{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Régression linéaire\n",
    "\n",
    "Ce notebook s'intéresse à la façon d'interpréter les résultats d'une régression linéaire lorsque les variables sont corrélées puis il explore une façon d'associer arbre de décision et régression linéaire pour construire une régression linéaire par morceaux."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Un cas simple\n",
    "\n",
    "Une façon d'interpréter des résultats statistiques est de les calculer dans un cas où la réponse cherchée est connue. On simule un modèle simple $Y=\\alpha X_1 + 0.X_2 + \\epsilon$ et on cale une régression linéaire. On suppose que $X_1, X_2, \\epsilon$ sont des variables aléatoires gaussiennes de même variance et moyenne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1000, 3), (1000,))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy.random as npr\n",
    "\n",
    "eps = npr.normal(1000)\n",
    "X = npr.normal(size=(1000, 3))\n",
    "alpha = 2\n",
    "Y = alpha * X[:, 0] + X[:, 2]\n",
    "X.shape, Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.0312982 ,  0.05188551],\n",
       "       [-0.0312982 ,  1.        , -0.00356494],\n",
       "       [ 0.05188551, -0.00356494,  1.        ]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import corrcoef\n",
    "\n",
    "corrcoef(X.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.regression.linear_model import OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "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>   0.815</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.815</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   2204.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 15 Oct 2018</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:34:12</td>     <th>  Log-Likelihood:    </th> <td> -1385.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th> <td>   2774.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   998</td>      <th>  BIC:               </th> <td>   2784.</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>x1</th> <td>    2.0519</td> <td>    0.031</td> <td>   66.347</td> <td> 0.000</td> <td>    1.991</td> <td>    2.113</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>   -0.0032</td> <td>    0.033</td> <td>   -0.097</td> <td> 0.922</td> <td>   -0.067</td> <td>    0.061</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.709</td> <th>  Durbin-Watson:     </th> <td>   1.990</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.701</td> <th>  Jarque-Bera (JB):  </th> <td>   0.674</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.063</td> <th>  Prob(JB):          </th> <td>   0.714</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.010</td> <th>  Cond. No.          </th> <td>    1.07</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:                      y   R-squared:                       0.815\n",
       "Model:                            OLS   Adj. R-squared:                  0.815\n",
       "Method:                 Least Squares   F-statistic:                     2204.\n",
       "Date:                Mon, 15 Oct 2018   Prob (F-statistic):               0.00\n",
       "Time:                        10:34:12   Log-Likelihood:                -1385.2\n",
       "No. Observations:                1000   AIC:                             2774.\n",
       "Df Residuals:                     998   BIC:                             2784.\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             2.0519      0.031     66.347      0.000       1.991       2.113\n",
       "x2            -0.0032      0.033     -0.097      0.922      -0.067       0.061\n",
       "==============================================================================\n",
       "Omnibus:                        0.709   Durbin-Watson:                   1.990\n",
       "Prob(Omnibus):                  0.701   Jarque-Bera (JB):                0.674\n",
       "Skew:                           0.063   Prob(JB):                        0.714\n",
       "Kurtosis:                       3.010   Cond. No.                         1.07\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, X[:, :2])\n",
    "results = model.fit()\n",
    "su = results.summary()\n",
    "su"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.8153831029946165, 0.8150131292531227)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.rsquared, results.rsquared_adj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On vérifie que le coefficient devant $X_1$ est non nul (P-value nulle, 0 n'est pas l'intervalle de confiance). Le coefficient devant $X_2$ n'est pas nul mais presque, la P-value est élevée, le coefficient $R^2$ est élevé. Dessinons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\python370_x64\\lib\\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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",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "ax[0].plot(X[:, 0], Y, \".\")\n",
    "seaborn.kdeplot(X[:, 0], Y, cmap=\"Reds\", shade=True, shade_lowest=False, ax=ax[1])\n",
    "ax[0].set_title(\"nuage de points\")\n",
    "ax[1].set_title(\"estimation de la densité\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evolution de R2\n",
    "\n",
    "Dans la régression précédente, le coefficient $R^2$ transcrit en quelque sorte la part du bruit $\\epsilon$ par rapport au terme $\\alpha X_1$. Faisons varier $\\alpha$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "alphas = []\n",
    "r2s = []\n",
    "for a in [0.1 * i for i in range(50)]:\n",
    "    Y = a * X[:, 0] + X[:, 2]\n",
    "    model = OLS(Y, X[:, :2])\n",
    "    results = model.fit()\n",
    "    alphas.append(a)\n",
    "    r2s.append(results.rsquared)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(alphas, r2s, \".\", label=\"observed\")\n",
    "ax.plot(alphas, [a**2 / (1 + a**2) for a in alphas], label=\"theoretical\")\n",
    "ax.set_xlabel(\"alpha\")\n",
    "ax.set_ylabel(\"r2\")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans ce cas de régression simple, la valeur à prédire est $y_i$, la valeur prédite est $\\hat{y_i}=\\alpha X_{1i}$ et la moyenne $\\bar{y} = \\alpha \\bar{X_1} + \\bar{\\epsilon} = 0$.\n",
    "\n",
    "$$R^2 = 1 - \\frac{\\sum_{i=1}^n (\\hat{y_i}-\\bar{y})^2}{\\sum_{i=1}^n (y_i - \\bar{y})^2}=1-\\frac{\\mathbb{V}\\epsilon}{\\alpha^2\\mathbb{V}X_1+\\mathbb{V}\\epsilon} = 1 - \\frac{1}{1+\\alpha^2}=\\frac{\\alpha^2}{1+\\alpha^2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deux variables corrélées\n",
    "\n",
    "On ne change pas le modèle mais on fait en sorte que $X_2=X_1$. Les deux variables sont corrélées."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "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>   0.810</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.810</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   4271.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 27 Nov 2017</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:06:03</td>     <th>  Log-Likelihood:    </th> <td> -1411.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th> <td>   2824.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   999</td>      <th>  BIC:               </th> <td>   2829.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</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>x1</th> <td>    1.0288</td> <td>    0.016</td> <td>   65.349</td> <td> 0.000</td> <td>    0.998</td> <td>    1.060</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>    1.0288</td> <td>    0.016</td> <td>   65.349</td> <td> 0.000</td> <td>    0.998</td> <td>    1.060</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 8.165</td> <th>  Durbin-Watson:     </th> <td>   1.944</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.017</td> <th>  Jarque-Bera (JB):  </th> <td>   6.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.064</td> <th>  Prob(JB):          </th> <td>  0.0492</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.642</td> <th>  Cond. No.          </th> <td>1.61e+16</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.810\n",
       "Model:                            OLS   Adj. R-squared:                  0.810\n",
       "Method:                 Least Squares   F-statistic:                     4271.\n",
       "Date:                Mon, 27 Nov 2017   Prob (F-statistic):               0.00\n",
       "Time:                        12:06:03   Log-Likelihood:                -1411.2\n",
       "No. Observations:                1000   AIC:                             2824.\n",
       "Df Residuals:                     999   BIC:                             2829.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             1.0288      0.016     65.349      0.000       0.998       1.060\n",
       "x2             1.0288      0.016     65.349      0.000       0.998       1.060\n",
       "==============================================================================\n",
       "Omnibus:                        8.165   Durbin-Watson:                   1.944\n",
       "Prob(Omnibus):                  0.017   Jarque-Bera (JB):                6.024\n",
       "Skew:                          -0.064   Prob(JB):                       0.0492\n",
       "Kurtosis:                       2.642   Cond. No.                     1.61e+16\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 7.69e-30. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:, 1] = X[:, 0]\n",
    "Y = 2 * X[:, 0] + X[:, 2]\n",
    "model = OLS(Y, X[:, :2])\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.rank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les variables corrélées n'ont pas l'air de déranger l'algorithme de résolution car il utilise la méthode [SVD](https://en.wikipedia.org/wiki/Singular-value_decomposition) pour résoudre le même problème dans un espace de moindre dimension. Le problème survient que les deux variables ne sont pas complétement corrélées. On étudie le modèle $Y \\sim X_1 + X'_2$ avec $X'_2 = \\alpha X_1 + (1-\\alpha) X_2$ et on réduit la variance du bruit pour en diminuer les effets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_ = npr.normal(size=(1000, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "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>c1</th>\n",
