{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TP3 :  régression linéaire"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "import  numpy as np #charger les bibliothèque\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la taille de notre échantillon est : (50,)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# un exemple simple x réel et y aussi \n",
    "\n",
    "rng = np.random.RandomState(42) #pour générer les mêmes données\n",
    "\n",
    "#constituer  un exmple de points aléatoires  \n",
    "x = 10 * rng.rand(50) #genere un tbl de 50\n",
    "print('la taille de notre échantillon est :',x.shape)\n",
    "\n",
    "y=2*x-1 + rng.randn(50) # définir une relation entre x et y + bruit \n",
    "\n",
    "#afficher data y=f(x) [y en fonction de x]  comme un nuage de points \n",
    "plt.scatter(x, y);\n",
    "#observation(x,y), i = 1 ... 50\n",
    "y = a*x + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Y-a-t-il une relation entre $x$ et $y$ : trouver $f$ tel que  $y=f(x)$ ? \n",
    "\n",
    "Pour répondre à cette question, nous allons supposer que $f$ est une fonction affine de la forme : \n",
    "\n",
    "$$f(x)=a*x+b$$\n",
    "\n",
    "avec $a$ et $b$ sont des inconnus (réels) à déterminer. \n",
    "\n",
    "On connaît $(x_i,y_i)$ pour  $i=1 \\ldots 50$\n",
    "\n",
    "Et la relation $y_i=a*x_i + b,$ pour  $i=1 \\ldots 50$ \n",
    "\n",
    "qui forme un système linéaire facile à résoudre (plus de données que d'inconnus)\n",
    "\n",
    "Pour résumer : le but est de trouver la droite \"la plus proche\" de l'ensemble (nuage) de points. Un bon critère pour vérifier \"la plus proche\" est minimiser l'erreur quadratique moyenne : \n",
    "\n",
    "$$\\frac{1}{n} \\sum_{i=1}^{n}(y_i - a*x_i -b)^2$$\n",
    "\n",
    "Après calcul on trouve les valeurs optimales : \n",
    "\n",
    "$\\hat{a}=\\frac{\\sigma_{xy}}{\\sigma_{x}^2}$ et  $\\hat{b}=\\bar{y_n}-\\bar{x_n}*\\frac{\\sigma_{xy}}{\\sigma_{x}^2}$ avec : \n",
    "\n",
    "\n",
    "- $\\bar{y_n}= \\frac{1}{n} \\sum_{i=1}^{n} y_i$\n",
    "\n",
    "- $\\bar{x_n}= \\frac{1}{n} \\sum_{i=1}^{n} x_i$\n",
    "\n",
    "- $\\sigma_{y}= \\frac{1}{n} \\sum_{i=1}^{n} (y_i-\\bar{y_n})^2$\n",
    "\n",
    "- $\\sigma_{x}= \\frac{1}{n} \\sum_{i=1}^{n} (x_i-\\bar{x_n})^2$\n",
    "\n",
    "- $\\sigma_{xy}= \\frac{1}{n} \\sum_{i=1}^{n} (x_i-\\bar{x_n})(y_i-\\bar{y_n})$\n",
    "\n",
    "Au lieu de faire le calcul à la main, nous allons utiliser des bibliothèques python pour trouver la solution. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exemple1 : Formulation avec la biblio sklearn\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la tailles des entrées est : (50, 1)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-9 {color: black;background-color: white;}#sk-container-id-9 pre{padding: 0;}#sk-container-id-9 div.sk-toggleable {background-color: white;}#sk-container-id-9 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-9 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-9 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-9 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-9 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-9 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-9 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-9 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-9 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-9 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-9 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-9 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-9 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-9 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-9 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-9 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-9 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-9 div.sk-item {position: relative;z-index: 1;}#sk-container-id-9 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-9 div.sk-item::before, #sk-container-id-9 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-9 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-9 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-9 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-9 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-9 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-9 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-9 div.sk-label-container {text-align: center;}#sk-container-id-9 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-9 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-9\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-9\" type=\"checkbox\" checked><label for=\"sk-estimator-id-9\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# On peut résoudre ce problème de régression linéaire avec sklearn \n",
