMdn9lc7piAIgvA7KaUpvHrgVVLLUvGw88DTzhN3O3c87DwIcgpiQuAEfBx81I7ZO1QVwH8GKucyrn5T7TSdp9fDO7HgFga3rFA7jSCYB1mGd4eBgyfcsV7tNN0i5mCpJL+ijhUJOaxMyOVkXiUaSdnhOltSw7a/T6Svh4PaEQVBEARBPSvvh8Rl8HASOJjZyJLMeKW73cKPIWaJ2mkEwXzs/g9sfhbuOwie/dRO02ViDpZKfFxsuXtCGOsejGPTw+O5b1I4EjAz2kcsrgRBEARh9P3QVAuHPu3Y9c1NkHNY2T1S27HvwNpR6YooCELHxd4AGis4+pXaSYxCLLB6UIS3E49Mj2T7o5P48Oar1I4jCIIgCOrz6g8R0+HAf6Gx7srXZh1Qhs1+PBm+XgiVuUaJ2KqGGkhaAVHXgLX4wFQQOsXJG/rNVD6kaGpQO02P69YCS5KkmZIkpUiSdFqSpCcMFUoQBEEQhF5s9P1QXXShYUQrakph1QPw6TSoLYVxDyvt3d8fDUnLjZu1RcpaaKhS5jUJgtB5V92m/L3//k9Qla92mh7V5TNYkiRpgVRgGpANHARukGU5ua3HWMIZLEEQBEEQ2iHL8NF4KEoBrwHgFaUMlPUaABU5sPk5qKuA0ffChCfAxhGKT8Mvf4HcIxBzPcx+XWkBbSxfLYTiNHjwGGhEAZAgdJosw4GPYdP/gc4e5v7H7Lpx9niTC0mS/n979x5sVVUHcPz7C1BIQxGQEChENPNRWvi2UnqgZlqWU1M5BuOUOkw2amVpVpO91NLp4WhjDzXzhTr5VizzUYziAwUfKRamRoqWKTqmyOqPvege6HLvuffsyzl37+9nZs3dZz9/Z/3gwG/vs9bdDfhGSmlGfv0VgJTSd9d2jAWWJEkCiqna5/8cnn6gaMuf6to2addilsFx265+zGuvwi2nFG3kRPj4ebDZDgMf6/NL4bRt4F3HwPQTBv56UpUte7i4WbJ0QTE2a9/vr9ubJS1otsBq5fdgTQAeb3j9BLBLC+eTJEl1MXoL2Oc7Xa9ffBaWPQgrXoYp07t/SjRkGOz9VZj6fpgzE361P3zyIpi8x8DGuvBiSCuLJ2eSWjN2KzjsRrj5ZLj1VFhyG3zkrIH/e7wODfgz7oj4bETcGRF3Llu2bKAvJ0mSBqMNRsPkPWHq+3r/Ct6knWDW9TByfDH5xcPXD1xcKcGCC2DizjBm6sBdR6qTIcNg+vEw64Zi+YWl7Y6oVK0UWE8CkxpeT8zrVpNS+llKaVpKadrYsWNbuJwkSVK20QSYeR2M3boYNL9wzsBcZ+m9xZM1J7eQyjdpJzhiHmz/sXZHUqpWCqz5wJYRsXlErAd8AriinLAkSZJ6scFoOPTKYszWpYfB/LPLv8a9F8KQ9WC7g8o/tyQYNrzdEZSu32OwUkorImI2cD0wBPhFSun+0iKTJEnqzfCR8Ok5cMlMuPoY+PO1xVcN37R7MQHG0PX7f+7XXoWFl8Bb9oURo8qLWVKltTLJBSmla4BrSopFkiSp74aNKGYUvOnb8OBVsPjGYv3Q4TDhnbD9wfCOQ/s2vXpKcMPX4KVnYIdPDUzckiqp39O094fTtEuSpAH34jPwt3nw2Dz4683w1CKYshcc+FPYaGLvx6cE134Z7jgLdj0SZnwHIgY6akkdrtlp2v1NeZIkqVo2GANv/VAxDfzht8H+p8Hj8+GM3YsxVT3dXF65Eq45tiiudpttcSWpzyywJElSdUXAtFlwxG0wbhu4/HNw8SGwvJtfHbNyJVx9dDFZxh5HwQdOsriS1GctjcGSJEkaFDaZAp+5Gub9BH5/Ejy0FYyeCuO2gzduV/x86Cq4+1zY82h474kWV5L6xQJLkiTVw+uGFE+mtpwBi+bAUw/Ak3fC/Zd17fPuL8Lex1tcSeo3CyxJklQvm24N00/oev3yv4tia+WKYop3iytJLbDAkiRJ9TZ8I3jzbu2OQlJFOMmFJEmSJJXEAkuSJEmSSmKBJUmSJEklscCSJEmSpJJYYEmSJElSSSywJEmSJKkkFliSJEmSVBILLEmSJEkqiQWWJEmSJJUkUkrr7mIRy4DH1tkFmzMGeKbdQWidMd/1Yr7rx5zXi/muF/NdL52Y7zenlMb2ttM6LbA6UUTcmVKa1u44tG6Y73ox3/VjzuvFfNeL+a6XwZxvvyIoSZIkSSWxwJIkSZKkklhgwc/aHYDWKfNdL+a7fsx5vZjvejHf9TJo8137MViSJEmSVBafYEmSJElSSSywJEmSJKkkHVdgRcSkiLgpIh6IiPsj4qi8fpOImBsRj+Sfo/L6rSNiXkT8JyKO7eZ8QyLinoi4qodrHprP+0hEHNqw/rqIuDfHcWZEDGk23rzt7Tm2hRFxZUSMbLV/qmYQ5nt4RNzRsN83G7ZtHhG3R8TiiLgoItZrtX+qpmL5np1znSJiTKt9U0WdlO+G7VdExKIejt8nIv6cc3tcw3rz3YSK5fz8vH5RRPwiIob1tT+qrmL5/nn+rL8vIuZExIZ97Y+qq1K+G7b/KCKWN9sHTUspdVQDxgPvyMtvAB4GtgFOBo7L648Dvp+XNwV2Ar4NHNvN+Y4GfgNctZbrbQL8Jf8clZdH5W0j888ALgU+0Wy8+fV84D15eRbwrXb3b6e1QZjvADbMy8OA24Fd8+uLVx0DnAkc0e7+7bRWsXzvCEwGlgBj2t23ndg6Kd95+0H5+EVrOX4I8CgwBVgPuJeuz3PzXb+c75c/AwK4AD/Tq57vkQ37/XBV/LZq5jtvnwacBywvu6867glWSmlpSunuvPwC8CAwATgQOCfvdg7w4bzP0yml+cCra54rIiYCHwTO7uGSM4C5KaV/ppT+BcwF9snnfj7vM5QiMf83I0gP8QJsBdySl+cCH+3t/dfNIMx3SimtutMxLLcUEQFMB+asGbO6VCXfeds9KaUlzb3zeuqkfOe70UcDJ/Vw/M7A4pTSX1JKrwAX5ljNd5MqlvNr8mdAAu4AJjbRBbVSsXw/n88TwAi6+Teh7qqU7yi+tXIK8KUm3nqfdVyB1SgiJlPcNbwdGJdSWpo3/QMY18QpTqfouJU97DMBeLzh9RN0FUhExPXA08ALdP3nuZl4Ae4nJxI4GJjURMy1NVjynR9pL8j7zU0p3Q6MBp5LKa3o7rz6f4M83+qjDsj3t4AfAC/183j1UVVynr8aeAhwXRMx11YV8h0Rv8zxbg38uImYa6sC+Z4NXNEQd6k6tsDKlemlwBca7jQDxV1lermzEBH7A0+nlO5qJY6U0gyKR6LrUzyh6Eu8s4AjI+Iuikepr7QSS5UNpnynlF5LKe1AcTdz54jYrpVr1pH5rpd25zsidgC2SCld3p/j1XcVy/kZwC0ppVtLOFclVSXfKaWZwGYUT2Y+3sq5qmyw5zsiNqN48DFgRXRHFlj5btGlwPkppcvy6qciYnzePp7ibnJP9gAOiIglFI8Ep0fEryNil4hYkNsBwJOs/mRpYl73Pymll4HfAgfmAX6rjj+8h3hJKT2UUvpASumdFN/ffrQf3VF5gy3fDfs9B9xE8bj6WWDjiBi6tvOqUJF8q0kdku/dgGn5+NuArSLiD93ku9c/L+pdlXIeEV8HxlJ8FUndqFK+obiplmNwWEc3KpLvHYGpwOJ8jtdHxOJ+dcjapA4YNNfYKAaTngucvsb6U1h9AN3Ja2z/Bt0MoMvb9qLnAXR/pRg8NyovbwJsCIzP+wwFLgJmNxtv3rZp/vm6vM+sdvdvp7VBmO+xwMZ5eQRwK7B/fn0Jq09ycWS7+7fTWpXy3bDPEpz0oKPzvcY+k1n7gOihFIOoN6drQPS25rueOQcOA/4EjGh3v3Zqq0q+8/uY2vCeTgVObXf/dlqrSr672a/0SS7anqxu3uSeFI8W7wMW5LYfxRiX3wGPADeu6mDgjRTfqXweeC4vj1zjnGtNXt4+C1ic28y8bhzFLID3AYsoHiMObTbevO0oihlWHga+B0S7+7fT2iDM99uAexr2O7Fh2xSKgdCLKYqt9dvdv53WKpbvz+d4VgB/B85ud/92WuuUfK+xfTJr+cc4b9+P4jP7UeB4813rnK/I61a9jxOb7Ye6tKrkm+JG+B+BhRSf9eevGZetOvnuZp/SC6zIJ5YkSZIktagjx2BJkiRJ0mBkgSVJkiRJJbHAkiRJkqSSWGBJkiRJUkkssCRJkiSpJBZYkiRJklQSCyxJkiRJKsl/AW/JZwN7EHEsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot forecast (red) vs prev 3 days actual (blue) vs actual outcome (green)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(12, 4))\n",
    "\n",
    "ax.plot(\n",
    "    df_march.index.values[-72:], \n",
    "    df_march.temp.values[-72:], \n",
    "    label=\"train data\")\n",
    "\n",
    "ax.plot(\n",
    "    df_april.index.values[:72], \n",
    "    df_april.temp.values[:72], \n",
    "    label=\"actual outcome\")\n",
    "\n",
    "ax.plot(\n",
    "    pd.date_range(\"2014-04-01\", \"2014-04-4\", freq=\"H\").values,\n",
    "    result.predict(\"2014-04-01\", \"2014-04-4\"), \n",
    "    label=\"predicted outcome\")\n",
    "\n",
    "ax.legend()\n",
    "fig.tight_layout()\n",
    "#fig.savefig(\"ch14-timeseries-prediction.pdf\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}