       "      <th>c2</th>\n",
       "      <th>r2</th>\n",
       "      <th>rank</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.90</th>\n",
       "      <td>0.976370</td>\n",
       "      <td>1.028982</td>\n",
       "      <td>0.997391</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.91</th>\n",
       "      <td>0.973150</td>\n",
       "      <td>1.032202</td>\n",
       "      <td>0.997416</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.92</th>\n",
       "      <td>0.969125</td>\n",
       "      <td>1.036227</td>\n",
       "      <td>0.997440</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.93</th>\n",
       "      <td>0.963950</td>\n",
       "      <td>1.041402</td>\n",
       "      <td>0.997464</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.94</th>\n",
       "      <td>0.957049</td>\n",
       "      <td>1.048303</td>\n",
       "      <td>0.997489</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.95</th>\n",
       "      <td>0.947389</td>\n",
       "      <td>1.057963</td>\n",
       "      <td>0.997513</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.96</th>\n",
       "      <td>0.932898</td>\n",
       "      <td>1.072454</td>\n",
       "      <td>0.997536</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.97</th>\n",
       "      <td>0.908747</td>\n",
       "      <td>1.096605</td>\n",
       "      <td>0.997560</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.98</th>\n",
       "      <td>0.860444</td>\n",
       "      <td>1.144908</td>\n",
       "      <td>0.997583</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.99</th>\n",
       "      <td>0.715536</td>\n",
       "      <td>1.289816</td>\n",
       "      <td>0.997606</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.00</th>\n",
       "      <td>1.001279</td>\n",
       "      <td>1.001279</td>\n",
       "      <td>0.997627</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             c1        c2        r2  rank\n",
       "alpha                                    \n",
       "0.90   0.976370  1.028982  0.997391     2\n",
       "0.91   0.973150  1.032202  0.997416     2\n",
       "0.92   0.969125  1.036227  0.997440     2\n",
       "0.93   0.963950  1.041402  0.997464     2\n",
       "0.94   0.957049  1.048303  0.997489     2\n",
       "0.95   0.947389  1.057963  0.997513     2\n",
       "0.96   0.932898  1.072454  0.997536     2\n",
       "0.97   0.908747  1.096605  0.997560     2\n",
       "0.98   0.860444  1.144908  0.997583     2\n",
       "0.99   0.715536  1.289816  0.997606     2\n",
       "1.00   1.001279  1.001279  0.997627     1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphas = [0.9 + i * 0.01 for i in range(11)]\n",
    "res = []\n",
    "for a in alphas:\n",
    "    X = X_.copy()\n",
    "    X[:, 1] = a * X[:, 0] + (1 - a) * X[:, 1]\n",
    "    Y = X[:, 0] + X[:, 1] + 0.1 * X[:, 2]\n",
    "    model = OLS(Y, X[:, :2])\n",
    "    results = model.fit()\n",
    "    res.append(\n",
    "        dict(\n",
    "            alpha=a,\n",
    "            r2=results.rsquared,\n",
    "            rank=model.rank,\n",
    "            c1=results.params[0],\n",
    "            c2=results.params[1],\n",
    "        )\n",
    "    )\n",
    "\n",
    "import pandas\n",
    "\n",
    "df = pandas.DataFrame(res)\n",
    "df = df.set_index(\"alpha\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "df[[\"r2\"]].plot(ax=ax[0])\n",
    "df[[\"c1\", \"c2\"]].plot(ax=ax[1])\n",
    "ax[0].set_title(\"R2\")\n",
    "ax[1].set_title(\"coefficients\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le $r^2$ augmente quand la corrélation augmente mais les coefficients sont moins fiables. Les résultats devraient être sensiblement identiques en théorie mais en pratique, plus le déterminant devient proche de zéro, plus l'ordinateur est limité par sa précision numérique. Pour en savoir plus, vous pouvez lire un examen écrit que j'ai rédigé, en python bien sûr : [Examen Programmation ENSAE première année\n",
    "2006](http://www.xavierdupre.fr/site2013/enseignements/tdnote/ecrit_2006.pdf). Cette précision est aux alentours de $10^{-15}$ ce qui correspond à la précision numérique des [double](https://en.wikipedia.org/wiki/Double-precision_floating-point_format)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "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>c1</th>\n",
       "      <th>c2</th>\n",
       "      <th>r2</th>\n",
       "      <th>rank</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha_1</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>-1.000000e-10</th>\n",
       "      <td>-2.898180e+08</td>\n",
       "      <td>2.898180e+08</td>\n",
       "      <td>0.811519</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1.000000e-11</th>\n",
       "      <td>-2.898201e+09</td>\n",
       "      <td>2.898201e+09</td>\n",
       "      <td>0.811519</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-9.999779e-13</th>\n",
       "      <td>-2.898941e+10</td>\n",
       "      <td>2.898941e+10</td>\n",
       "      <td>0.811519</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1.000311e-13</th>\n",
       "      <td>-2.891422e+11</td>\n",
       "      <td>2.891422e+11</td>\n",
       "      <td>0.811518</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-9.992007e-15</th>\n",
       "      <td>-2.915101e+12</td>\n",
       "      <td>2.915101e+12</td>\n",
       "      <td>0.811508</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-9.992007e-16</th>\n",
       "      <td>1.012789e+00</td>\n",
       "      <td>1.012789e+00</td>\n",
       "      <td>0.811359</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1.110223e-16</th>\n",
       "      <td>1.012789e+00</td>\n",
       "      <td>1.012789e+00</td>\n",
       "      <td>0.811359</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.000000e+00</th>\n",
       "      <td>1.012789e+00</td>\n",
       "      <td>1.012789e+00</td>\n",
       "      <td>0.811359</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         c1            c2        r2  rank\n",
       "alpha_1                                                  \n",
       "-1.000000e-10 -2.898180e+08  2.898180e+08  0.811519     2\n",
       "-1.000000e-11 -2.898201e+09  2.898201e+09  0.811519     2\n",
       "-9.999779e-13 -2.898941e+10  2.898941e+10  0.811519     2\n",
       "-1.000311e-13 -2.891422e+11  2.891422e+11  0.811518     2\n",
       "-9.992007e-15 -2.915101e+12  2.915101e+12  0.811508     2\n",
       "-9.992007e-16  1.012789e+00  1.012789e+00  0.811359     2\n",
       "-1.110223e-16  1.012789e+00  1.012789e+00  0.811359     1\n",
       " 0.000000e+00  1.012789e+00  1.012789e+00  0.811359     1"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alphas = [1 - 10 ** (-i) for i in range(10, 18)]\n",
    "res = []\n",
    "for a in alphas:\n",
    "    X = X_.copy()\n",
    "    X[:, 1] = a * X[:, 0] + (1 - a) * X[:, 1]\n",
    "    Y = X[:, 0] + X[:, 1] + X[:, 2]\n",
    "    model = OLS(Y, X[:, :2])\n",
    "    results = model.fit()\n",
    "    res.append(\n",
    "        dict(\n",
    "            alpha_1=a - 1,\n",
    "            r2=results.rsquared,\n",
    "            rank=model.rank,\n",
    "            c1=results.params[0],\n",
    "            c2=results.params[1],\n",
    "        )\n",
    "    )\n",
    "\n",
    "import pandas\n",
    "\n",
    "df = pandas.DataFrame(res)\n",
    "df = df.set_index(\"alpha_1\")\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On fait un dernier test avec [scikit-learn](http://scikit-learn.org/stable/) pour vérifier que l'algorithme de résolution donne des résultats similaires pour un cas où le déterminant est quasi-nul."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": 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>c1</th>\n",
       "      <th>c2</th>\n",
       "      <th>r2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.90</th>\n",
       "      <td>7.601931e-01</td>\n",
       "      <td>1.293903e+00</td>\n",
       "      <td>0.796916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.91</th>\n",
       "      <td>7.275372e-01</td>\n",
       "      <td>1.326559e+00</td>\n",
       "      <td>0.798417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.92</th>\n",
       "      <td>6.867173e-01</td>\n",
       "      <td>1.367379e+00</td>\n",
       "      <td>0.799911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.93</th>\n",
       "      <td>6.342346e-01</td>\n",
       "      <td>1.419862e+00</td>\n",
       "      <td>0.801399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.94</th>\n",
       "      <td>5.642576e-01</td>\n",
       "      <td>1.489839e+00</td>\n",
       "      <td>0.802880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.95</th>\n",
       "      <td>4.662898e-01</td>\n",
       "      <td>1.587807e+00</td>\n",
       "      <td>0.804355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.96</th>\n",
       "      <td>3.193382e-01</td>\n",
       "      <td>1.734758e+00</td>\n",
       "      <td>0.805823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.97</th>\n",
       "      <td>7.441878e-02</td>\n",
       "      <td>1.979678e+00</td>\n",
       "      <td>0.807283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.98</th>\n",
       "      <td>-4.154200e-01</td>\n",
       "      <td>2.469516e+00</td>\n",
       "      <td>0.808736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.99</th>\n",
       "      <td>-1.884936e+00</td>\n",
       "      <td>3.939033e+00</td>\n",
       "      <td>0.810182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.00</th>\n",
       "      <td>8.512221e+13</td>\n",