    "# on choisit et on charge le modèle \n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "X = x[:, np.newaxis]\n",
    "print('la tailles des entrées est :',X.shape)\n",
    "\n",
    "models = LinearRegression(fit_intercept=True)\n",
    "models.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "----- la solution -----\n",
      "la valeur trouvée de a est :  1.9776566003853122\n",
      "la valeur trouvée de b est :  -0.9033107255311235\n"
     ]
    }
   ],
   "source": [
    "a=models.coef_\n",
    "print('-'*5,'la solution','-'*5)\n",
    "print('la valeur trouvée de a est : ', a[0]) # = 2 de base\n",
    "\n",
    "b=models.intercept_\n",
    "print('la valeur trouvée de b est : ', b) # = -1 de base"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si maintenat on a un nouveau $xnew=2.5$ qui est différent de tous les $x_i$ observés on peut trouver son image $ynew$ avec la relation :  $$ynew=a*xnew+b$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.04083078]\n"
     ]
    }
   ],
   "source": [
    "#solution pour un seul point\n",
    "xnew=np.array([2.50])\n",
    "ynew = models.predict(xnew.reshape(-1, 1))\n",
    "print(ynew)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut aussi appliquer la même méthode sur xnew comme tableau de valeurs au lieu d'un seul scalaire\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.88096733 -0.02435224  2.83226285  5.68887794  8.54549303 11.40210812\n",
      " 14.25872321 17.1153383  19.97195339 22.82856848]\n"
     ]
    }
   ],
   "source": [
    "#solution pour un tableau de points\n",
    "xnew=np.linspace(-1,12,10)\n",
    "#s'assurer d'avoir le bon format \n",
    "xnew=xnew[:, np.newaxis]\n",
    "\n",
    "ynew = models.predict(xnew)\n",
    "print(ynew)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vérification visuelle\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y,color='k');# données apprentissage en noir \n",
    "plt.scatter(xnew, np.zeros(xnew.shape[0]),color='b');# x_i non observés en bleu\n",
    "plt.scatter(xnew, ynew,color='r', marker='*');# y_i prédit ave la régression linéaire (x_i,y_i) en rouge "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,)\n",
      "Biais ou erreur en chaque point : \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L'erreur globale peut être donnée l'erreur quadratique moyenne :  6.893473346225456e-30\n"
     ]
    }
   ],
   "source": [
    "#on peut aussi afficher la fonction f\n",
    "plt.scatter(x, y,color='k');\n",
    "#plt.scatter(xnew, ynew);\n",
    "plt.plot(xnew, ynew,'r');\n",
    "#l'erreur est donnée par la somme cumulée des distances \n",
    "#entre les points en noir et la droite en rouge\n",
    "\n",
    "ypred=models.predict(X)\n",
    "print(ypred.shape)\n",
    "print('Biais ou erreur en chaque point : \\n')\n",
    "plt.figure()\n",
    "plt.plot(x, (y-ypred), 'g*')\n",
    "plt.show()\n",
    "print('L\\'erreur globale peut être donnée l\\'erreur quadratique moyenne : ',np.mean((y-ypred)**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nous venons de faire notre premier exemple pour le cas simple $ x$ réel et  $y$ réel   \n",
    "\n",
    "\n",
    "On peut généraliser ce résultat quelque soit la taille de $x :  x\\in R^d$ et pour toute dimension finie $d$\n",
    "\n",
    "Exemple : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "#constituer  un exmple de data \n",
    "x = np.array(10 * rng.rand(100,2))\n",
    "y=2*np.inner(np.array([-1,1]), x)+ 2*rng.randn(x.shape[0]) \n",
    "\n",
    "fig=plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "ax.scatter(x[:,0], x[:,1],y,c='b', marker='o');\n",
    "ax.set_xlabel('valeur de x[:,0]')\n",
    "ax.set_ylabel('aleur de  x[:,1]')\n",
    "ax.set_zlabel('valeur de y ')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-10 {color: black;background-color: white;}#sk-container-id-10 pre{padding: 0;}#sk-container-id-10 div.sk-toggleable {background-color: white;}#sk-container-id-10 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-10 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-10 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-10 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-10 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-10 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-10 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-10 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-10 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-10 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-10 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-10 