       "      <td>-8.512221e+13</td>\n",
       "      <td>0.811404</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 c1            c2        r2\n",
       "alpha                                      \n",
       "0.90   7.601931e-01  1.293903e+00  0.796916\n",
       "0.91   7.275372e-01  1.326559e+00  0.798417\n",
       "0.92   6.867173e-01  1.367379e+00  0.799911\n",
       "0.93   6.342346e-01  1.419862e+00  0.801399\n",
       "0.94   5.642576e-01  1.489839e+00  0.802880\n",
       "0.95   4.662898e-01  1.587807e+00  0.804355\n",
       "0.96   3.193382e-01  1.734758e+00  0.805823\n",
       "0.97   7.441878e-02  1.979678e+00  0.807283\n",
       "0.98  -4.154200e-01  2.469516e+00  0.808736\n",
       "0.99  -1.884936e+00  3.939033e+00  0.810182\n",
       "1.00   8.512221e+13 -8.512221e+13  0.811404"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "alphas = [0.9 + i * 0.01 for i in range(11)]\n",
    "res = []\n",
    "for a in alphas:\n",
    "    X = X_.copy()\n",
    "    X[:, 1] = a * X[:, 0] + (1 - a) * X[:, 1]\n",
    "    Y = X[:, 0] + X[:, 1] + X[:, 2]\n",
    "    model = LinearRegression()\n",
    "    model.fit(X[:, :2], Y)\n",
    "    r2 = r2_score(Y, model.predict(X[:, :2]))\n",
    "    res.append(dict(alpha=a, c1=model.coef_[0], c2=model.coef_[1], r2=r2))\n",
    "\n",
    "import pandas\n",
    "\n",
    "df = pandas.DataFrame(res)\n",
    "df = df.set_index(\"alpha\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(12, 4))\n",
    "df[[\"c1\", \"c2\"]].plot(ax=ax[1])\n",
    "df[[\"c1\", \"c2\"]].plot(ax=ax[2])\n",
    "df[[\"r2\"]].plot(ax=ax[0])\n",
    "ax[0].set_title(\"R2\")\n",
    "ax[1].set_title(\"coefficients\")\n",
    "ax[2].set_ylim([-5, 5])\n",
    "ax[2].set_title(\"coefficients, échelle tronquée\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le second graphe est trompeur mais il ne faut pas oublier de regarder l'échelle de l'axe des ordonnées."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indicatrices\n",
    "\n",
    "$X_1$ est une variable aléatoire gaussienne. On teste maintenant un modèle $Y = X'_1 + X'_2 + \\epsilon$ avec $X'_1 = X_1 \\mathbb{1}_{X_1 < 0}$ et $X'_2 = X_1 \\mathbb{1}_{X_1 \\geqslant 0}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.47358312, -0.03083914],\n",
       "       [ 0.47358312,  1.        , -0.01293737],\n",
       "       [-0.03083914, -0.01293737,  1.        ]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = npr.normal(size=(1000, 3))\n",
    "X[:, 1] = X[:, 0]\n",
    "X[X[:, 0] >= 0, 0] = 0\n",
    "X[X[:, 1] < 0, 1] = 0\n",
    "Y = X[:, 0] + X[:, 1] + X[:, 2]\n",
    "corrcoef(X.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas import DataFrame\n",
    "\n",
    "names = [\"X%d\" % i for i in range(X.shape[1] - 1)]\n",
    "ax = (\n",
    "    DataFrame(X[:50, :2], columns=names)\n",
    "    .sort_values(names)\n",
    "    .reset_index(drop=True)\n",
    "    .plot()\n",
    ")\n",
    "ax.set_title(\"Représentation des features tronquées\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "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>2.212e+33</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 15 Oct 2018</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:56:29</td>     <th>  Log-Likelihood:    </th>  <td>  33713.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th> <td>-6.742e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   997</td>      <th>  BIC:               </th> <td>-6.740e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</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>x1</th> <td>    1.0000</td> <td> 2.42e-17</td> <td> 4.14e+16</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>    1.0000</td> <td> 2.39e-17</td> <td> 4.18e+16</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th> <td>    1.0000</td> <td> 1.73e-17</td> <td> 5.78e+16</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 4.249</td> <th>  Durbin-Watson:     </th> <td>   2.031</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.119</td> <th>  Jarque-Bera (JB):  </th> <td>   4.338</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.107</td> <th>  Prob(JB):          </th> <td>   0.114</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.242</td> <th>  Cond. No.          </th> <td>    1.40</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:                      y   R-squared:                       1.000\n",
       "Model:                            OLS   Adj. R-squared:                  1.000\n",
       "Method:                 Least Squares   F-statistic:                 2.212e+33\n",
       "Date:                Mon, 15 Oct 2018   Prob (F-statistic):               0.00\n",
       "Time:                        10:56:29   Log-Likelihood:                 33713.\n",
       "No. Observations:                1000   AIC:                        -6.742e+04\n",
       "Df Residuals:                     997   BIC:                        -6.740e+04\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             1.0000   2.42e-17   4.14e+16      0.000       1.000       1.000\n",
       "x2             1.0000   2.39e-17   4.18e+16      0.000       1.000       1.000\n",
       "x3             1.0000   1.73e-17   5.78e+16      0.000       1.000       1.000\n",
       "==============================================================================\n",
       "Omnibus:                        4.249   Durbin-Watson:                   2.031\n",
       "Prob(Omnibus):                  0.119   Jarque-Bera (JB):                4.338\n",
       "Skew:                          -0.107   Prob(JB):                        0.114\n",
       "Kurtosis:                       3.242   Cond. No.                         1.40\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, X[:, :3])\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On découpe en trois."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.00347584,  0.16846101,  0.06722762],\n",
       "       [-0.00347584,  1.        ,  0.00326437, -0.04707208],\n",
       "       [ 0.16846101,  0.00326437,  1.        ,  0.08754832],\n",
       "       [ 0.06722762, -0.04707208,  0.08754832,  1.        ]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "X = npr.normal(size=(1000, 4))\n",
    "for i in range(3):\n",
    "    X[:, i] = X_[:, 0]\n",
    "X[:, 3] = X_[:, 2]\n",
    "X[X_[:, 0] > -1, 0] = 0\n",
    "X[(X_[:, 0] < -1) | (X_[:, 0] > 1), 1] = 0\n",
    "X[X_[:, 0] < 1, 2] = 0\n",
    "Y = X[:, 0] + X[:, 1] + X[:, 2] + X[:, 3]\n",
    "corrcoef(X.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas import DataFrame\n",
    "\n",
    "names = [\"X%d\" % i for i in range(X.shape[1] - 1)]\n",
    "ax = (\n",
    "    DataFrame(X[:50, :3], columns=names)\n",
    "    .sort_values(names)\n",
    "    .reset_index(drop=True)\n",
    "    .plot()\n",
    ")\n",
    "ax.set_title(\"Représentation des features tronquées\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "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>1.910e+32</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 15 Oct 2018</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:57:27</td>     <th>  Log-Likelihood:    </th>  <td>  32608.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th> <td>-6.521e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   996</td>      <th>  BIC:               </th> <td>-6.519e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</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>x1</th> <td>    1.0000</td> <td> 8.75e-17</td> <td> 1.14e+16</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>    1.0000</td> <td> 1.22e-16</td> <td> 8.23e+15</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th> <td>    1.0000</td> <td> 8.33e-17</td> <td>  1.2e+16</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th> <td>    1.0000</td> <td> 5.23e-17</td> <td> 1.91e+16</td> <td> 0.000</td> <td>    1.000</td> <td>    1.000</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>457.967</td> <th>  Durbin-Watson:     </th> <td>   1.816</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>1967.636</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-2.198</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 8.282</td>  <th>  Cond. No.          </th> <td>    2.35</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:                      y   R-squared:                       1.000\n",
       "Model:                            OLS   Adj. R-squared:                  1.000\n",
       "Method:                 Least Squares   F-statistic:                 1.910e+32\n",
       "Date:                Mon, 15 Oct 2018   Prob (F-statistic):               0.00\n",
       "Time:                        10:57:27   Log-Likelihood:                 32608.\n",
       "No. Observations:                1000   AIC:                        -6.521e+04\n",
       "Df Residuals:                     996   BIC:                        -6.519e+04\n",
       "Df Model:                           4                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             1.0000   8.75e-17   1.14e+16      0.000       1.000       1.000\n",
       "x2             1.0000   1.22e-16   8.23e+15      0.000       1.000       1.000\n",
       "x3             1.0000   8.33e-17    1.2e+16      0.000       1.000       1.000\n",
       "x4             1.0000   5.23e-17   1.91e+16      0.000       1.000       1.000\n",
       "==============================================================================\n",
       "Omnibus:                      457.967   Durbin-Watson:                   1.816\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1967.636\n",
       "Skew:                          -2.198   Prob(JB):                         0.00\n",
       "Kurtosis:                       8.282   Cond. No.                         2.35\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, X[:, :4])\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Régression linéaire par morceaux\n",
    "\n",
    "On se place dans un cas particulier où le problème est linéaire par morceaux :\n",
    "\n",
    "$$Y = -2 X_1 \\mathbb{1}_{X_1 + \\epsilon_1 <0} + 4 X_1 \\mathbb{1}_{X + \\epsilon_1 > 0} + \\epsilon_2$$\n",
    "\n",
    "La régression donne de très mauvais résultat sur ce type de problèmes mais on cherche une façon systématique de découper le problème en segments linéaires."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = npr.normal(size=(1000, 4))\n",
    "alpha = [4, -2]\n",
    "t = (X[:, 0] + X[:, 3] * 0.5) > 0\n",
    "switch = numpy.zeros(X.shape[0])\n",
    "switch[t] = 1\n",
    "Y = alpha[0] * X[:, 0] * t + alpha[1] * X[:, 0] * (1 - t) + X[:, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\")\n",
    "ax.set_title(\"Nuage de points linéaire par morceaux\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "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>   0.094</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.093</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   104.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 15 Oct 2018</td> <th>  Prob (F-statistic):</th> <td>2.69e-23</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:59:28</td>     <th>  Log-Likelihood:    </th> <td> -2594.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th> <td>   5192.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   999</td>      <th>  BIC:               </th> <td>   5197.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</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>x1</th> <td>    1.0252</td> <td>    0.101</td> <td>   10.197</td> <td> 0.000</td> <td>    0.828</td> <td>    1.222</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.882</td> <th>  Durbin-Watson:     </th> <td>   1.092</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.144</td> <th>  Jarque-Bera (JB):  </th> <td>   3.834</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.151</td> <th>  Prob(JB):          </th> <td>   0.147</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.015</td> <th>  Cond. No.          </th> <td>    1.00</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:                      y   R-squared:                       0.094\n",
       "Model:                            OLS   Adj. R-squared:                  0.093\n",
       "Method:                 Least Squares   F-statistic:                     104.0\n",
       "Date:                Mon, 15 Oct 2018   Prob (F-statistic):           2.69e-23\n",
       "Time:                        10:59:28   Log-Likelihood:                -2594.9\n",
       "No. Observations:                1000   AIC:                             5192.\n",
       "Df Residuals:                     999   BIC:                             5197.\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1             1.0252      0.101     10.197      0.000       0.828       1.222\n",
       "==============================================================================\n",
       "Omnibus:                        3.882   Durbin-Watson:                   1.092\n",
       "Prob(Omnibus):                  0.144   Jarque-Bera (JB):                3.834\n",
       "Skew:                           0.151   Prob(JB):                        0.147\n",
       "Kurtosis:                       3.015   Cond. No.                         1.00\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, X[:, :1])\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "yp = results.predict(X[:, :1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\", label=\"expected\")\n",
    "ax.plot(X[:, 0], yp, \".\", label=\"predicted\")\n",
    "ax.legend()\n",
    "ax.set_title(\"Régression linéaire sur un nuage linéaire par morceaux\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Passons à un arbre de décision qui n'est pas le meilleur modèle mais on va détourner ses résultats pour revenir à un problème de régression par morceaux."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "model = DecisionTreeRegressor(min_samples_leaf=10, max_depth=3)\n",
    "model.fit(X[:, :1], Y)\n",
    "yp = model.predict(X[:, :1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\", label=\"expected\")\n",
    "ax.plot(X[:, 0], yp, \".\", label=\"predicted\")\n",
    "ax.legend()\n",
    "r2 = r2_score(Y, model.predict(X[:, :1]))\n",
    "ax.set_title(\"Arbre de décision sur un nuage linéaire par morceaux\\nR2=%f\" % r2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "dot = export_graphviz(model)\n",
    "\n",
    "src = graphviz.Source(dot)\n",
    "src.render(\"tree_dot.gv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On extrait tous les seuils de l'arbre et on ajoute les milieux de segments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-2.0,\n",
       " -1.8018612563610077,\n",
       " -1.6037225127220154,\n",
       " -1.323736995458603,\n",
       " -1.0437514781951904,\n",
       " -0.3109976723790169,\n",
       " 0.4217561334371567,\n",
       " 0.678125374019146,\n",
       " 0.9344946146011353,\n",
       " 1.0011553764343262,\n",
       " 1.067816138267517,\n",
       " 1.2776717841625214,\n",
       " 1.4875274300575256,\n",
       " 1.7147845923900604,\n",
       " 1.9420417547225952]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "th = list(sorted(set(model.tree_.threshold)))\n",
    "th += [(th[i] + th[i - 1]) / 2 for i in range(1, len(th))]\n",
    "th = list(sorted(th))\n",
    "th"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On fait une régression sur les variables $W_{i>0} = X_1 \\mathbb{1}_{X_1 > t_i}$, $W_0 = X_1$ où les $(t_i)$ sont les seuils."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = numpy.zeros((X.shape[0], len(th) + 1))\n",
    "x = X[:, 0]\n",
    "W[:, 0] = x\n",
    "for i in range(len(th)):\n",
    "    W[x > th[i], i + 1] = x[x > th[i]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "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>   0.849</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.847</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   346.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 15 Oct 2018</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:07:03</td>     <th>  Log-Likelihood:    </th> <td> -1697.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th> <td>   3427.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   984</td>      <th>  BIC:               </th> <td>   3506.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    16</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>x1</th>  <td>   -1.8316</td> <td>    0.124</td> <td>  -14.806</td> <td> 0.000</td> <td>   -2.074</td> <td>   -1.589</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th>  <td>   -0.0573</td> <td>    0.210</td> <td>   -0.273</td> <td> 0.785</td> <td>   -0.469</td> <td>    0.354</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th>  <td>   -0.2440</td> <td>    0.235</td> <td>   -1.038</td> <td> 0.300</td> <td>   -0.705</td> <td>    0.217</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th>  <td>    0.3291</td> <td>    0.218</td> <td>    1.508</td> <td> 0.132</td> <td>   -0.099</td> <td>    0.757</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th>  <td>   -0.3610</td> <td>    0.206</td> <td>   -1.756</td> <td> 0.079</td> <td>   -0.764</td> <td>    0.042</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x6</th>  <td>    0.5528</td> <td>    0.197</td> <td>    2.811</td> <td> 0.005</td> <td>    0.167</td> <td>    0.939</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x7</th>  <td>    3.2628</td> <td>    0.395</td> <td>    8.253</td> <td> 0.000</td> <td>    2.487</td> <td>    4.039</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x8</th>  <td>    1.4566</td> <td>    0.449</td> <td>    3.244</td> <td> 0.001</td> <td>    0.576</td> <td>    2.338</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x9</th>  <td>    0.2701</td> <td>    0.311</td> <td>    0.869</td> <td> 0.385</td> <td>   -0.340</td> <td>    0.880</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x10</th> <td>    0.7213</td> <td>    0.374</td> <td>    1.928</td> <td> 0.054</td> <td>   -0.013</td> <td>    1.456</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x11</th> <td>   -0.4599</td> <td>    0.457</td> <td>   -1.006</td> <td> 0.315</td> <td>   -1.357</td> <td>    0.437</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x12</th> <td>    0.4177</td> <td>    0.378</td> <td>    1.105</td> <td> 0.269</td> <td>   -0.324</td> <td>    1.159</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x13</th> <td>   -0.2703</td> <td>    0.253</td> <td>   -1.069</td> <td> 0.285</td> <td>   -0.766</td> <td>    0.226</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x14</th> <td>    0.5325</td> <td>    0.226</td> <td>    2.360</td> <td> 0.018</td> <td>    0.090</td> <td>    0.975</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x15</th> <td>   -0.3703</td> <td>    0.229</td> <td>   -1.618</td> <td> 0.106</td> <td>   -0.819</td> <td>    0.079</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x16</th> <td>    0.1996</td> <td>    0.194</td> <td>    1.026</td> <td> 0.305</td> <td>   -0.182</td> <td>    0.581</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>228.022</td> <th>  Durbin-Watson:     </th> <td>   1.978</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 716.200</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.110</td>  <th>  Prob(JB):          </th> <td>3.01e-156</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.502</td>  <th>  Cond. No.          </th> <td>    36.3</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:                      y   R-squared:                       0.849\n",
       "Model:                            OLS   Adj. R-squared:                  0.847\n",
       "Method:                 Least Squares   F-statistic:                     346.9\n",
       "Date:                Mon, 15 Oct 2018   Prob (F-statistic):               0.00\n",
       "Time:                        11:07:03   Log-Likelihood:                -1697.7\n",