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-10 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-10 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-10 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-10 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-10 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-10 div.sk-item {position: relative;z-index: 1;}#sk-container-id-10 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-10 div.sk-item::before, #sk-container-id-10 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-10 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-10 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-10 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-10 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-10 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-10 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-10 div.sk-label-container {text-align: center;}#sk-container-id-10 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-10 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-10\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-10\" type=\"checkbox\" checked><label for=\"sk-estimator-id-10\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LinearRegression(fit_intercept=True)\n",
    "model.fit(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "xnew = np.array(10 * rng.rand(1000,2))\n",
    "ynew = model.predict(xnew)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "ax.scatter(x[:,0], x[:,1],y,c='b', marker='o');\n",
    "ax.scatter(x[:,0], x[:,1],-y,c='b', marker='o');\n",
    "ax.set_xlabel('valeur de x[:,0]')\n",
    "ax.set_ylabel('aleur de  x[:,1]')\n",
    "ax.set_zlabel('valeur de y ')\n",
    "\n",
    "ax.scatter(xnew[:,0], xnew[:,1],ynew,c='r', marker='*');\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice TD2 : \n",
    "Reprendre l'exercice de la régression linéaire dans le TD2.\n",
    "\n",
    "1- Faire un programme python qui répond aux questions.\n",
    "\n",
    "2- Comparer les résultats théoriques vu en TD et les résultats par le code. \n",
    "\n",
    "3- Prédire le taux de scolarisation pour des PIBs non observés.\n",
    "\n",
    "4- Suivre les mêmes étapes que l'exemple 1 au dessus pour visualiser et inerpréter le biais. \n",
    "\n",
    "5- Commenter la qualité du modèles : bon ou mauvais ? Pourquoi ? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "moyenne PIB :  5473.375 moyenne scolarisation : 65.75\n",
      "variance PIB :  2128.73747427319 variance scolarisation : 10.720890821195784\n",
      "(8,)\n",
      "(8,)\n",
      "----- la solution -----\n",
      "la valeur trouvé est [0.00485763]\n",
      "la valeur trouvée de b est : 39.16236270608056\n",
      "la covarience : 2643809.964285714\n",
      "â = 1241.9614894919741 b^ = -6797655.217548134\n"
     ]
    }
   ],
   "source": [
    "pib = np.array([8802,5872,4775,5680,7964,5680,3072,1942])\n",
    "scol = np.array([83,69,63,62,81,62,56,50])\n",
    "print(\"moyenne PIB : \", pib.mean(), \"moyenne scolarisation :\", scol.mean())\n",
    "print(\"variance PIB : \", pib.std(), \"variance scolarisation :\", scol.std())\n",
    "\n",
    "print(pib.shape)\n",
    "print(scol.shape)\n",
    "models = LinearRegression(fit_intercept=True)\n",
    "models.fit(pib[:, np.newaxis], scol)\n",
    "\n",
    "a=models.coef_\n",
    "print('-'*5,'la solution', '-'*5)\n",
    "print('la valeur trouvé est', a)\n",
    "\n",
    "b=models.intercept_\n",
    "print('la valeur trouvée de b est :', b)\n",
    "\n",
    "cov = np.sum(pib * scol) -len(pib) * (pib.mean() * scol.mean()) / (len(pib) - 1)\n",
    "print('la covarience :', cov)\n",
    "\n",
    "a_chap = cov /pib.std()\n",
    "b_chap = scol.mean() - a_chap * pib.mean()\n",
    "\n",
    "print(\"â =\", a_chap, \"b^ =\", b_chap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Un test de la régression logistique  sur des données réelles\n",
    "## C'est un cas particulier où $y \\in \\{0, \\ldots, k\\}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "#importer les bibliothèques \n",
    "#pour l'affichage (si déjà fait pour np, plt) \n",
    "%matplotlib inline \n",
    "\n",
    "#charger des datasest de sklearn\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'sklearn.utils._bunch.Bunch'>\n",
      "<class 'numpy.ndarray'>\n",
      "(150, 4)\n"
     ]
    }
   ],
   "source": [
    "#charger la base iris \n",
    "iris = datasets.load_iris()\n",
    "#vérifier le type de la variable iris \n",
    "print(type(iris))\n",
    "#vérifier le type de données \n",
    "print(type(iris.data))\n",
    "#vérifier les dimensions \n",
    "print(iris.data.shape)\n",
    "\n",
    "#Sur wikipédia chercher la signification de ces données "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2]\n",
      "(150, 2)\n",
      "[0 1]\n"
     ]
    }
   ],
   "source": [
    "X = iris.data[:, :2] # Utiliser les deux premières colonnes afin d'avoir un problème de classification binaire.\n",
    "\n",
    "print(np.unique(iris.target))\n",
    "#on va garder deux classes seulement pour un test simple\n",
    "y = (iris.target != 0) * 1 # re-étiquetage des fleurs\n",
    "print(X.shape)\n",
    "print(np.unique(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hmELbCSm9UxulhgIAZIQB6AAAAAtgADoAAECLEEwBAAAkQDAFAACQAMEUAABAAgRTGQslr1vcdoayfwBQNy5sqEBuvgyFktctbjtD2T8AqBsXNlTB1AgZCiWvW9x2hrJ/AFA3LmyFNd/UCARTGVq0SKrW/WbSqVPpt6eWuO0MZf8AoG5c2AqLeabaVCh53eK2M5T9A4C6cWFDFQRTGQolr1vcdoayfwBQNy5sqIJgKkOh5HWL285Q9g8A6saFDVUwZgoAAGABjJkCAABoEYIpAACABAimAAAAEiCYAgAASGDBYMrMlpjZ35vZATM7ZGZ/UGWdDWZ2zMz2lx+fbk1zAQAA2ks9d6Z+LOlKd++XtFLSR83s0irr7XD3leXHA81sJMK1caPU0RH9grijI1pu5XYh5R8Nqa0AgNoWTHTs0dwJb5YXF5cf2cyngKBs3Cht2zazfPLkzPLWrc3fLqT8oyG1FQAwv7rmmTKzkqRxScsk/Ym7f77i9Q2S7pZ0TNI/S/qsu78433syz1T+dXREgVClUkk6caL524WUfzSktgIAmjDPlLufdPeVkrolXWJmKypW+StJve7eJ+mbkh6u0ZAhMxszs7Fjx47VvQMIU7WAaL7ypNsdOdJYeZZCaisAYH4N/ZrP3V+X9C1JH60on3T3H5cXH5C0qsb2I+4+4O4DXV1dMZqLkJRKjZUn3S6k/KMhtRUAML96fs3XZWZnlf9+u6SrJP1TxTrnzlq8VtLhJrYRgZoeA1RvedLtQso/GlJbAQDzq+fO1LmSvmVmT0t6StI33f3rZrbZzK4tr3N7edqEA5Jul7ShNc1FSLZulYaHZ+4olUrR8nyDyJNsF1L+0ZDaCgCYH4mOAQAAFkCiYwAAgBYhmAIAAEiAYAoAACABgikAAIAECKYylnZ+trg579KuL26/ZJHvLu0+zb20D2JIJxuA9uTumTxWrVrlRbd9u3tnp7s08+jsjMpbYXh4bl3Tj+Hh9qovbr+k3Z/u6fdp7qV9EEM62QBkStKY14hpmBohQ2nnZ4ub8y7t+uL2Sxb57tLu09xL+yCGdLIByNR8UyMQTGVo0aLov7SVzKRTp5pfn1nt11pxGsStL26/pN2f0+9dS0YfrbClfRBDOtkAZIp5ptpU2vnZ4ua8S7u+uP2SRb67tPs099I+iCGdbADaFsFUhtLOzxY3513a9cXtlyzy3aXdp7mX9kEM6WQD0L5qDaZq9YMB6JHt2917etzNoudWj18dHnYvlaLxsqVS6wdKx60vbr+k3Z/u6fdp7qV9EEM62QBkRgxABwAAiI8xUwAAAC1CMAUAAJAAwRQAAEACBFMAAAAJEEyhpUh7htwqQlLGIuwj0AQdWTcA+TU6Gs23NDUVLU9MzMy/NDjY/O2A1GzcKG3bNrN88uTM8tat2bSp2Yqwj0CTMDUCWoa0Z8itIiRlLMI+Ag1gagRk4siRxsqTbgekplqQMV95iIqwj0CTEEyhZUh7htwqQlLGIuwj0CQEU2gZ0p4ht4qQlLEI+wg0CcEUWmZwUBoZicY6mUXPIyMLDyKPux2Qmq1bpeHhmbs0pVK0nKeB2UXYR6BJGIAOAACwAAagAwAAtAjBFAAAQAIEUwAAAAkQTAEAACRAMAUAAJAAwVSFtBPsxq0vlPyjJCwuMA5+dUk+vKH0adoZzkO5cCO/3D2Tx6pVq7zdbN/u3tnpLs08Ojuj8naqb3h47jbTj+Hh1rQzrrT7E22Eg19dkg9vKH0at51pbxdXKMcBTSdpzGvENMwzNUvaCXbj1hdK/lESFhcYB7+6JB/eUPo07QznoVy4Ebz55pkimJpl0aLovxmVzKRTp9qnPrPar2V0OKtKuz/RRjj41SX58IbSp3HbmfZ2cYVyHNB0TNpZp7QT7MatL5T8oyQsLjAOfnVJPryh9GnaGc5DuXAj1wimZkk7wW7c+kLJP0rC4gLj4FeX5MMbSp+mneE8lAs38q3WYKpWP9pxALp7NIawp8fdLHpu9ZjCuPUND7uXStHYx1Kp/QafT0u7P9FGOPjVJfnwhtKncduZ9nZxhXIc0FRiADoAAEB8jJkCAABoEYIpAACABAimAAAAEiCYAgAASIBgKmOhpJQKJRcg0PZCyuu2bl30oZ9+rFuXr/qAJiGYytDoaDS9zMRENKHuxES03Kpra9z6Nm6Utm2byYJx8mS0TEAFNCjtD30S69ZJe/bMLduzp3UBTtr1AU3E1AgZCiWlVCi5AIG2F1Jet7TzVoWSJwuFxdQIberIkcbKs6qvWiA1XzmAGtL+0ANIBcFUhkJJKRVKLkCg7ZHXDcglgqkMhZJSKpRcgEDbCymv29q1jZWHVh/QRARTGRoclEZGouESZtHzyEhU3k71bd0qDQ/P3IkqlaLlrVtb004gt9L+0Cfx5JNnBjJr10bleagPaCIGoAMAACyAAegAAAAtQjAFAACQAMEUAABAAgRTAAAACSwYTJnZEjP7ezM7YGaHzOwPqqzzNjPbYWbPmNk+M+ttSWsbEDf9VUhps+KIm2OP/pxH2juZ9kGMK+12FiGBZNzcdWn3aSgffC5stdE3jXH3eR+STNJPl/9eLGmfpEsr1tko6Svlv2+StGOh9121apW3yvbt7p2d7lEOgujR2RmVt2K7UAwPz9236cfw8Pzb0Z/zSHsn0z6IobQzbn0hWbu2+j6uXTv/dmn3aSgffC5stdE3VUka81qxUq0Xqq4sdUr6rqTVFeVPSLqs/HeHpFdVnnah1qOVwVRPT/VrQE9Pa7YLRalUff9Kpfm3oz/nkfZOpn0QQ2ln3PpCUm3/ph/zSbtPQ/ngc2Grjb6par5gqq55psysJGlc0jJJf+Lun694/aCkj7r70fLys+WA69WK9YYkDUnS0qVLV01US/jZBIsWRUewkpl06lTztwtF3Dyi9Oc80t7JtA9iXGm3swhJckPp01A++FzYaqNvqko8z5S7n3T3lZK6JV1iZiviNMTdR9x9wN0Hurq64rxFXeKmv8p72qy4Ofboz3mkvZNpH8S40m4nCSRrS7tPQ/ngc2Grjb5pWEO/5nP31yV9S9JHK156SdJ7JMnMOiS9U9JkE9oXS9z0VyGlzYojbo49+nMeae9k2gcxrrTbWYQEknFz16Xdp6F88Lmw1UbfNK7W93/TD0ldks4q//12SX8r6eMV63xGcwegP7rQ+7ZyzJR7NN6tp8fdLHqud/xb3O1CMTw8MxSiVKp/fC79OY+0dzLtgxhX2u2MW19IKgehLzT4fFrafRrKB58LW230zRmUZMyUmfVJelhSSdGdrEfdfbOZbS6/8W4zWyLpTyV9QNJrkm5y9+fme19y8wEAgFDMN2aqY6GN3f1pRUFSZfnvz/r7LUk3JmkkAABAiJgBHQAAIAGCKQAAgAQIpgAAABIgmAIAAEiAYKpCUXM0IiB5T0Ca9v6Fsl0SoRz7vOM45FetORNa/Wj1PFNx5DxHI/Ig7wlI096/ULZLIpRjn3cch+ApaW6+VmjHeaZ6e6Vq6QJ7eqQXXki7NUAVcU/SUE7utPcvlO2SCOXY5x3HIXjzzTNFMDVLznM0Ig/ynoA07f0LZbskQjn2ecdxCF7iRMdFUeAcjQhF3hOQpr1/oWyXRCjHPu84DrlGMDVLkXM0IhB5T0Ca9v6Fsl0SoRz7vOM45FutwVStfrTjAHT3XOdoRF7kPQFp2vsXynZJhHLs847jEDQxAB0AACA+xkwBAAC0CMEUAABAAgRTAAAACRBMAQAAJEAwBYQmbn6vjRuljo5oksCOjmi5lfWlLe39S/s4JKkzbaG0MxQh9WdIbW2mWj/za/WjXadGANpa3Pxew8Nzt5l+DA+3pr60pb1/aR+HJHWmLZR2hiKk/gyprTGIqRGAnIib36ujQzp58szyUkk6caL59aUt7f1L+zgkqTNtobQzFCH1Z0htjYHcfEBexM3vZVb7tfmuAaHkE0t7/9I+DknqTFso7QxFSP0ZUltjYJ4pIC/i5vcqlRorT1pf2tLev7SPQ5I60xZKO0MRUn+G1NYmI5gCQhI3v9fQUGPlSetLW9r7l/ZxSFJn2kJpZyhC6s+Q2tpstQZTtfrBAHQgprj5vYaH3UulaFBoqVTfoOck9aUt7f1L+zgkqTNtobQzFCH1Z0htbZAYgA