       "No. Observations:                1000   AIC:                             3427.\n",
       "Df Residuals:                     984   BIC:                             3506.\n",
       "Df Model:                          16                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1            -1.8316      0.124    -14.806      0.000      -2.074      -1.589\n",
       "x2            -0.0573      0.210     -0.273      0.785      -0.469       0.354\n",
       "x3            -0.2440      0.235     -1.038      0.300      -0.705       0.217\n",
       "x4             0.3291      0.218      1.508      0.132      -0.099       0.757\n",
       "x5            -0.3610      0.206     -1.756      0.079      -0.764       0.042\n",
       "x6             0.5528      0.197      2.811      0.005       0.167       0.939\n",
       "x7             3.2628      0.395      8.253      0.000       2.487       4.039\n",
       "x8             1.4566      0.449      3.244      0.001       0.576       2.338\n",
       "x9             0.2701      0.311      0.869      0.385      -0.340       0.880\n",
       "x10            0.7213      0.374      1.928      0.054      -0.013       1.456\n",
       "x11           -0.4599      0.457     -1.006      0.315      -1.357       0.437\n",
       "x12            0.4177      0.378      1.105      0.269      -0.324       1.159\n",
       "x13           -0.2703      0.253     -1.069      0.285      -0.766       0.226\n",
       "x14            0.5325      0.226      2.360      0.018       0.090       0.975\n",
       "x15           -0.3703      0.229     -1.618      0.106      -0.819       0.079\n",
       "x16            0.1996      0.194      1.026      0.305      -0.182       0.581\n",
       "==============================================================================\n",
       "Omnibus:                      228.022   Durbin-Watson:                   1.978\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              716.200\n",
       "Skew:                          -1.110   Prob(JB):                    3.01e-156\n",
       "Kurtosis:                       6.502   Cond. No.                         36.3\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, W)\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dessinons les résultats de la prédictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2BWCpVIjI5SJSR0TqYuLbP1Ky4bAWiyVBrAOwVDaGYjrvcjGhj+vVNlMtlnLBhoAsFoulhmJbABaLxVJDsQ7AYrFYaijWAVgqJWLE2w6J0dffIkZY7Xhn3f0isswRGFsvIveX8hztRGS2iBwUI7R2QTHbNhYjerfD+UwUkfoxtjvHESvzivfVEiOSlitGbO9FEUmNsW8HETksIm95ll0mRqhvt3MfXhGRelH7XSAii0XkgBgRt5+X5n5Yah7WAVgqM5c7s2TPAM7E6MWAmRx2C9AII0j3axG5vhTHnwR8j5lt/DAwVUSaxdn2Med87TETj04gapKbY9SfxYzd9/IgRtagG0a2oSfwSIxzvAAsjFrWwDl3S8wksFbA/3nOeRpmnP3DzrZnUALZBEvNxjoAS6VHVbdghMXOcL7/XVUXq2pAVVcBHwADSnJMZ8ZoT+BPqnpIVadhhpxeHWeXk4H3VXWvqu4B3sNMQvJyL2ai3sqo5ZcDz6nqLmcm63PA7VHluR4z5+Fz73JHHuRTVT2oqnmYiVHea30EeFlVP3Hux05VjaW/Y7EUwToAS6VHRFoBgzEzaKPXCTAQWO5Z9oMTMon1edHZrCuQ6cyodVlKUaPu8gIwREQaiUgjjKP4xHPOthijPibWJRApaSFAKxFp4Oxb39nv3vh3IczZ3msF+jnH+FGMdv5bkmCOBIvFqoFaKjPvi4hi1Ci/wChfRjMaU5EJJzxR1e4JHPt4YE/Usj1Eqlt6WYzR33HVST/H5C5weQ54VFX3S9E0Cp8AvxOR2RjVSzf5SR3nnH8Bxqvqxhj7hhGRC4FbiZS/aIXRvLkIM3fiDYxu/01xD2SxONgWgKUy8zM1yXHOBTpjJInDiMivMX0Bl6nqkaK7F8t+TJISL/Ux+jOxmAKsxgiV1cfIHL/llONyoJ6qxtMF+iumr2EJRrfmfYyy5jZHqOwC4J/FFVZE+mFi/dc4eksuhzA6+qtVdT/wOJBwEntLzca2ACyVHlX9UkQmYKQh3Oxht2M6V89W1Rzv9iKynEjZYi9vqepdmDBKexGp5wkD9cAY2Vj0AH6lqgecc4ylUOhuENBLTOpFMJ2xQRE5XVWHquohTLa3Xzv7jgAyVDUoIudikpxskMIcDH4ROU1V3fSJZ2KE3m5X1Yg+Akw2Lzub01I6jlUmGvuxn+I+eDJ4Od+bYZQoz8CEN7YAXcp4jvkYp1IbuBLTCdsszrazMaGV45zPi8A8Z109jCa9+3kHU6Nv7Kw/CTOKRzAx+43ARc66OlH7/gMji93MWd8Nk7Tlujjluh2jqNneOda7wL+P9e9nP1XjY0NAliqBmtEzbwKPYoZFNgEWOvME9js18pJyPWZ4Zh5Givsa5zyIyE1OS8LldkxNPQejR98eJw+yqu5T1S3uBxOWOaCqu5x9T8GEfg5gYvQPqupMZ9+DUfvuBw675cB0DDfD5Gh2rzVcLlV9zbkv32EydB2hsI/BYikWqwVksVgsNRTbArBYLJYainUAFovFUkOxDsBisVhqKNYBWCwWSw2lUs8DaNq0qbZr1+5YF8NisViqDBkZGTtUNZ6oYQSV2gG0a9eORYsWHetiWCwWS5VBRLIT3daGgCwWi6WGYh2AxWKx1FCsA7BYLJYaSqXuA4hFQUEBOTk5HD58+FgXpUpTu3ZtWrVqRWpqkcyEFoulhlDlHEBOTg716tWjXbt2FKedbomPqrJz505ycnI4+eSTj3VxLBbLMaLKhYAOHz5MkyZNrPEvAyJCkyZNbCvKYqnhVDkHAFjjnwTsPbRYiicjO48XZq8lIzvvWBel3KhyISCLxWIpbzKy87jp1fnkB0KkpfiYeEc/0ts2OtbFSjoJtwBE5DUR2SYiyzzL/k9EVjpJuN8TkYZx9s1yklYvERE7s6uEZGVl8fbb8RJVxWfYsGFMnTq1HEpksVRv5mfuJD8QIqRQEAgxP3Pn0XeqgpQkBDQBuCRq2WdANzVJuFcDDxWz/3mqeoaq9ipZES2ldQAWi6V09GvfhLQUH36B1BQf/do3qbBzV2ToKWEHoKpfAbuils1U1YDzdT7QKollSxrJvqFvvfUWffr04YwzzuDOO+8kOzubDh06sGPHDkKhEAMHDmTmzJlkZWXRuXNnbr31Vrp3784111zDwYMHTZkyMjjnnHNIT0/n4osvZvPmzQCsXbuWCy64gB49etCzZ0/WrVvHgw8+yNy5cznjjDP45z//STAY5P7776d37950796dl19+GTCje379619z2mmncdlll7Ft27akXK/FUtNIb9uIiXf04w8XdarQ8I8benpq5ipuenV+uTuBZHYC3w58EmedAjNFJMNJiB0XERkhIotEZNH27duL2zQhkn1DV6xYwTvvvMO8efNYsmQJfr+fL7/8kgceeIC77rqLp556itNOO42LLroIgFWrVjFixAh++OEH6tevz4svvkhBQQG/+c1vmDp1KhkZGdx+++08/PDDANx0002MHDmSpUuX8s0339CiRQv+9re/MXDgQJYsWcLvf/97xo8fT4MGDVi4cCELFy7klVdeYf369bz33nusWrWKH3/8kVdeeYVvvvmmzPfPYqmppLdtxMjzTi218S9NxbOiQ09J6QQWkYeBADAxziYDVDVXRJoDn4nISqdFUQRVHQeMA+jVq1eZ81XGuqFl8eaff/45GRkZ9O7dG4BDhw7RvHlzRo8ezZQpUxg7dixLliwJb9+6dWsGDBgAwC9+8Quee+45LrnkEpYtW8aFF14IQDAYpEWLFuzbt49NmzZx5ZVXAmayVixmzpzJDz/8EI7v79mzhzVr1vDVV19xww034Pf7admyJeeff36pr9NisZSe0nYiu6GngkCoQkJPZXYAInIrMAQYpHESDKtqrvP/NhF5D+gDxHQAySbZN1RVufXWW3niiScilh88eJCcnBwA9u/fT7169YCiwy1FBFWla9eufPvttxHr9u7dm3AZnn/+eS6++OKI5R9//LEd3mmxVAJKW/F0Q0/zM3fSr32Tcg89lSkEJCKXAA8AV6jqwTjb1BWReu7fwEXAsljblgfJjuUNGjSIqVOnhuPru3btIjs7mwceeICbbrqJMWPGMHz48PD2GzZsCBv6SZMmcdZZZ9GpUye2b98eXl5QUMDy5cupX78+rVq14v333wfgyJEjHDx4kHr16rFv377wMS+++GJeeuklCgoKAFi9ejUHDhzg7LPPZvLkyQSDQTZv3szs2bPLdK0Wi6V0lKUTuayhpxKhqgl9gEnAZqAAyAF+CawFNgJLnM9YZ9uWwMfO3+2Bpc5nOfBwoudMT0/XaH766aciyyqayZMna48ePfT000/Xnj176pw5c7Rv374aCARUVfXKK6/U1157TdevX69dunTRO++8U08//XS96qqr9MCBA6qq+v333+vAgQO1e/fuetppp+m4ceNUVXX16tV63nnnhY+9bt06zc/P1/PPP1+7d++uTz/9tAaDQX3ooYe0W7du2rVrVz333HN19+7dGgqFdOTIkdqlSxcdOnSoDh06VKdMmRL3OirDvbRYqiuLsnbpv75Yo4uydlXoeYFFmqCNFY0dtakU9OrVS6MTwqxYsYIuXbocoxKVjKysLIYMGcKyZRXW4CkRVeleWiyWxBCRDE1wuH2VlIKwWCwWS9mxDqAcadeuXaWt/VssFot1ABaLxVJDsQ7AYrFYaijWAVgsFksNxToAi8ViKUcqc14B6wCOMccffzwAubm5XHPNNcVu+8wzz4TF5BJlzpw5DBkypNTls1gspadUWmQbF8Dcp8z/5Yx1AOVAMBgs8T4tW7Y8qnZ/aRyAxWI5dpRY3G3RBHjtEvj8LzDhsnJ3AjXDASTRo8aTeG7Xrh1jxozhrLPOYsqUKaxbt45LLrmE9PR0Bg4cyMqVKwFYv349/fv3p3fv3jz66KMRx+3WrRtgHMh9993H6aefTvfu3Xn++ed57rnnyM3N5bzzzuO8884DjChc//796dmzJ9deey379+8H4NNPP6Vz586cddZZTJ8+vczXbLFYSkeJJCE2LoD//AHVIKBoMB+Wlm8ekOqfEnLjAnjjCgjmgz8Nbv0QWvcp0yFXrVrF+PHjGTBgALfffjsvvvgiYNQ7v/76a8BoBo0dO5YOHTrw3Xff8atf/YovvviC3/3ud9x9993ccsstvPDCCzGPP27cONavX8/3339PSkoKu3btonHjxjz99NPMnj2bpk2bsmPHDh577DFmzZpF3bp1efLJJ3n66af54x//yPDhw/niiy849dRTue6668p0rRaLpfSUSNwtay6qQcJyjgrb9uXTvBzLV/0dQNZcY/w1aP7PmltmBxBL4hkIG9v9+/fzzTffcO2114b3OXLkCADz5s1j2rRpANx888088MADRY4/a9Ys7rrrLlJSzM/TuHHjItvMnz+fn376KVyO/Px8+vfvz8qVKzn55JPp0KFDuHzjxo0r0/VaLJbSk962UWLCbu0GEpRU/CEj8liAn6+Ou4DiewbLRvV3AO0Gmpq/2wJoN7DMh4wl8QxQt25dAEKhEA0bNozIC1Dc/tGoakLbXHjhhUyaNCli+ZIlS6wktMVSFWndh7WXTub7j14iFFI+knO4/8zzyvWU1b8PoHUfE/Y5/+GkhH8gtsSzl/r163PyySczZcoUwBjrpUuXAjBgwAAmT54MwMSJsfPnXHTRRYwdO5ZAwGTb3LXLZOL0ykL369ePefPmsXbtWsDkI1i9ejWdO3dm/fr1rFu3Llw+i8VSNejc+wI6/vJVdg/6O/ffcUvlzgdQZWjdBwbemxTjD9ClSxfeeOMNunfvzq5du7j77ruLbDNx4kTGjx9Pjx496Nq1Kx988AEAzz77LC+88AK9e/dmz549MY9/xx130KZNG7p3706PHj3CCeFHjBjB4MGDOe+882jWrBkTJkzghhtuoHv37vTr14+VK1dSu3Ztxo0bx2WXXcZZZ51F27Ztk3LNFoslCSQwIKUi8wFYOegSUtklnkvCsb6XFkuNohwGpMTCykFbLBZLZWPp2xA4HDkgJYqKnjVc/TuBk4yVeLZYLCVi4wKY9wys+gRwIi4+f5EBKaVNJF8WqmQLoDKHraoK9h5aLMkjbs194wIzo3flf0BDzkKBM39RJPxT4lnDSaBEDkBEXhORbSKyzLOssYh8JiJrnP9juiwRudXZZo2I3FraAteuXZudO3daA1YGVJWdO3dSu3btY10Ui6XKE1fvZ+MCmPOECfd48fmhxw1FjlOWRPKlpaQhoAnAv4A3PcseBD5X1b+JyIPO94jZTSLSGPgT0AvTBsoQkQ9VtcSBrlatWpGTk8P27dtLuqvFQ+3atWnVqtWxLobFUiXJyM4Lz+6NVXNP3/4BfHwvhKJ0wcQPlz4Vs/O3RLOGk0SJHICqfiUi7aIWDwXOdf5+A5hDlAMALgY+U9VdACLyGXAJUOJB6qmpqZx88skl3c1isViASONdGiMbHasfNaQraSk+CgIhUlN8DDo+yzH+AWcPH5x0JrToYWr+xYz8SXjWcJJIRifwCaq6GUBVN4tILOmKk4CNnu85zrIiiMgIYARAmzZtklA8i8ViMSSjozW6xp93MD+i5t55w2sQChXu4PPBJX8rlyGfZaWiOoFjaRPEDOKr6jhV7aWqvZo1a1bOxbJYLDWJZHS0NqqThk8Ewci6NKqTRvr2DxiZc78J/bQbCCm1AB/4UuKGfCoDyWgBbBWRFk7tvwWwLcY2ORSGiQBaYUJFFovFUmG4Ha1uuKakHa0Z2XmMmbGcQMjUX4MhZcWMZ1H/q6aWu+4LGPKsmeSVNdc4g0pq/CE5DuBD4Fbgb87/H8TY5r/A454RQhcBDyXh3BaLxZIwZe1odVsQLgpcyHeRG634AHoNi2n4y9r/kGxK5ABEZBKmJt9URHIwI3v+BrwrIr8ENgDXOtv2Au5S1TtUdZeI/AVY6BxqjNshbLFYLOVJtNEtS0er24LoGljJlf65CLCSdgzkx8KNugyNW46Knuh1NEo6Cqjo4FXDoBjbLgLu8Hx/DXitRKWzWCyWMlBaoxuvpp7ethGfDsykzTd/QTBDPNWXhvS/B7b8YIx/r2ExjxlzuGhVcgAWi8VSlSiN0S19k39YAAAgAElEQVTWaWxcQLv5o4DC8f0SKoDa9eHm94o9bln7H8oD6wAsFku1pSRG1631b9p9KLbTcGf2Rk/u8qcmlGjqWEz0OhrWAVgslmpLPKMbHeLx1vpT/D5SfEIwpIVOIyzlfATT9SsgPug0GAb8LuGRPhU90etoWAdgsViqNdFGN1aIxxsqCgZDXN+nDS0bHlfoNObORYNHEA2h+JBTzoVzH6rUQzwTwToAi8VSo4jVLxAdKrqqZyszqWvmm1DvRLIaD+CEUAqpBCgghezOI+lcxY0/WAdgsViqGUcba+8a+/xAqHAmb3SoaPUzRsPfoRWf8mhgGI3YzwLtwnn729G5Ii+qnLAOwGKxVBsSGfaZ3rYRw/q3Y9zcTAIhZcyM5XQ6sV5hqGjRBJj3bMQ+foI08x/ghYKhpKb4eCiqMzmRCV6VbRIYWAdgsViqEYkM+8zIzuPVr9fjqDmQXxA10ufje4mWKhNfCpdedi219rcrYsATcTqVcRIYVNGMYBaLxQJFM3FFJ1VpVCetSKau+Zk7CXkSSvl8Ykb6LJoA793pkXF2aPs/cNsndO59ASPPO7WI4U5EYO5YZPtKBNsCsFgsVYLihm56a9VuLL9RnTTGzFheZL23D8Anwpih3UyH74zfRZ7QVfKMM7PXJdZcg+iyugqioJVmEhhYB2CxWKoARxu66Q33uJ8XZq+Nu77I3IB/R2lYNm4PV76c0DDP6OMBRRLGjJmxnGBI8fuEUUO6VorwD1gHYLFYqgCJDN2MrlUXtz69bSNT6//qA6Pf02WokXJ2+Z/EJ3eFj+cY9WjH88myzeQHQigmH3fewfziD1aBWAdgsVgqPbGM+dGkFWKtd0MzN635PQ1zvzIbOhr+Wf/zOLLiQ7TLFbQ7StinJGUd3K0FC7N2VSoNIBdRjZmYq1LQq1cvXbRo0bEuhsViqQQkK5fv4/o8V/rnGTUHZ92elgPpu3Fk0kbpxOqvqKghoCKSoaq9EtnWtgAsFkuVoKw6OtMX53BaYCU/S5sHROapzah7dlKlmqPLWtk0gFzsMFCLxVJioodfVvZzZmTnMWXRRvr5VhgpN/GM9G9/Pg3OGh4xfLQyhWnKE9sCsFgsJeJYTGoq6znnZ+4kEFLm04V80kgjH0HY2X4oTW95g3SodFLNFYF1ABaLpUQci8xW3nPmF4R4ZtZqBndrQd7B/IQMttsxuzTQkVuDD9NXVvBNsDPL13RmYnZemVNFVlXK7ABEpBPwjmdRe2CUqj7j2eZcTLL49c6i6ao6pqzntlgsFU9FZLaK7jQNT94qCBECvl6zg7lrdiBArdSjtwjcEUF7vn6FVps/4/W808kIdURCIaYvzqlxht+lzA5AVVcBZwCIiB/YBMTKjTZXVYeU9XwWi+XYUt6ZrYqb4fvMrNXMW7sjrOOjJNgK2biA9C/+BNnfoMDjKQtQhcmhQUxZtNHIP8fQ76nuIaFkh4AGAetUNTvJx7VYLJWI8gyXFDfD954LOrIwa1d4vY+inbZFDPe04fDju+H1AqjAYP8CJocGEQxpEQdSWcXbkk2yHcD1wKQ46/qLyFIgF7hPVZfH2khERgAjANq0aZPk4lkslsrO0WbwjhrSlU+WbeYG3xf03PURaY1OorGvCdCHt7/bwKgPlhFSJS3Fx9cdJtM08/2I47ujf2bRN+6on2PRz3EsSNpEMBFJwxj3rqq6NWpdfSCkqvtF5FLgWVXtcLRj2olgFkvNxFuLB8J/r9qyj1EfLOMPMpG7U2aEB/MHSeGLfq/zq69SCDjxoRv8n/PX1PHhse7q/BMCxocu5/ghj8fsRM7IzmPa4hymZuQQDBonVJVaAMdqIthgYHG08QdQ1b2evz8WkRdFpKmq7kji+S0WSzUg2vh7k7UHgyHu9b3NXSkzgMLJXD4N8MPXMwiEhnK973Nu93/KKb5NEZO9AJYH2zIqeBtL6cgfDuYz8rxTi5w7fD6fcH2fNjH7B6oLyXQANxAn/CMiJwJbVVVFpA8mdFc5BLEtFkulITr2fnXPVuFQTLfgSsakvE5Xn+liFMe6q0II4dtQF95IeYKz/T+aFY7UgzqfrBaXcU3OzRQQf/RSRHJ4pyXhavdXRyeQFAcgInWAC4E7PcvuAlDVscA1wN0iEgAOAddrZRYhslgsx4To2Pu2fUfwiXAmq3gnbQx+QoAzk9exIEFgVOB2bvZ/Fjb+bs1fgZAKjwRu572cCxk1pGuxcwe8/Q9+v48pizYSCGm17QhOigNQ1YNAk6hlYz1//wv4VzLOZbFYqhYlyZfbqE5a2ACLT/hi5TZCIWVE6gz8hCJq/QALtDOrut5Lz/WfMvRwocaPW7sMYYz/pOAg/KEQeTHCPl68Q1w37T7E5AUbqnVHsJ0JbLFYyo1E8+XeMO5bCoJKql8YfUU3lufuYfKCDdzre5sb02ZTl4Ph7VUBgZXNBrOu199p+9GNhTV/T8sgM3QiD+ndLJFO+CXxSWvukNOM7DymL86plDLOycI6AIvFUm4kMpxy2uIc8oPGaucHlWW5ezip4XF87v8tbf2R40Rc476z/c/ocssbHHj1t6THMP7TgwO4NzASv8B1fVpxUsPjSjyhq7wnvFUGrAOwWCzlRiKyEdEjdQT4+ffDaOoY/3DYBwj4arGp359od9FIMrLzaLvt8/A2rvF/KTCEvwdvxOeM8b+6DKN4qrs+kHUAFoul3DhaLdqVdk7xC8GgSZj+69BbNN1btFaPQGr/u2l34chwaOl3egZ3+XNMzF/gy8Dp/D14I6l+4dperbm6ZyvApGmsrrX4smAdgMViKVfi1aIjxtz7fZx/WnMuOfJfTvzRjB/xGv8C9bGz+whaXPhnoDC09KTeCApX1FrMh/k9eTJwIwDBoHJSw+MAaoSkQ2mxCWGiOBaJLiyWqkpZ3hdv/0AgGOKLldtouuETUGckj5qwz+Jgey5t+D65vR4M7+uGlnzAk8EbGXDwH2HjD+DzCf3aN4nZB2EpxDoAD26N5KmZq7jp1fnWCVgsxRDvfUnUKbhG3C8gIgRCysfBPkDhMM6xgSFcHXiMtdv2c8MrhedwQ0sDOjTF5+lEECDFJ4wZ2i1CRrqmZfpKFBsC8lBTBKAslmQQ/b5MW5zD9MU5CU+eco349MU5vLNoI2DkmSmAS/0L+K/25bvGl8P2AwDkByK1+6PVQUWEQZ2bc+c5p0Rs457DzjwtinUAHioi0YXFUl3wvi8i8M7CjWH5BIisRMUSd2tUJ428g/ls33eEQLBwv8mhQUwODcIv0K1WpInyGnH3mMP6t+PVr9cTDClfrdnOneecUqSs0xbnhB2I7QcopFo6gNImcqgJ434tlmThvi/TFucUMf5CYcglWmANEQLBEKFiquTu/tf1bsOKzcvCk8TcUT3eY/pECIY0bnIY27KPT7VzAGVN5FDdx/1aLNGUJfNVettGzM/cSchjzf0+4brercPj71+YvbbQAAeNNNvRwjE+gWH925F3MJ/RV3Qrot/jNeqg+H2CqsZsuduWfXyqnQOw3t5iSZxkZL7q174JtVJNvl6f0wF7Y9824eNv2n0oLOXsj2oBuLo9XvE2MCOAXv16fTixi1uuWJpBqSm+mCJvXsdmW/axqXYOoLJ7+9LUtmpCblLLsSEZFaZ4odN42vrueRvVSWNZ7h6mLNrotAwKEYGQapHhm15nVZyyZyzHVpwIXE2l2jmAyhzHL01tq6bkJrUcG4qrMB2t4hG9Pnqb+Zk7OVIQMhIOQaWlMzHLu88Ls9cSDCk9ZTXPpTzHiZLHfq3FhyfczeNb+0aUK9pZFafsaSMBiVHtHABAum8N6SlzwTcQ6HOsixMmkYcy+qWyD7KlPEmk9h6r4pFIxaRRnTSPLDPsO1RQZJ9+7ZvQJ2Utb/tGh8NADeQwN+/4J2cPfJxxB84OLy9J676yRwIqC9XPAWxcAG9cAcF88KfBrR9C68rhBI72UMZ6qcryINvQkSUeidTei6t4JFIxWZa7J+L7t1H7TF+cw4WbXuLf/skIkaJwCjTK+oTpG9uT78wxmHhHv4Rb95U5ElCZqH4OIGuuMf4aNP9nzT2mDiD6RSvuoYz1Uo0879RSPcg2dGSJRyLPxtEqHtGZszbtPsTb322IiMnv2HckYp8T6tdmxZZ9FARMZ/EtGT+noz+3cIMo4beMumfHfB8SfY7tiL6jU/0cQLuBpubvtgDaDYy93cYFxjm0G1huDiLeixbvoYz30pXmQS5NuMlSM0jk2YiurIBR1GxUJ43luXtQYNSQrix3OnHdzFkC1Eo1HbRzVm0D4Hrf51zqX0DW3gv4ItSbM2U1E3xPUM9nHER0lq/DIT8/dH+YBn1uJ23lfBvGKUeS5gBEJAvYh0nRGVDVXlHrBXgWuBQ4CAxT1cXJOn+Y1n1M2Kc4415BYaKSxu+T2WwtTbjJOoGaQaJhRfd5cOUdCoKR4/f9AoO6nEAgpOFJXe5krE+WbeZ0XcWzqc9xkm8XAAO3/0hd3wCu9M8Lh3sijL/AD7XSWX7+hPAwUhvGKV+S3QI4T1V3xFk3GOjgfPoCLzn/J5/WfYo36MWFiZLYMihN/D5ZzdbShJvsC1YzKK7j17vMrSS4I3miCSp8vmIrKX5feFy/DzOD98GUSXRJfT3C0KsSNv7RtX4EZMA99Ljwz/SIKqt9LsuPigwBDQXeVFUF5otIQxFpoaqbK7AMhnhhoiS3DI51R1Rpwk2W6kmsTt+jjepxKwnFzdoNKQzq2IxDBUG6tqhPveNS+dmy39By/TfGqDvbuYY+lvHfF6rFzPSxXHPhVcm+bMtRSKYDUGCmiCjwsqqOi1p/ErDR8z3HWRbhAERkBDACoE2bNkksnod4YaJyaBlU1hpMaZ2T7TeoOnhnzY6ZsTyceOWa9FZhTR33t4zVImxUJw2fmLm67n7b9x3hs5+2hs/h8wlzVm0jEFIWZu3i8+bP0XLHN0CMWj6EPYKr9f99sD0/Dz7G8LT2NmvXMSCZDmCAquaKSHPgMxFZqapfedZHp/4EilYuHMcxDqBXr17lpuCaEerA/EBj+oWakO4uPGrL4AiIDy59CnoNK6+iJYVEDLVXV8X7vbhj2n6DqkG0WJo7qzY/EGLSdxuYmpEDqmHZ5lFDupKWYuQcAL5ctY0lOXsIhozOzujLu3Jj3zZkZOcxd832sOzD+Z2bM2vFVn4un3M/79B4536gqPH35vX1av3/PWiSuIz9KjPcgWyfq4ojaQ5AVXOd/7eJyHuYGVheB5ADtPZ8bwV4xoBVHHENWbEtgyOgIfP5+F6z/NDOchlFVNZadqKG+u3vNjDqg2VF9FbiUVy/QaJlti2IiiFCLE0VnyOW5hrggoAx9ArkF5hO22H92/HK3EyCCguyCpO5qCp5B/OB2KODeq15huG+j8Lbe1M5hijMOuV29B5IbcpfDw5lUnBQRJnjqXlayo+kOAARqQv4VHWf8/dFwJiozT4Efi0ikzGdv3uOSfyfo3SAxupAbjfQ1PzVvDSEgoT+c6/57k/DN+yjpDmBZNSyEzHUjeqk8egHy8ISvvkJGPR4/QaJltm2ICqO6N/KO2QzGFL8fp9pAQSVEDBv7Q6+XbeTKEkeBMLj/DOy84r2H3z2J3r6PwpvC4QTtO+t04bPG13PkE3/JFULAPgqeDrf9nmFSV9lFimzV0LaUjEkqwVwAvCeGelJCvC2qn4qIncBqOpY4GPMENC1mGGgtyXp3CWmxB2grfuQ1W8Mrb99FJ8qKj40FMQvSiCQz+YlMzmpdZ/CfoLjmpS6dVDW0TkZ2Xnk7j5kanxB86LHMtQCES+7iBzVoMfrN4gu8/TFOTFr+XbkUcUR77e6qmer8LJVW/Yx7qt1ZO88WCirLIXPhU+gfbPjydqxn8kLNhRJprJ73OU0yDWN/OjO3q+CpzN878ME8kJM8j1Cb35ifqgLS+lItxh5eQU4q0NT7rmgo30mKpCkOABVzYSI0Vvu8rGevxUYmYzzlZWSdoBmZOdx09z2dA0+yoCUlbRr3YbBOc+QqgEKSOHb4Glc4+0nUKfh60+BM38BPW5I2BEUV8v2ZlHyZlaKHrZXqJNORA9cpIZ6JOd3bh7XoHsNdaxO7ehZoe8s3EAwBKl+YdKI/kdtQVgqltzdhxj75Tq+XL2dAmeUjwBpKT4TBnKya4UU1m7bH97vSIGRZEhv24gdb95Kk02O8ffE98EkcR8WeAgwx84IdeB76Yg6uv0/bd4bUR6fmHNb41/xVL+ZwAlSktE5rkHM0I4sKejI9U3b8O6G40nX5WRIV+4/8zzIeg0NHkHUfaFCpjN50Wuw+M2EO45jOadowy4Y4+rqqkcP2/Ma+GBIwwY8wlD7hBAQdDIt3eVJo1dSQ+2WedriHBas3xU2GvlBDRsM73Y2P2v5E6sVB3DDK2ZZNCKE5ZVVY/86CkzNyOGWVlvpmPlBeD83tq/AB8EB3BccGX4+g8FIvf6lG3cz0zuKSOAGRybaGv+Kp8Y6gJIQbRCv6tkKet7C/Myd3O8Y6ZXbetA2lEIqBfhRVARxzVwoYDqOTzjNfF/6NiBxWwbRzinasCs4szIj4/duOb0Td/y+wtBOrA68WK2g0g4Rnb44h8MFkcYl1tAvm5+1/IkVllu2aU9M4w+AQt7BfBrVSUO8vbgYI+0+ewWBED998zEd0YjO3szgifwxeBc/+jpzXZ9WdGvZgGW5exAIG/eM7DyenbW6yHlbNjwuvN4OEKhYrANIgFg112gj/fn+dnxR8L/0lRXs5nhuaLOb07e8b+YUgAkLLZ0E379lWgYA30+EYTOOGh5yDbvXCfg8sdqQGund9LaNGDWkK4++/2N4XXRdLrrcxQ0RLclLOH1xDkeijH+a6yw9VEQ/gDUkMcJyizZGJF4H8wwJ5vnx+YR9hwp4dtbqiNy+APf73uYX/lmkEODjUF/e2nIhg9PSSCMfAd53av0hBb+a/iV33oH3GZifuZNA1LHTUovmDfZJZFYxS/lhHUAJKK7m2q99E573d2ZJoCOpKT6uvqQfbD/b1Pw1BP5agEKwoPCA3slmxUw08zqgdxZtJBjUiLF2PkztLSM7j0+WbY7o3A04YRjXeV1dDk3tjOw8pizaGHY2qX7h2l6tY56rvPsB7Egjg7cVt2n3ISZ9t6HINik+4fYBJ/OqE/N/9ev1RQz06ylPcK7/x/D3q/zzALgp/3/p71/BwZb96ZA+iLQZy8O/qULYyXtHl0WHIK/t1TrcOvDmDQ6pMuqDZXQ6sV6N/O0qEusAEuRoNdeYYZO2w0zYxzXsYGr9bgvAnWy2cQGhCZeb5b4UfK17Q+AwnHlLuN8gvW1h8m0ztFtJ8STCblQnLWz4espq+vlWMD/UhR98nSJS7k1dtDGiYzZZ98Y1HAJc26s1j195OhnZeUVmd5a3PIb3d/J2WtYE4sk9ZGTnMTUjp0j4JxhSlm/eS8iZHxBSjQj3zEn5LW39RtrLO7HrYt8ieskq6kg+2+rWoWvf2+h0Yr2I0UWhqNYpFP/b92vfJDxhDSDk6buylB/WASRIIjXXmGGT6HkFw/7D9q9fZ8veI6T2vJHOrfuw6aPHOCGQT4qE0GA+mu2oJW7KgEWvsjJ9NMs27eWinR/TODWPqYGzWEon7jjrZOodlxoxlf8MVjMp7THSJADALn8zPjnSnekykMXakYJg8l+s6Htzdc9WxdbE44WXkhG66de+CSk+Id9RrpyakVMurZ7KxtHu96Th/Xj5y3XMWrG1cJCACF1b1Gdh1q6wRr8bJpqW8khM4w9QV45QV4yUc9PM19k8rRb0ejBclryD+eFk797WqfvbxkrjmN62EWOGdjMTE0MaDg1ZyhfrABIkWTXXjFAHbvrpCvOi5hQwsXke64OncRkpiBbgQyMzI235kVNnXE1HTO36VB/8PHUW+7QO7347iPQ7ng+XJS3Fx9U6lzQC4RewcWA7N/k/53r/bB4puI3pckGZXqyM7DymL85h274jNK9XK9yEj7433iZ9IrH+aANWXMLv4khv24hre7Xm7e82oEAwWP3mG8RylIlM/mtar1bEcYIhZcK3WeFJYpOcewZwui8biKPnE7U8ZdUMblpybvi3G9a/nRll5hhyb+vU65yir+PGvm0iWhLV6TerrFgHUAJK2jGa6Iva78zzuC3jES7XL/m5fzYphApldAG/+7ez0Ac0kIMMl48omDAT2vQi/YLRTLyjH2mfTgnL60n4H9M590TaeEanTmXTh2eyst9v6Nz7ghKVPyM7r8gwwikZOUwa3q/IviWN9XvvS35BqEQSFdFc1bMV0xbnVOn5BvFaQ658RzCkYd0cMGP7U3wS1u7JdWbuAmHjm+L3RYR4wNzrZbl72LjrIN4A0Y+htvT0ZxYx/FDUKSyvfw75+wrDbq/MzTS1f5+EHXn0M+8tV/RkQ2v4Kw7rAMqJeE3yWIYxvW0j7r/jFuZnXsa647PonDEa3fJjxPG84629L2CqHoHseTD+YtLb9odA4SxLDf/j7A/Uyt9D+x1zCM2Yw+YNd9Hi6icTLv/8zJ1hDRmX/ECIsV+uMwJhUdeaSIvJO8HNvS/iES8r7Uihq3q2ihiCWJWI9+xkZOcx6oNl4f6W/AIzIMEdnJDi93F+l+Z8uXo7kxZsYNpiE/7ydsj6osblhiCi5u9ydeAxpvEI3X1ZBPFRSwIxNfxzm/wPn510N77NGwk5YTd3EIKg4aGlPucBdp95Oyu8cmAdQDkR7wGPZxgLaz6nktE8nfdffYyrmU2aBOjiyw7rq0BRhUVDyDgCl1oNkFABR1Lrk3ZwS3i2p3sMn8KJP46F5eNNR/Qt78Ut/xHH0FzVsxWpznBUL1+s3BbunD5cEOLlL9cx7pZeEa0e9xq9xAr7LMvdw459R5izent4ElFJavDRx4wehloViPfszM/cGe4kBUCMaqc79yIYDHG4IBhOznKkIMS2fUdI8Rf+ZrFmgceblHd14DHApHR8InV8RGvggKYxvdlIHt/al/zcDUjkwxjW9XGlqEOOIN2oIV0jQpZVuZVWHbAOoJwoLgRytGbu/MydTAycz7/1fPwCr3Rbzvmhb6HLUL5bv5O2PzxHc9/uwjdXik640iN7mN3hYRqcNZz0RX+EH98NtwhEClsEGiqAzC+QN68k45zXwo6pX/smYcOhwJRFG7mqZysmDTfDUb/L3Mna7QfMuTRyUtDMn7by9ncb6HRivWKHZEYbumW5e5ju1mZ9wvWlmCFaHWqW8Z4d728Cxpjn7D4c3k98wuBuLfguc2e4E/zL1ds5t2MzPvtpa6lnX08ODYICuN3/KYryenAw0+UCrj2pNfmbnFzAzggideYU9GzTkI4n1GN57h7PDPb4qqJV7TeqLlgHUE6U5QGPNgANzhoObf8IQN9e8Le6l7Lw60+53zeZU325HNf4JI7LW41gJp0JgELKyg+5aeXpTLzj76TXb4lkTEAP7y40BJ7pBAVZ87hpTaSxvia9VTg8UBBUXv5yHT1aN+Sqnq24qmcrbnq1MGF3k7ppbPIYoxdmryHV7wvXTmMZ4/AEtwIT9tmx70jYWARDGp4hWhKqg95Qca1E728STbsmdbmxbxuW5+6J6ARvWq8WtVJ9cVM7enFbidGx/8mhQUzRQfzlZ6fjy93DtUDXlg0iJii6+wRDysKsPDKy80jxCSl+X8zWnI33H3usAyhHSvuAH815PHhpFzK6nsj8zMtJdV6o/3v1TR7R8XT1Z6NOc+DjYB8K1BjeVfV/ySfNLuXmk7Zy0e53OLx6NrWCB8Iv7U+p3cg/FFlzvrpnK6Yu2hiuTc78aSuf/bQ1PNHLO1Ln5S/XRTgA799g1Ebd8eDe6xw1pGu4w3fO6u3hjsx4xjsRUbzqULOM9+x4f5No2jetCxTtBL+6p8kAdu+7S8jaeTC8/anNj6dump8fcvZEOAafCNfKLH7nn0o9Ocx/Q724PziS87ucABBupblhu3cWbmBpzp4i5XEd+XV9WnNSw+Oq9O9RXbEOoBxIxnj2ozkP7ySfZ2atZkHgVIboE9yonzOs0Y/8e093puj5pKb42HeogP/77yoA5q7x8/iVT9Cpfz32v3o5vWUVC7UTm86fQMpHy8PjwTftPsSqLfvo0qJ+xMutGJG3t7/bEHYEAHeecwpfrNpWRG7AJRBSRn+4jOW5eyLCOnkH88MdvsFgiOv7tAmfJ/peAhFJyn0CKa6ufUiLjCapaiT83Ig7yDeSczs1D/99dc9WRWZ+jzj7FP73vcLBBbcPOJkb+7aJGFn0x5S3ucP3H1Kk8PhXOYnc71sxktkrt0V00OcdzKfbSQ1iOgCfEHZAVfH3qAlIPOW/ykCvXr100aJFx7oYJaIipQjcc7kGUTDib2OGdosYT/3MrNXMXbMjvN/ADk359y/7FjGuN4z7NlyzdE1M9P+xSPGcc/riHFZv3cdCT0apeNu7KQbdUJLf7+Pcjs3COWZTfJGKp1f1LBr+8CYh8Qv84aJOMScaVUZiObfinpuM7DzGfLS8SI3dJc0vnNupOXNWb49QiY0eRvrOwg3h85zctC47D+TTpG4av192DW38hc+Jd9RPnh5Pz3yT5tsdSRStMmp+Q+G6Xq3p2rJBqeZxWMqOiGSoaq9EtrUtgCRTkZ2Q0xwBNtdAi5jp/GNmLGfiHf3ChnBwtxYRDmBwtxYApPvWkL71WchYyIHD+fxeBvAkJkera2Dc2ZwDOjRlcLcWLMvdE5YVeD3lCfr7VrAp1JQHP7ybK6+4Kjwk0e+DUCiinzr8dyCkPPK+qYne2LcNE+8ws1Q/X7E1QirYyFeY8NORghBrt+4rYvxTU3yEVAlGJb8pLRUlJBddUfAO1ywImJFUhwqCDO7WIuwovQ4aIMVvZvK6te/8oEbcP68Ojzd0tjx3D+5ArqU5e/ij/22G+/9Dit9x/jEmf80OFab7CKlx4t4RPZOGV/2wWz7G22sAACAASURBVE3EOoAkU1GdkK6+i/uO+pxRPd5hm+6L6KoqfrJsc9igsHEBvH4phApQoA5wl38Gv/R9zGptzajAbSzWjuFkHYO7tSDvYD5X9zRSvy0/upFzHJGw9v4tvMOfyP/kr+zRi3hSb8TvnLdlw+NoVCeNZbl7mLxgQ4RGjCv4BWYoaUSGMoyonNsBrc41ex1J91YNuK53G0Z/uMx0f5eyNes1jl4Vy/JsvUVXFJTCYZHik7Ahdx133sH8sJ6Ty/nhkE/R8AuYe/zlqm0R1+Uud5mW8gg9/YXpGSOMv4AiLGlwIfdvGxZxbG+eYLAdulUV6wCSTDI7IYurjc7P3EkgaF5oAQZ1OYE5q7cXGbbpdQJuWCgjO4/0DXMhVBDeH4xhTZUQXSWbabVGE8RP0FeLtW2v4+oZRNRWf+YzfQri2bkW+dzln8Et8l9+yaNc1fN/IuQI3l24IcL4uIJfQIQEsd8nXNfbqImO/XIdnznG0B1i6G67YvNe3vs+J1wr9ia/Kck99soQl3UCWqLn3LT7UMToGLejdn7mTmYu3xIRU/9k2WbuuaAjqX4JX6tPSGho5wJnNE5II0N44Vq/xK/1H/bV4bhRm9HsPNJenU9+QcgkeRebu7e6UGYHICKtgTeBEzETC8ep6rNR25wLfACsdxZNV9XopPHVhrLWhly9nSmLNhbp3HSJbmncec4pNK1XKxwjjzaG0SGH96/oQUdJQTQQMVvYRYEUgqSEDnLa+tdZJBPZlNKUN0KDUW5jYagTZ/t/RD3zCgBUoI6/gEmMQl4fBY3bw5UvMz+zcZFJSCn+wmQ17jBFERh+1slmpFN2Hl+u3h7e3uczqStdw5cf1Ii+BhFKbJQiku04k5WE+KOQyor3d4g11yG9bSMa1UljaU5hZ+3gbi2MoNuI/kxbnMParftYEKOPxZvP10tQCY/RB/g05T46peSG10fn8w0qzNABtL59IulEypFHa0BZqjbJaAEEgHtVdbGI1AMyROQzVf0paru5qjokCeer1kR37EIJ5KcxQ/RihZ8itHYCIR74rja1CkZxOx/S27eSRrI/oooYNbGTupJPR8nlr77x6NLXOJRWly35DTjRvydiZnKRDGC7MmH8hdyY1oKNcimTdVB4VVAJyxW4w0FdXXqA5Zv3RkhPKIWdnLEyW3Vt2aDEKqPRjnRY/3Ys37w3bHSTjfd3iDfXwRuy69qiflhN061Y3Dz+uyLH9fuE4WedzIRvs4pkZfMLDB/Ynox5/2Wi78+k+gpbji7ub7gh2JS/dnyHpvVq0TrqHNM8wz+r4gxrS1HK7ABUdTOO/Jiq7hORFcBJQLQDsCSAayC8naeJyk8XF36KzipmQgynsoA/IMCwNtv4zaGXqLd/PX7NL+oMPIm/BaVOaD91/CYBeEM5SHvflkKtoqhyKtDwyGaeSB3Pn3UC44OD+XvwRoIhM5z03YUbOb9zc4KOnEQgpIz9KpNoNGTizvEmQ13Xu2gGKXeIYzxhOe8988bKF2btKpeEJIn2EXU60cyifW3e+nAr0J130bVF/YhOfTAx+XrHpXJJ1xN5f0luxLqOJ9RjZOZdHJ+6JLzMG/ZzF2w5vivzBk7mK+ceeBMfVYcZ1paiJLUPQETaAWcCRaso0F9ElgK5wH2qujzOMUYAIwDatKl5KeG8hlpEOL9zc+4655SY8rmxiBd+cg3dM7NW8/WaHRHGU4EO6YNo3Pc2AF56axIDVz5BJ99Gk6PAs2F0mKinP5OHCn7J6kBrXk55iib+fUUcgHd2aZoEuTtlBnf6Z/B+aAD3BkYSCCmfr9gaEd/37usOe/dqxE91ktz4BLqdZDqDo1MIFhFPi2G4vPc0lpGD2HmTS0u0w4mlk+S2Ar01+SMFofDIqbQUHz87o2WEoQ8p7DtUwIdLI40/wGM7fsfx/swizlmdfwpCwl/4JT+79hHy4hj66jDD2lKUpDkAETkemAbco6p7o1YvBtqq6n4RuRR4H+gQ6ziqOg4YB2YeQLLKV1Xwzo4NhpS5a7Zz1zmnJGV+QXrbRtxzQUcWZu2KCDG5STtcvg914MnAE4ARAht53Gc0K9hELQlGhnscoz7Yv4DJBYPoXfAyaerjm46Tabz+I9BghKy1eFoRPoGrxIjX3Rsw+WRPaVqHzB0HIvoKUv3C6Cu6RYwpf/u7DQSdTk2/38eoy7vGvBfzM3cWcSje2cixxOi8Ri6ejn0sSjJ81F0f79iuI/LidFEAxpGt33GgyHGXb95bZCBUT1nNmc4onyK1fmB1sCUXB/6BX+BEp/yxDH11mWFtiSQpDkBEUjHGf6KqTo9e73UIqvqxiLwoIk1VdUf0tpbC2bFKZE000SZ4PGPkLndVN6dm5BAMhiL049PbNopIHDI5NIgVja5iac4eXk95goG+ZfjEM6REIPuEC5AcwtozT9e7j+mB6+kaXMnzKc/Rwrcr9uQtgfN8S83fQOaOAxE1VMHMbnUlhedn7uSz5VsYNzcz7CQKAiGembWaey7oWORac3cfihg5E1KTrNwN7UTX+PMO5kcYuUTDHiVxzu5vkLv7UESfjPcaGtVJK3Z0jwA/bY6sY/l9wubdhyJE+QBG+GdEOl/npytQH38O3sa7XIBPNCzVUZyht0M9qx/JGAUkwHhghao+HWebE4Gtqqoi0gdT6dwZa1tL/DhxIk3w4rTko5df7WjGTM3IYdKCDUzJyOGadDPOP80vFASVVL9wXe82rNi8jNsCDwGmVnmnfwbpTQ7TdOBwujYbSi2PMNyOfUc4UhAig46cVfAv/uF/gct83+InhF8ia6BzQj3CI1SMYmQhChGTw2LNRlbg6zU7+C5zZzjJOBTWrn0+iTCK8ZKUe3MzeI2cN4m510l6SdRRePsjXJE0V7r56zU7WJi1i1FDuvKnD5fFndLgEzPkd9aKwglf9WunsPdwIKzO6t7PT1Puo6Mz2sc93v+3d+ZhUtVnvv+851R3C9hCK8jWgBCFyBINEMRoEr0uoz4aI2ok5mYzSswlzx0TJyZqhjhOkpkkZib3SXgS1+QmV5Aw6GCYLMYloigItE6gRRZbgaaRzWZRlu6q87t/nDqnzjl1qrq6q+nqrno/z8NSVaf7/Koa3vf3e5fva4C72r/sKnyCa/xxE9JB56iGvjLojhPAecDngHUi4mWZ7gJGAxhjfglcB3xVRJLAEWC26c0aFCUm1y6skCN4Pi356PNzLzzd7yfwdqILV22jpsrywy6e6NpN543lwReaSBl4zYxnyfgfMvgTH2DwmDqmpdfmlQk+t3F3KG/wjeRcvsFcwG08OttqwkF40vkotyfd5708s22JH7OHcFlj9B9MMKTh6RMtXrOd0Sf39+PnJt1E5mGJ5AxrANzymzXsPnjUzyk8evPMkJNcEkiMehQSH4/mI5KOYfaMUWx/97Cfk2lPOixavS2r4cuTXrAkI7mxfPMeP4x38GgydP33TvwPbmh/HCv4OaUd776BU1i852L/0wxGyI61OywJNBAq5U93VAG9SEz1X+SanwM/L/ZelUTcLqyQnVk+Lfl8z3vGxDNEXsw93CTl3sPBbUJavnlPyBgGpSnA/Ucx7tQT2bL7PX993pCRKN7XDKixOXQ0GTu4JMrVZ4/gT43vhNbeljL+ThjSxlPc+bSeTlJcWGPt1lZuuP+lgERCRqoi6CQ7U5IbJJqPsES4Nn1a8YayVyUsTj3pBKKdveOGnMiMsSf7omprt7byoZEDY3sB/pr434xp2+v/jwzV+Au8P+kzjF3XP/wZ4f5MDfAfa5tD99GYf3mjncBlRi5jlK/6xNu9L16znWQqEw8ONUnhGlCvVDOan/jp05uyjH9NlcVN543lH5euI5Vdth/LgSPJnK8F59kKsO/9Nr547mm83LSP13ceJBnZ7YNX6ZIx/tFKIY+VTft84+/xyIq3uPGc0QXt8DtyzjPHnUJNlTv7wLKEKz80nJ8+vYnLJw9n3pWTfJmOCcNqee6NXaG1NO15j+bWw1w7tT62QgjgJ4n5XG2twI4z/Gk2JUdw1fJxJFPv+9dUpQXkvOa6VCr/zF6lvFAHUIbkKwUFsipfWg+3MWtqPZNGDPRj1Pcua8yqiokmj6OVMp6tSVhuTX6mWSgcvb/DXsD19nIGmMPUSIokwjLnXD8cFMUWmD1jNLU1Cb8/wODq5Lywea9vyC6Z6MbGQ3ITXuzbGBpbDuTc1c4cdwoJi5Dh3bL7PX+y2cfOGOKHhrpiCIMO+NCRdv99vLB5L1W2pIeovMujN89k0Vc+ypKGZhp3HGDdjgP+yePxhma2vXuYYwHjf4e9gDn2Mt/wQ7jayn3v8LwzhZuSdwIZKe3zTh/MbRePB2D55j0hB6d1/5WBOoAKI9QR3O5kkpK2xZnDarO03uNOE55mTdRQeFiW5UsFzH9uC44TNv5fTSxzH6QD/9UYZskKrrFWYIDlzhQ/4ezpHM1K3zNXIjjlGIbU1uTUrDbAY+lEd5xU8rQxddx8/jgeerEp5AQWrd7Ghp0H/UqiDe80drlBLFcnrxfzD85eHjmoH5NHDGTjrkZfKntxuvfBe4uNic/T3076n2UwJ+L9/WjK5szkbwHXMVtWRn8oWDkV93NOWG4hgG1JzqIDpW+jDqDCCIYzJCB+1pZ0fAGyoNhXIbmIYA4BMmGEuJLGy+zVQLbUhCEjJXGBvY4my5Wl3uSM4IoN97F88x6+eO5pWUlij6qE5aqh5nnvKQOpZPyIygWrtsV2H9ckrFBStjt2w1F57mBobdHqsJOad+UkGlsOhGYw/ynxD4y3WvzPMKrgKbifwwvJKXwh4Ei9U1nBJZ5eB170h6WUDeoAKow46YNoU1gwNDD/uS0ddh57OYRFa7b7uvx1/auZ/9wWduw/Err+z85HuNVelolNR4wY4AvMAUywW9hs3UgKi2UvnYtj5oZyAQAjB53ApBED/fLVuHGJHna6RjIay//j+p2x1zds348dCA15X1dIgjTX+MrWw23c+vFxvubQ+pYDARE/SDmOn2NpbDnA4vQIyKmyid/Z92DbmXtEVTwdwJ7yaX5x8re4Lz0FDlwVVe9UVojz8hLfwbyAhoDKD3UAFUjQCHhTvBav2e7P4vWMf6FJQO/5xWu2kwIcx+Ge3zeSTDkkbItqW9LJZXh1/Nd5+XAdk3Y/SX9zhCrTFupyhWxnYAlYOFxjr+CTsgJL4IhVw98nvsuz75/Gjv1H2bH/KM++sYt7r57CE682s2Zra2wt/S3nj+XQsWRWpChOXwcgmTJcOnEog2trEFzBOW94jWPcRHeu6V25xld6EhYXnTnUn4fgnQIsAbEE47jKpH9ctzNj/KvvwbP90c8I4L1UNdP4DQunz2QmrrPyOoqlA+HotVtbWdLQjODOFFbph8pAHUCF4zmDaGhg/nNbQrmCuG7bIG4VjSfmhjsODEimHD4zY7RfYvj0hl08ZS4HLvdHQ05e9U0m7v0TFoQ7WSXb0Nnp4vb+5hgPtt9FW8Liu6kv8ZhzEUkHnni1mYa08bfSEYxgWOjQsaSvavl4Q7OfBG+KkVbwGFJbw/evmRI7lastXTsfPQ1ERf28MJtHysBTr+/i2Td2IZIJa6WM+59y2pg6Xnm7lXcPuzMbZlob/M8n+Hl4J6iNqRFclrwPwfHXcuawWn98pDHk7WQOvq/Fa5tZeMtMlX6oANQBKEB2DNgXpUsPAVmxZa9fpRJnDKLXezgG9hw6xpDaGr+W3iPpGOYtXc8NH/kOC1o+j8GtYx9tpXfikYxvVt7AQLXl8C/Ww/zAPIwDLG0+j9Vmrn/vM4fVsuGdQ/7XrHoro4PkJcG9+HscVbYbOlm7tZWfPr0pK7wkAr/zQ1/Cp6e7g2xyfR5RXJ8Q/p7JlAn1TgCsdM7EEZDIQg9zAp9r+zYNZry/Hq8yKzwuVEI6SKHv3bQvNs8x98LT1fCXOToUXsmJZ/RWbNmLY8Klg7l2ktEB9JCpN/cGvAedgAAXTxzKC+kyRNty69IBPmxt5saWH3Di4W1YkX+mcSEQD09S4igJ7rNu4pGjF2St1cKNi3tJ8OB6LgmEfGZNrWfjO4f4x7SjCH0PgenpnXqQaltYOOdcwDWuz2/c7V8TVEb1Hsf9D6wfdALN+4+G1nX90Bb+6cB3qOEo7di8Nulu3hx9PXc9kRkec+vHx1Hbr4qfPLXR/xy8U1W+cFXwBFCdsFh4i9b991U6MxReHYCSl6CGkGdQchkS7/rPPLgyS83SFrhhxmhGDurH5l2HWPpaS6ZvwBb+x4RTGVxbw0k1CR588S3f2Fan1UDfW3YXV8oKTjXv+mEgj3zOAEiPQxSWpqUnBDg/PeT+nifXh3b1nvH23tvara18+v6XY2WqvaayR1dty7rnjeeM5gde2CjweSRs4copw/33n2uK160fH8fDK97KkoUI4q114zuHQvOePYPu5RpM+jOwBb5x6QTmXnh61veK5gDU+PddOuMANASk5K1oiZsjkK8UctqYOhbektEFen7THpIpt+R08oiBTBhWy8+e3Rza9SZThqde34VtuZINwdfaUu4QmJk3/4wn0hU1Zzz1eT7c/mpsziBL897LBWCYZa/gU9YKDtKflsQN/PXw1zh71KDQ7nz0KQN4vKHZfy9xktLgOkHvdBCHkDkRBaeapRzD0v9uCeUG4qjtV8Vjc84NzUSO0pYyLGloZuSgftmnsnQJp1iCLeLX/udK5qoAXGWiDqDCKUTKODhHoJCqkKAx8RQwPbXJa6fWx45zBGINLeDLFHuzAK5//5v+a15NPGSMve8PYpLIlsAgOcygpl8x/s1f8VkGsMC+kB+lbsTgdv9u2f2enwgNDujxsAXmXTnJdxBxYZzamkTWaE9vDUEscUNRwZ2+bWWkmY+2pwBX6uGT1ktYGF5zxnFt8ntY4ibWg41tgO903BJOw+CTqvlQ/SC+kh4spCgeVseXKOVMrilYUbyTwDcundApXZjobAODG2O2xf3zI6fV5e0zsiQ8rCZar39Z8j7OaF/AB9rcX4+nzgvIP2R+QcYheLdLCAyU9/lqYhlN1TfyZvWN/CrhDsJpC3wWF4wfEjpVOMZdx9qtrcwcd0pWSArg5UAVkJBR9Iy+t3/+1BROH3Ji6HnPWe79zRf41fZLaaq+kVn2ChLihnSm2k0sSXyHkwdU0x742S1paOazD61kxZbMxDcDvHPwGE+9vss/razd2sr857awdmu2mJxSWegJoMLpTL13V8IE0e9/7dR6X0rCa0TzrFV0J22lnURwTdEu2hmn1fHq9v2k0jvoO5y53JGay4/s+VxhvUIN7VlDUuJOBtEu5OedKaw68mD8Lh5Xw+elN/dxy/ljMTFngPUtB0ika/uDie2/btxNMuXW+HvSzm/syoSRZlvPcJu9hCGyH8trTI7p+J1ibWXvexnHaFuCkBkaZAmc1K+K/ekyUnCd1oRhtSrypvioA6hwjveov2CnsAk8F+w1MKQ7kM8YzKThJ9G48yCThp9Ebb+qrDV5idc/rt/pX5uMDA245WPjuOOFudyenIst8OIJX2doKj1UJtpnQLwzuMBex8n/PZcHkrfnLBFNOYb7X2iKTTynHLhoopvY9vofEmlHYIBTa2uYMKyWJQ3NfNNawJftP5IglXVSEP+3zPoA1jljQtd5w3CWNDT71VTjTz0xVKF0+eThKvKmhFAHoPRIAjDYfOXFqnfsP0LCzoiTXT55OPcua6Qt6eTtOZgwrJbGlgM8kq6SicbYDx5LYtsWTtIBEc478u9+Lf5PEu7JIEGSBNn1/8Fd9gfb1pNIaw/lStYa44qmecnr4GVDamtCoa+2dLLbW8eUV1dyNims4P/CSBLbu0eQfakBobkKXq+C52y9ATZrtrZSZQsTh5/kD7hZu7VVO3wVH3UAynEnuutc0tDM42mHkLCE2TMyImUd7U6jEgtRLMs1oL6OTcRy356cy+3p6WSzrWf4pr2IOnGbrkTCBvyl9vFZDiaKbQk3p+UlHntlW6iks7YmwSMvve1//R32Am6y/0QVyeydfkyTW+bF9FB4hE1DLuPfav8BSev3C+7uP/g5Ne44kJGAcAyXThrmn5yO94lP6Vt011D4y4D/A9jAQ8aYf428XgP8BpiGOwv4BmPM291xb6X3E80DBGPVKccwYlA/3xB1tDuNSixEmTRioB8KyeUkPB5zLmKRucg3tt4MXQMsT2UkqaNU2cLpQ07kjV2HSDmGX7/8NlNGDsyq51/wyja+zv/jluplWTIOxDyO7vSNgTZj80/OF1nkXOSqg06fxPO/b8yI9wlMHjEQyG7oArDt7M9RSz4Vj+4YCm8D84FLgGZgtYg8aYx5PXDZl4FWY8zpIjIb+CFwQ7H3VvoGcbN3g7Hq4LD1jnanQWdi2xZn1Q9kdSDO7Q1siU45s9I79YdWvOU+Todagkb7suR9fKS+joZt+3OWpIrAl88by0MvvuUb7KPtTmgN7pCW/8JyDGJnf32QOKN/DJtfpS7nR6kbQ6+1eTODAyWpjsFNpOPmRaJSFddN06YuJTdFdwKLyLnAPcaYv0s/vhPAGPMvgWv+nL7mZRFJAO8AQzoaDK+dwOWL13karWMvxFgFG9cAZge6Xr/3qSmhsY/Ba1c27QtJJMT94zurfqAvoJaLQf3D1TUQ7kcoaKcfWID3v2CT4wq65SLOaXnPW5Ita6GSDpVJT3cCjwS2Bx43A+fkusYYkxSRA8ApQLb+rtLn6MrwcK+JKt+w9Xxf6103/7kt/m7dMTBv6frQxK644TXe6SGqSwQwdvAAfzBOLjzjP9t6hnn2/+UESXY6vOMAe8wgfpq8lkXORVwycSjPbdxNzpFmwMkDqkOln55DEMkMlLEEpowcyOSRA1XSQemQ7nAAcW08WcUVBVzjXigyB5gDMHp0/ABvpfdQSCdxLrqiOR91NjPHneLvfgEcx+SVqQgOw5m3dF2WA3hr7/s5TwfgdeS+jI3TeaMvkJIa9k3+Ei3Tv+1+bk5GAG9wbQ0LYnSFPAb1DzuAi88cylmjBvn9FP7s5qsmqeFXCqI7HEAzMCrwuB5oyXFNczoENBB4N+6bGWMeAB4ANwTUDetTjiPF1JV3tiIll7O59+rJ7mxjx1BdVVgz2/zntsSWdjbuPEhVwi1NtW2LT4wfwhWb5nGVtaJLiVxPiO4FZzI3Je/kK2m1zpm4chLzlq4n6Ri+85/r+ORZIzihKl5C2hIYN3gAb+97n1TKHdwTlHaYMKxWK3uUTtMdDmA1cIaIjAV2ALOBGyPXPAl8AXgZuA54tqP4v9I3KHZyVGcqUnI5mxvPGd1pAxhcN2Ti6qmU4cKJp/I/Dz7CzL2LqGpKIsH/JaawRK4hPNze45fLm/wO52un1ofCV//5Wos/KjJLUlvEbSazLT59zigmjxjoS1V4n6EafqWzFO0A0jH9rwF/xi0DfcQY0ygi9wJrjDFPAg8DvxWRLbg7/9nF3lfpHfRkXfnMcaeQSAun2ZaEnE1nDWA0HOTJQn9YNjF/82epigwg8I2+1yjm/5b+Q8BBeIqP8b+O3Zr33p4DM0Q6k3FPILddPJ5Vb73r1/LbAiad4E2lHPYeOuYL7OWT5laUjuiWPgBjzB+AP0Semxf4+1Hg+u64l9L76NHdZ1rmOK+CXICOpK695xpbDrDhladzzt2FTPVOWnUaR2BvspavOrezzvognxg/hKc3xEs3B7EEXxfppJoEv1ze5L92+eThIUntPYeOYYDnN+3xw1LPbNjln1ja2lXOQek62gms9Bm8qiFX5rhjwxfMGSQs4frpo5g0YiDrWw6EBp8sWLWN9TsO8LHEBmzyD5hxfYAF4y7gF6N+7JeV4jg5dfs9BLj67BGcMbTWd0jTxtQx+pQBoYEugP++guufnZ6t/NgrmUSxFTkJKUpnUAeg9Bk6m28I5gzaUiZrcteiNduZGhgIY8uZ3FYDdkxM3wGedM5j00d/4ovUzcTVAYo2X+XCAMv+tpNFXzkt5LgmDKul9XAbE4bVZvUt+DmP9D2unVrvy2hY4iqK6u5f6SrqAJQ+Q2fzDZ7DyCUJkUyZkFpmgxnPXQPv47vv3kk/accBHnKuYungOa5kswGTDtck0nLOF0w41Rd4KwSvTBUISWK3JR0StgXGkHSMK/tw5SQStuVLXyxes51ZU+tD6qoThtUWfG9FiaIOQOlTdCbf4DmMe3/f2GFzl8fJE87nwy/9lrZ2tz7/lvPHsjkg++DhlW7GDXrJh2UJh460+6EdS1y1UXClHrwehPakQ+vhNq6bVs/CVdt8YTvP+UXVVfUUoHQFnQimlDXTxtQx76pJVNvuwJSELVwycSiXThzqTyZL2MJZ9QP5wTVTqO1XRTKVrsI3hsadB3PqAjkGcky3jEUAxxgeevGtkBheENtyq368ENe1U+upqbJCzxU6xU1ROkJPAErZM21MHQvnnJsVOoqrEFq7tTVUanr55OGsfvtdjrW7nb+j6vqz9d3Dee/nDXGJSyCb9G+WJQgmS8bhho+MZsSgfqE1xYW9VNNf6Q7UAShlS9TA5ysDDREpNf34GUN45o3dGGNoOXAEy30VS7xO3+jXZxv/IImExT1XTaL1cFuWjEOcfk90nd3Ve9EVDSelvFAHoJQlXdUoCpaaJlOO33Dl2XMn5U4A9gbB/Prlt33pBi9+31GP+yfGD/Gnc61s2se8K11n0FkxvWlj6vwB794poFhZDaWyUAeglCVd1SiKSkQkY+L/BjeW37jzoG+86/pX88f1O7