4AABAfY6YAAABahGAKAAAgAYIpAACABAimAAAAEiCYQr4UIS9U2vt44YXRpHvTjwsvbG19oRzDtHP6AWhftX7m1+oHUyOg6XKeF8rd09/H5cur55Jbvrw19YVyDNPO6Qcgc2JqBBRCzvNCSUp/H5OkP4kjlGOYdk4/AJkjNx+KIed5oSSlv49pB1OhHMO0c/oByBzzTKEYipAXKu/7GMr+pZ3TD0BbI5hCfhQhL1Ta+7h8eWPlSYVyDNPO6QegrRFMIT8GB6WRkWj8iVn0PDISledF2vt46NCZgdPy5VF5K4RyDOO2M5T9A9AQxkwBAAAsgDFTAAAALUIwBQAAkADBFAAAQAIEUwAAAAkQTAEAACRAMAVkJe2Et3lPzBtKO4E8K+jnsCPrBgCFNDoqDQ1JU1PR8sREtCy1Zs6huPWl3c64QmknkGcF/hwyzxSQhbQT3uY9MW8o7QTyLOefQxIdA+0m7YS3eU/MG0o7gTzL+eeQSTuBdpN2wtu8J+YNpZ1AnhX4c0gwBWQh7YS3eU/MG0o7gTwr8OeQYArIQtoJb/OemDeUdgJ5VuDPIWOmAAAAFsCYKQAAgBYhmAIAAEiAYAoAACCBBYMpM3uPmX3LzP7RzA6Z2R1V1vmwmf3AzPaXH7/fmuYCAAC0l3ruTJ2Q9FvuvlzSpZI+Y2bLq6z3t+6+svzY3NRWInuh5JELSdq58orQp2nauFHq6Ih+tdTRES3nDecMUB93b+gh6b9Luqqi7MOSvt7I+6xatcoRiO3b3Ts73aO5baNHZ2dUnof6shB3H9PeDtUND8/ty+nH8HDWLWsezhlgDkljXiOmaWhqBDPrlfS/JK1w9x/OKv+wpD+XdFTSv0j6j+5+aL73YmqEgISSRy4kaefKK0KfpqmjQzp58szyUkk6cSL99rQC5wwwR1Ny85nZT0v6n5K2uPtfVLz2M5JOufubZnaNpPvc/X1V3mNI0pAkLV26dNVEtQ8q2k8oeeRCknauvCL0aZrMar+W0dx9Tcc5A8yReJ4pM1us6M7TaGUgJUnu/kN3f7P89zckLTazc6qsN+LuA+4+0NXV1dBOIEOh5JELSdq58orQp2kqlRorDxHnDFC3en7NZ5IelHTY3b9UY52fK68nM7uk/L6TzWwoMhRKHrmQpJ0rrwh9mqahocbKQ8Q5A9Sv1mCq6YekX5Dkkp6WtL/8uEbSr0v69fI6vyHpkKQDkv5O0uULvS8D0AOzfbt7T4+7WfTc6kGoadeXhbj7mPZ2qG542L1UigZml0r5Gnw+jXMGOE3NGoDeTAxABwAAoSA3HwAAQIsQTAEAACRAMAUAAJAAwRQAAEACBFMAAAAJEEyhPiQ8bb4iJMoFgALoyLoBCMDoaDQZ4dRUtDwxMTM54eBgdu0K2caN0rZtM8snT84sb92aTZsAALEwzxQWRsLT5itColwAyBHmmUIyR440Vo6FVQuk5isHALQtgiksjISnzVeERLkAUBAEU1gYCU+brwiJcgGgIAimsLDBQWlkJBojZRY9j4ww+DyJrVul4eGZO1GlUrTM4HMACA4D0AEAABbAAHQAAIAWIZgCAABIgGAKAAAgAYIpAACABAimmoTUdTXQMbXRN2Hj+AEoIzdfE5C6rgY6pjb6JmwcPwCzMDVCE5C6rgY6pjb6JmwcP6Bw5psagWCqCRYtkqp1o5l06lT67WkbdExt9E3YOH5A4TDPVIuRuq4GOqY2+iZsHD8AsxBMNQGp62qgY2qjb8LG8QMwC8FUE5C6rgY6pjb6JmwcPwCzMGYKAABgAYyZAgAAaBGCKQAAgAQIpgAAABIgmAIAAEiAYApAe9m4UeroiH4l19ERLbcSOfYAJERuPgDtY+NGadu2meWTJ2eWt25tfn3k2APQBEyNAKB9dHREAVSlUkk6caL59ZFjD0CdmBoBQBiqBVLzlSd15Ehj5QBQBcEUgPZRKjVWnhQ59gA0AcEUgPYxPV6p3vKkyLEHoAkIpgC0j61bpeHhmTtRpVK03IrB5xI59gA0BQPQAQAAFsAAdAAAgBYhmAIAAEiAYAoAACABgikAAIAECKYAAAASIJgCAABIgGAKAAAgAYIpAACABAimAAAAEiCYAgAASIBgCgAAIAGCKQAAgAQIpgAAABIgmAIAAEiAYAoAACABgikAAIAEFgymzOw9ZvYtM/tHMztkZndUWcfM7Mtm9oyZPW1mH2xNcwEAANpLPXemTkj6LXdfLulSSZ8xs+UV6/yypPeVH0OStjW1lQjX6KjU2ystWhQ9j45m3SIAAJpqwWDK3V929++W/35D0mFJ51Wstl7SIx75O0lnmdm5TW8twjI6Kg0NSRMTknv0PDREQAUAyJWGxkyZWa+kD0jaV/HSeZJenLV8VGcGXCiaTZukqam5ZVNTUTkAADlRdzBlZj8t6c8l/aa7/zBOZWY2ZGZjZjZ27NixOG+BkBw50lg5AAABqiuYMrPFigKpUXf/iyqrvCTpPbOWu8tlc7j7iLsPuPtAV1dXnPYiJEuXNlYOAECA6vk1n0l6UNJhd/9SjdV2S7ql/Ku+SyX9wN1fbmI7EaItW6TOzrllnZ1ROQAAOdFRxzprJN0s6R/MbH+57D9JWipJ7v4VSd+QdI2kZyRNSfq1prcU4RkcjJ43bYq+2lu6NAqkpssBAMgBc/dMKh4YGPCxsbFM6gYAAGiEmY27+0C115gBHQAAIAGCKQAAgAQIpgAAABIgmAIAAEiAYAoAACABgikAAIAECKYAAAASIJgCAABIgGAKAAAgAYIpAACABDJLJ2NmxyRNZFJ5a50j6dWsG9GG6Jfa6Jvq6Jfa6Jvq6Jfq6JfaGumbHnfvqvZCZsFUXpnZWK3cPUVGv9RG31RHv9RG31RHv1RHv9TWrL7haz4AAIAECKYAAAASIJhqvpGsG9Cm6Jfa6Jvq6Jfa6Jvq6Jfq6JfamtI3jJkCAABIgDtTAAAACRBMxWRmJTP7npl9vcprG8zsmJntLz8+nUUbs2BmL5jZP5T3e6zK62ZmXzazZ8zsaTP7YBbtTFsd/fJhM/vBrHPm97NoZxbM7Cwz22Vm/2Rmh83ssorXi3rOLNQvhTxnzOznZ+3zfjP7oZn9ZsU6hTtn6uyXQp4zkmRmnzWzQ2Z20Mz+zMyWVLz+NjPbUT5n9plZbyPv39HU1hbLHZIOS/qZGq/vcPffSLE97eQj7l5r3o5flvS+8mO1pG3l5yKYr18k6W/d/eOptaZ93Cfpr939BjP7N5I6K14v6jmzUL9IBTxn3P1/S1opRf+plfSSpL+sWK1w50yd/SIV8Jwxs/Mk3S5pubv/yMwelXSTpIdmrfYpSf/q7svM7CZJ90j6RL11cGcqBjPrlvQxSQ9k3ZYArZf0iEf+TtJZZnZu1o1CNszsnZKukPSgJLn7T9z99YrVCnfO1NkvkNZKetbdKyeALtw5U6FWvxRZh6S3m1mHov+Y/EvF6+slPVz+e5ektWZm9b45wVQ8fyTptyWdmmed68u3l3eZ2XvSaVZbcEl/Y2bjZjZU5fXzJL04a/louSzvFuoXSbrMzA6Y2f8wswvTbFyGzpd0TNJ/LX9t/oCZ/VTFOkU8Z+rpF6mY58xsN0n6syrlRTxnZqvVL1IBzxl3f0nSvZKOSHpZ0g/c/W8qVjt9zrj7CUk/kHR2vXUQTDXIzD4u6RV3H59ntb+S1OvufZK+qZlotwh+wd0/qOg2+2fM7IqsG9QmFuqX7ypKVdAv6b9Ieizl9mWlQ9IHJW1z9w9I+n+SfifbJrWFevqlqOeMJKn81ee1knZm3ZZ2skC/FPKcMbN3KbrzdL6kfyfpp8zsV5tZB8FU49ZIutbMXpD0NUlXmtn22Su4+6S7/7i8+ICkVek2MTvl/wHI3V9R9H39JRWrvCRp9p267nJZri3UL+7+Q3d/s/z3NyQtNrNzUm9o+o5KOuru+8rLuxQFEbMV8ZxZsF8KfM5M+2VJ33X3/1vltSKeM9Nq9kuBz5l1kp5392PuflzSX0i6vGKd0+dM+avAd0qarLcCgqkGufvvunu3u/cqupW6193nRLgV381fq2igeu6Z2U+Z2Tum/5Z0taSDFavtlnRL+dc2lyq63fpyyk1NVT39YmY/N/39vJldouizWfcHOVTu/n8kvWhmP18uWivpHytWK9w5U0+/FPWcmeXfq/ZXWYU7Z2ap2S8FPmeOSLrUzDrL+79WZ/67vFvSreW/b1D0b3vdE3Hya74mMbPNksbcfbek283sWkknJL0maUOWbUvRv5X0l+XPaoek/+buf21mvy5J7v4VSd+QdI2kZyRNSfq1jNqapnr65QZJw2Z2QtKPJN3UyAc5cP9B0mj564nnJP0a54ykhfulsOdM+T8lV0m6bVZZ4c+ZOvqlkOeMu+8zs12KvuY8Iel7kkYq/t1+UNKfmtkziv7dvqmROpgBHQAAIAG+5gMAAEiAYAoAACABgikAAIAECKYAAAASIJgCAABIgGAKAAAgAYIpAACABAimAAAAEvj/cIhBmjoGY4YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    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sation des données\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[y == 0][:, 0], X[y == 0][:, 1], color='b', label='classe 0')\n",
    "plt.scatter(X[y == 1][:, 0], X[y == 1][:, 1], color='r', label='classe 1')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-11 {color: black;background-color: white;}#sk-container-id-11 pre{padding: 0;}#sk-container-id-11 div.sk-toggleable {background-color: white;}#sk-container-id-11 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-11 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-11 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-11 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-11 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-11 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-11 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-11 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-11 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-11 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-11 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-11 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-11 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-11 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-11 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-11 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-11 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-11 div.sk-item {position: relative;z-index: 1;}#sk-container-id-11 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-11 div.sk-item::before, #sk-container-id-11 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-11 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-11 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-11 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-11 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-11 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-11 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-11 div.sk-label-container {text-align: center;}#sk-container-id-11 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-11 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-11\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(C=1e+20)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-11\" type=\"checkbox\" checked><label for=\"sk-estimator-id-11\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(C=1e+20)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(C=1e+20)"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#charger le modèle pour y binaire\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "  \n",
    "model = LogisticRegression(C=1e20) #  Régression logistique\n",
    "# Entrainement du modèle avec toutes les données \n",
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 0])"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xnew = np.array([\n",
    "    [5.5, 2.5],\n",
    "    [7, 3],\n",
    "    [3,2],\n",
    "    [5,3]\n",
    "])\n",
    "\n",
    "model.predict(Xnew)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Analyse des résultats : \n",
    "\n",
    "   * La première observation [5.5, 2.5] pour $y=1$\n",
    "   * La deuxième observation [7, 3] pour $y=1$\n",
    "   * La troisième observation [3,2] pour $y=0$\n",
    "   * La quatrième observation [5,3] pour $y=0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4,)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#vérification visuelle\n",
    "\n",
    "#visualisation des données\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[y == 0][:, 0], X[y == 0][:, 1], color='b', label='y= 0')\n",
    "plt.scatter(X[y == 1][:, 0], X[y == 1][:, 1], color='r', label='y= 1')\n",
    "\n",
    "s = np.random.rand(*Xnew[:, 0].shape) * 800 + 500\n",
    "print(s.shape)\n",
    "Color='kygm' #noir jaune vert magneta\n",
    "for i in range(Xnew.shape[0]):\n",
    "    plt.scatter(Xnew[i, 0], Xnew[i, 1],s[i], color=Color[i],marker=r'$\\clubsuit$',)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rappel de votre cours de BD\n",
    "## Pandas : un moyen efficace pour lire et manipuler des données"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.4.3'"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " # comme n'importe quelle librarire, il faut commencer par la charger à l'aide de la commande import\n",
    "import pandas\n",
    "# maintenat que c'est fait on peut utiliser son contenu\n",
    "# par exemple :vérifier la version installée sur votre machine \n",
    "pandas.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.4.3'"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# et si on lui donne un nom pour faciliter les appels\n",
    "import pandas as pd\n",
    "pd.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## L’objet DataFrame\n",
    "\n",