MkHOJ4ftMeFqza5lf/dLWcM9rngEjB0to6G1gBTQIrZYpnyIPJ00Lwwis3zBidt9vYMfDi5r3c8+R6WvYfYcKwWm67eLxriAPMOK0u67lUynGHt6QNcNIxzFu6nrVbW8mHt9v3rov2CbTnSQxHv7arn49SXugJQClLolo/QeG0Qr728YbmnNU/Ht6g9wWrX7qLHQAACz9JREFUtrEkXY558/ljuf+FJj8M1LB9Pxd+8FQE+GtazqEqYXH55OG8/Oa+gmSsITPusT1lqLKFhXPODU9HS58AvO8fNOi5wj3F5BE0f1AeqANQypaonEJnYt1R03/6kAG8te9wrFMwuJo83rD7YA4gmTI8/fouaqoyid+g0QzKWNf1r/bj+dE1/vL5N/2O47aUYUlDMz+4ZkrWqM04o5wr3NNVDSfNH5QP6gCUsqarse5rp9bzu/Q84YQt/PC6s9j4ziHfYFu2MPSkE9jRegRwpSL2HjrmK3gGCTZ2eXX8QEjGOtoRfN20eq5NVwSt3drKs2/sDn1PL6gUVyEUpVjJ7iiaPygf1AEoZU1Xp4493tAMxq348RJlnsH2Zhm3pI0/uCWhg2trQtPJwG3qAjfOXte/OiuMExxQ4+sWJR0Wrtrmd/mubNqHEzh52JYwa2p9wZ9Bd0t2d7dDUUqHOgClrOnq1LGgflAqEJ8PzjL2XhcyA16i8s63fGycLx63pKE5K4zjrSeqW+SdGrx116QnhVlW5yqGgrH6uReeHnp+SUNzSBW1UHpyBoRyfFEHoPRJciUh454vJNbtfd2O/Ud88TVwjXt0lxtNvl4/fZRvRFc27fMbxCyB2n5VvuF9vKE5dM9gbZBnVB9vaGbxmu2kHOPft6sGN1es3ksoe85o8dpmFt7SuTi+TiArD9QBKH2OfIatK8nJUD29bZGwXHkGOxKL98hnkPOFR2ZNrWfx2uZQ128Qz6jOmlrfJScWJVesfmXTPl9eGsJlo7qrryzUASh9jnyGrZDkpBfjN8DkEQNDNfmplMPsGdl6PFFyGeR8zsGb9NWRkS12d+2dZur6V2c5o7VbW2nZfwTbygjZefkJreypPIpyACLyY+AqoA14E/iSMWZ/zHVvA4eAFJA0xkwv5r5KZZNrl11IcnLt1lY+8+DKULWOJ+EggG3H6/HEfZ9c5Zf5DPjxDp1ET0FBmQkgdNK55INDOLW2xj9xaGVP5VHsCeAvwJ3pwfA/BO4EvpXj2guNMR33yStKB+TaZRcSK1/ZtM+XefAwwT87EvKhOAmG403UkLcebvNzEMFKo1TK4exRg/yy1LjTglL+FOUAjDFPBR6uBK4rbjmKUhj5QjD5DPDMcadQlbBi6/UhXPGTi+xRjSZUtRP92p7sms13Coq+Fg37dEWUTunbdGcO4CZgUY7XDPCUiBjgfmPMA7m+iYjMAeYAjB49uhuXpyiZOPz9z7/JMxt2+dU6liU4gcqbfBQqwQA93zXbUQ4i+Fq+04JSGXToAETkaWBYzEt3G2OWpq+5G0gCj+b4NucZY1pE5FTgLyLyhjFmedyFaefwAMD06dMLm7atKHmImwtw1qhBPL1hlx/+uX76KEZ2kPj1iBpSyF0909Ox9Y5OG9ETkoZ9KpsOHYAx5uJ8r4vIF4ArgYuMiQ+gGmNa0n/uFpEngBlArANQlO4k1w48Gg6Jlnp2RCESDNCzXbOdPW1oQ5dSbBXQZbhJ308YY2Ln5InIAMAyxhxK//1S4N5i7qsohZJPCK0njF9Pqm525bShDV2VTbE5gJ8DNbhhHYCVxphbRWQE8JAx5gpgKPBE+vUEsMAY86ci76soBZFvB95Txq+nVDdVo0fpLMVWAcVmjNIhnyvSf28CzirmPopSDLOm1ndJ86bUdHZHryEdpbNoJ7DSJ+hKKWV0B90ZBc3upKtloF3Z0WtIR+kM6gCUXk8xA95L3d1aTBloMTt6ndilFII6AKXX0x0D3nPV6B9vI1msE+rKjl4ndimFog5A6fV0NbmZbwfdU0ayFInZ3nDyUfoG6gCUXk8xevilbtAqRWJWq4GUQlEHoPQJOhsK6WiH35NGsqcTsx2dfDQ3oHioA1B6FcWMKgzS0Q6/0J15XzWYcU5HcwNKFHUASq+hO0YVehSyw+9oZ15uBlNzA0oUdQBKryHXqMKuGKnuiL2Xm8H0nGJb0kFEqOtfXeolKSXGKvUCFMVj5rhTqLIzo9KLjc1PG1PH3AtP77LR9gymLcWvpTcwbUwd866chCXuzON7lzWydmtrqZellBA9ASi9hmlj6lg459xuyQF013rKTVqh9XAbjsk/wEapHNQBKL2K3iZl0NvWUyxaIqoEUQegKBVEOZ5qlK6jDkBRKoxyO9UoXUeTwIqiKBWKOgBFUZQKRR2AoihKhaIOQFEUpUIpygGIyD0iskNEXkv/uiLHdZeJyEYR2SIi3y7mnoqiKEr30B1VQP9ujLkv14siYgPzgUuAZmC1iDxpjHm9G+6tKIqidJGeCAHNALYYY5qMMW3AY8DVPXBfRVEUJQ/d4QC+JiJ/E5FHRCSuuHgksD3wuDn9XCwiMkdE1ojImj179nTD8hRFUZQ4OnQAIvK0iKyP+XU18AvgA8DZwE7gJ3HfIuY5E/Oc+4IxDxhjphtjpg8ZMqTAt6EoiqJ0lg5zAMaYiwv5RiLyILAs5qVmYFTgcT3QUtDqFEVRlONGsVVAwwMPrwHWx1y2GjhDRMaKSDUwG3iymPsqiqIoxVNsFdCPRORs3JDO28BXAERkBPCQMeYKY0xSRL4G/BmwgUeMMY1F3ldRFEUpkqIcgDHmczmebwGuCDz+A/CHYu6lVAZ9dQavovRFVA1U6TWU2wxeRentqBSE0muIm8GrKMrxQx2A0msotxm8itLb0RCQ0mvQaVWK0rOoA1B6FTqtSlF6Dg0BKYqiVCjqABRFUSoUdQCKoigVijoARVGUCkUdgKIoSoWiDkBRFKVCEWNySvOXHBHZA2zt4pcPBvZ243J6A+X4nqA835e+p75Dub2vMcaYgoap9GoHUAwissYYM73U6+hOyvE9QXm+L31PfYdyfV+FoCEgRVGUCkUdgKIoSoVSzg7ggVIv4DhQju8JyvN96XvqO5Tr++qQss0BKIqiKPkp5xOAoiiKkgd1AIqiKBVKWTsAEflnEfmbiLwmIk+lh9X3aUTkxyLyRvp9PSEig0q9pmIRketFpFFEHBHp0+V4InKZiGwUkS0i8u1Sr6c7EJFHRGS3iKwv9Vq6CxEZJSLPiciG9L+9vy/1mkpBWTsA4MfGmA8ZY84GlgHzSr2gbuAvwGRjzIeATcCdJV5Pd7AemAUsL/VCikFEbGA+cDkwEfiMiEws7aq6hV8Dl5V6Ed1MErjdGHMmMBOYWyY/q05R1g7AGHMw8HAA0Ocz3saYp4wxyfTDlUB9KdfTHRhjNhhjNpZ6Hd3ADGCLMabJGNMGPAZcXeI1FY0xZjnwbqnX0Z0YY3YaYxrSfz8EbABGlnZVPU/ZTwQTke8DnwcOABeWeDndzU3AolIvQvEZCWwPPG4GzinRWpQCEZHTgA8Dq0q7kp6nzzsAEXkaGBbz0t3GmKXGmLuBu0XkTuBrwHd7dIFdoKP3lL7mbtxj7KM9ubauUsh7KgMk5rk+f+osZ0TkRGAJcFskYlAR9HkHYIy5uMBLFwD/RR9wAB29JxH5AnAlcJHpI40cnfg59WWagVGBx/VAS4nWonSAiFThGv9HjTGPl3o9paCscwAickbg4SeBN0q1lu5CRC4DvgV80hhzuNTrUUKsBs4QkbEiUg3MBp4s8ZqUGEREgIeBDcaYfyv1ekpFWXcCi8gSYALg4MpK32qM2VHaVRWHiGwBaoB96adWGmNuLeGSikZErgF+BgwB9gOvGWP+rrSr6hoicgXwU8AGHjHGfL/ESyoaEVkIXIArm7wL+K4x5uGSLqpIROR84AVgHa59ALjLGPOH0q2q5ylrB6AoiqLkpqxDQIqiKEpu1AEoiqJUKOoAFEVRKhR1AIqiKBWKOgBFUZQKRR2AoihKhaIOQFEUpUL5/4GXu45ASg74AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "yp = results.predict(W)\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\", label=\"expected\")\n",
    "ax.plot(X[:, 0], yp, \".\", label=\"predicted\")\n",
    "ax.legend()\n",
    "ax.set_title(\n",
    "    \"Régression linéaire par morceaux\\nsur un nuage linéaire par morceaux\\nR2=%f\"\n",
    "    % results.rsquared\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le modèle nous suggère de ne garder que quelques seuils. En s'appuyant sur les p-values :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  5,  6,  7, 13])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "keep = numpy.arange(len(results.pvalues))[results.pvalues < 0.05]\n",
    "keep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "W2 = W[:, keep]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "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>   0.846</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.845</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1094.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 15 Oct 2018</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:07:38</td>     <th>  Log-Likelihood:    </th> <td> -1708.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  1000</td>      <th>  AIC:               </th> <td>   3427.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   995</td>      <th>  BIC:               </th> <td>   3452.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     5</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>x1</th> <td>   -1.9504</td> <td>    0.066</td> <td>  -29.574</td> <td> 0.000</td> <td>   -2.080</td> <td>   -1.821</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x2</th> <td>    0.3384</td> <td>    0.148</td> <td>    2.287</td> <td> 0.022</td> <td>    0.048</td> <td>    0.629</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x3</th> <td>    3.2628</td> <td>    0.397</td> <td>    8.209</td> <td> 0.000</td> <td>    2.483</td> <td>    4.043</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x4</th> <td>    2.0247</td> <td>    0.385</td> <td>    5.260</td> <td> 0.000</td> <td>    1.269</td> <td>    2.780</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x5</th> <td>    0.4635</td> <td>    0.119</td> <td>    3.901</td> <td> 0.000</td> <td>    0.230</td> <td>    0.697</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>248.807</td> <th>  Durbin-Watson:     </th> <td>   1.984</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td> 829.417</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-1.190</td>  <th>  Prob(JB):          </th> <td>7.84e-181</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 6.774</td>  <th>  Cond. No.          </th> <td>    20.1</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:                      y   R-squared:                       0.846\n",
       "Model:                            OLS   Adj. R-squared:                  0.845\n",
       "Method:                 Least Squares   F-statistic:                     1094.\n",
       "Date:                Mon, 15 Oct 2018   Prob (F-statistic):               0.00\n",
       "Time:                        11:07:38   Log-Likelihood:                -1708.6\n",
       "No. Observations:                1000   AIC:                             3427.\n",
       "Df Residuals:                     995   BIC:                             3452.\n",
       "Df Model:                           5                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "x1            -1.9504      0.066    -29.574      0.000      -2.080      -1.821\n",
       "x2             0.3384      0.148      2.287      0.022       0.048       0.629\n",
       "x3             3.2628      0.397      8.209      0.000       2.483       4.043\n",
       "x4             2.0247      0.385      5.260      0.000       1.269       2.780\n",
       "x5             0.4635      0.119      3.901      0.000       0.230       0.697\n",
       "==============================================================================\n",
       "Omnibus:                      248.807   Durbin-Watson:                   1.984\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              829.417\n",
       "Skew:                          -1.190   Prob(JB):                    7.84e-181\n",
       "Kurtosis:                       6.774   Cond. No.                         20.1\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = OLS(Y, W2)\n",
    "results = model.fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "yp = results.predict(W2)\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(X[:, 0], Y, \".\", label=\"expected\")\n",
    "ax.plot(X[:, 0], yp, \".\", label=\"predicted\")\n",
    "ax.legend()\n",
    "ax.set_title(\n",
    "    \"Régression linéaire par morceaux\\nsur un nuage linéaire par morceaux\\n\"\n",
    "    + \"réduction du nombre de segments\\nR2=%f\" % results.rsquared\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le coefficient $R^2$ est quasiment identique pour un nombre de segments moindre. Je me suis amusé à rendre ce code plus générique pour comparer la première étape, le découpage en morceaux, via deux modèles, un arbre de décision et le nouvel objet [KBinsDiscretizer](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.KBinsDiscretizer.html) qui segmente une variable sans tenir compte de la cible. La régression n'est plus nécessaire linéaire : [Piecewise linear regression](http://www.xavierdupre.fr/app/mlinsights/helpsphinx/notebooks/piecewise_linear_regression.html). Je me suis également amusé à faire de même pour une classification par morceaux [PiecewiseClassifier](http://www.xavierdupre.fr/app/mlinsights/helpsphinx/mlinsights/mlmodel/piecewise_estimator.html?mlinsights.mlmodel.piecewise_estimator.PiecewiseClassifier). Celle-ci pose quelques soucis pratiques car toutes les classes ne sont pas forcément représentées dans chaque compartiment..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}