    "La DataFrame est un objet bi-dimentionnel avec des colonnes de types potentiellement différents. \n",
    "On peut voir la DataFrame comme une feuille Exce ou une table SQL."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "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>age</th>\n",
       "      <th>distance métro</th>\n",
       "      <th>magasins proches</th>\n",
       "      <th>prix au m2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>32.0</td>\n",
       "      <td>84.87882</td>\n",
       "      <td>10</td>\n",
       "      <td>37.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>19.5</td>\n",
       "      <td>306.59470</td>\n",
       "      <td>9</td>\n",
       "      <td>42.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.3</td>\n",
       "      <td>561.98450</td>\n",
       "      <td>5</td>\n",
       "      <td>47.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.3</td>\n",
       "      <td>561.98450</td>\n",
       "      <td>5</td>\n",
       "      <td>54.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>390.56840</td>\n",
       "      <td>5</td>\n",
       "      <td>43.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    age  distance métro  magasins proches  prix au m2\n",
       "0  32.0        84.87882                10        37.9\n",
       "1  19.5       306.59470                 9        42.2\n",
       "2  13.3       561.98450                 5        47.3\n",
       "3  13.3       561.98450                 5        54.8\n",
       "4   5.0       390.56840                 5        43.1"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lecture d'un fichier de données et le récupérer sous forme de dataframe sous le nom df \n",
    "df = pd.read_csv(\"Prix_Appartements.csv\") # à partir d'un csv \n",
    "df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "la taille : (414, 4)\n",
      "Avec : 414  lignes\n",
      "Avec : 4  colonnes\n"
     ]
    }
   ],
   "source": [
    " ## On peut afficher les dimensions (nombre de lignes et de colonnes) ## avec l'attibut shape (comme avec numpy)\n",
    "print('la taille :',df.shape) ## (nb lignes, nb colonnes) print('*'*40)\n",
    "print('Avec :',df.shape[0],' lignes') ## (nb lignes, nb colonnes) print('*'*40)\n",
    "print('Avec :',df.shape[1],' colonnes') ## (nb lignes, nb colonnes) print('*'*40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "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>age</th>\n",
       "      <th>distance métro</th>\n",
       "      <th>magasins proches</th>\n",
       "      <th>prix au m2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>32.0</td>\n",
       "      <td>84.87882</td>\n",
       "      <td>10</td>\n",
       "      <td>37.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>19.5</td>\n",
       "      <td>306.59470</td>\n",
       "      <td>9</td>\n",
       "      <td>42.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.3</td>\n",
       "      <td>561.98450</td>\n",
       "      <td>5</td>\n",
       "      <td>47.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.3</td>\n",
       "      <td>561.98450</td>\n",
       "      <td>5</td>\n",
       "      <td>54.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>390.56840</td>\n",
       "      <td>5</td>\n",
       "      <td>43.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7.1</td>\n",
       "      <td>2175.03000</td>\n",
       "      <td>3</td>\n",
       "      <td>32.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    age  distance métro  magasins proches  prix au m2\n",
       "0  32.0        84.87882                10        37.9\n",
       "1  19.5       306.59470                 9        42.2\n",
       "2  13.3       561.98450                 5        47.3\n",
       "3  13.3       561.98450                 5        54.8\n",
       "4   5.0       390.56840                 5        43.1\n",
       "5   7.1      2175.03000                 3        32.1"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " ## La commande df.head(n) permet d'afficher uniquement les n premiers éléments # car la taille de la dataframe est grande avec 4622 lignes\n",
    "df.head(6) # les 6 premières lignes de 0 à 5 = 6-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "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>age</th>\n",
       "      <th>distance métro</th>\n",
       "      <th>magasins proches</th>\n",
       "      <th>prix au m2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>411</th>\n",
       "      <td>18.8</td>\n",
       "      <td>390.96960</td>\n",
       "      <td>7</td>\n",
       "      <td>40.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>412</th>\n",
       "      <td>8.1</td>\n",
       "      <td>104.81010</td>\n",
       "      <td>5</td>\n",
       "      <td>52.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>413</th>\n",
       "      <td>6.5</td>\n",
       "      <td>90.45606</td>\n",
       "      <td>9</td>\n",
       "      <td>63.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      age  distance métro  magasins proches  prix au m2\n",
       "411  18.8       390.96960                 7        40.6\n",
       "412   8.1       104.81010                 5        52.5\n",
       "413   6.5        90.45606                 9        63.9"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## De même df.tail(n) affiche les n=3 derniers éléments\n",
    "df.tail(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "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>age</th>\n",
       "      <th>distance métro</th>\n",
       "      <th>magasins proches</th>\n",
       "      <th>prix au m2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>414.000000</td>\n",
       "      <td>414.000000</td>\n",
       "      <td>414.000000</td>\n",
       "      <td>414.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>17.712560</td>\n",
       "      <td>1083.885689</td>\n",
       "      <td>4.094203</td>\n",
       "      <td>37.980193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>11.392485</td>\n",
       "      <td>1262.109595</td>\n",
       "      <td>2.945562</td>\n",
       "      <td>13.606488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>23.382840</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>9.025000</td>\n",
       "      <td>289.324800</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>27.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>16.100000</td>\n",
       "      <td>492.231300</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>38.450000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>28.150000</td>\n",
       "      <td>1454.279000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>46.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>43.800000</td>\n",
       "      <td>6488.021000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>117.500000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              age  distance métro  magasins proches  prix au m2\n",
       "count  414.000000      414.000000        414.000000  414.000000\n",
       "mean    17.712560     1083.885689          4.094203   37.980193\n",
       "std     11.392485     1262.109595          2.945562   13.606488\n",
       "min      0.000000       23.382840          0.000000    7.600000\n",
       "25%      9.025000      289.324800          1.000000   27.700000\n",
       "50%     16.100000      492.231300          4.000000   38.450000\n",
       "75%     28.150000     1454.279000          6.000000   46.600000\n",
       "max     43.800000     6488.021000         10.000000  117.500000"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# La commande describe() est très utile. Elle permet d'obtenir, en une seule commande,\n",
    "# des statistiques des colonnes (UNIQUEMENT pour les colonnes de type numérique)\n",
    "\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice  : Use case\n",
    "\n",
    "## dataset dans le fichier Prix_Appartements.csv\n",
    "\n",
    "\n",
    "1- Avec la commande pd.read_csv ouvrir le fichier csv dans une dataframe  df_1.\n",
    "\n",
    "2- Afficher les 7 premières lignes. \n",
    "\n",
    "3- Afficher les noms des colonnes. \n",
    "\n",
    "4- Créer une nouvelle colonne dans la dataframe ne contenant que l'âge et le prix.\n",
    "\n",
    "5- Affichier les lignes d'index impair.\n",
    "\n",
    "6- En utilisant la colonne prix, calculer le prix moyen $p_m$, la médiane $k_m$ et l'écart-type $\\sigma_m$. \n",
    "\n",
    "7- Afficher les lignes dont le prix est supérieur au prix moyen $p_m$.\n",
    "\n",
    "8- Choisir deux colonnes qui représentront les variables $X$ et $Y$. Par exemple la distance au métro le plus proche et le prix au mètre carré. Pouvez les récupérer dans deux tableaux numpy.  \n",
    "\n",
    "9- Appliquer une régression linéaire pour vérifier la corrélation entre $X$ et $Y$ à l'aide des graphiques comme dans l'exircice du TD2.\n",
    "\n",
    "10- Quelle variable (colonne) est la plus corrélée avec le prix ? \n",
    "\n",
    "11- Pour éviter à ce que les grandes valeurs dominent les petites, on peut normaliser en divisant chaque colonne par le maximum en valeur absolue. Reprendre la question 10 avec des valeurs normalisées. \n",
    "\n",
    "11- Vérifier la corrélation entre le prix et deux voire plusieurs colonnes. Conclure. "
   ]
  }
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