{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TP4 - Outils numériques pour les Statistiques Descriptives \n",
    "\n",
    "Les commandes suivantes, écrites en Python, s'exécutent directement dans ce notebook Jupyter avec la commande `Ctrl+Entrée`, ou `Shift+Entrée` pour passer directement à la cellule suivante."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Préparatifs : \n",
    "Le but de ce TP est de comprendre le concept de régression linéaire et de le mettre en œuvre sur des données. Les calculs et les graphiques seront réalisés sur une feuille de papier **et** avec Python. Avant de démarrer, assurez-vous d'avoir :\n",
    "- le cours sur la régression linéaire (cf amphi du 13 avril) en version papier ou pdf, \n",
    "- de quoi écrire (papier + stylo), \n",
    "- le fichier de données `footprint.xlsx` (dans votre répertoire de travail)\n",
    "\n",
    "Vous êtes prêt·e ? Allez-y!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# On importe les bibliothèques qui nous seront utiles.\n",
    "from pandas import *  # Pour lire, importer et manipuler des données sous forme\n",
    "# de tableur\n",
    "from numpy import *  # Pour faire des calculs\n",
    "from matplotlib.pylab import * # Pour faire des graphiques"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1.** A faire sur une feuille.\n",
    "\n",
    "On considère un échantillon de taille $n = 4$ de deux variables quantitatives $X$ et $Y$ données par $((0,0);(0,1); (1,0);(1,1))$.\n",
    "\n",
    "Sur votre feuille : \n",
    "- représentez le nuage de points associé à ces données,\n",
    "- calculez et représentez le centre de gravité du nuage, c'est-à-dire le point de coordonnées $(\\overline{X},\\overline{Y})$,\n",
    "- calculez les coefficients $a$ et $b$ de la droite de régression de $Y$ en fonction de $X$,\n",
    "- représentez cette droite, d'équation $y = ax + b$, sur le graphique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2.** On va reprendre le même exercice en python. Suivez les consignes dans les blocs qui suivent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "[[0 0]\n",
      " [0 1]\n",
      " [1 0]\n",
      " [1 1]]\n"
     ]
    }
   ],
   "source": [
    "# Saisir les données dans un array nommé data\n",
    "data = array([\n",
    "    [0, 0],\n",
    "    [0, 1],\n",
    "    [1, 0],\n",
    "    [1, 1]\n",
    "])\n",
    "print(type(data))\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Définir les variables X et Y à partir de data\n",
    "X = data[:,0] # colonne d'indice 0\n",
    "Y = data[:,1] # colonne d'indice 1\n",
    "# Représenter le nuage de points associé aux données (utiliser l'instruction\n",
    "# scatter) et ajouter sur le graphique le centre de gravité du nuage (toujours\n",
    "# avec l'instruction scatter)\n",
    "mX = mean(X)\n",
    "mY = mean(Y)\n",
    "scatter(X, Y)\n",
    "scatter([mX], [mY], color='red')\n",
    "title('Nuage de points et centre de gravité en rouge')\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La covariance de X et Y est égale à : 0.0\n",
      "Le coefficient de corrélation entre X et Y est égal à :\n",
      "0.0\n",
      "[[0.33333333 0.        ]\n",
      " [0.         0.33333333]]\n",
      "La droite de régression de Y en fonction de X a pour équation :\n",
      "y = 0.0 x + 0.5\n"
     ]
    }
   ],
   "source": [
    "# Calculer la covariance de X et Y en se rappelant qu'elle est donnée par \n",
    "# \"la moyenne des produits moins le produit des moyennes\"\n",
    "CXY = mean(X * Y) - (mX * mY)\n",
    "print(\"La covariance de X et Y est égale à :\", CXY)\n",
    "print(\"Le coefficient de corrélation entre X et Y est égal à :\")\n",
    "print(CXY / (std(X) * std(Y)))\n",
    "# Tester la fonction cov prédéfinie dans numpy, juste pour voir, on ne\n",
    "# l'utilisera pas ensuite\n",
    "print(cov(X, Y))\n",
    "# Calculer les coefficients a et b de la droite de régression de Y en fonction\n",
    "# de X (équation y = ax + b)\n",
    "a = CXY / std(X) ** 2\n",
    "b = mY - a*mX\n",
    "print(\"La droite de régression de Y en fonction de X a pour équation :\")\n",
    "print(\"y =\", a, \"x +\", b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# reprendre le graphique et y ajouter la droite de régression de Y en fonction de X en noir\n",
    "scatter(X, Y)\n",
    "scatter([mX], [mY], color='red')\n",
    "plot(X, a*X + b, color='black')\n",
    "title('Nuage de points, centre de gravité en rouge et droite de régression en noir')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3.** Effectuer les mêmes calculs et construire le même graphique avec les données \n",
    " suivantes issues d'un échantillon de taille 5: {(0,0);(0,0);(0,1);(1,0);(1,1)}. Commenter le graphique obtenu."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Les données sont déjà saisies ci-dessous\n",
    "data  =array([\n",
    "    [0, 0],\n",
    "    [0, 0],\n",
    "    [0, 1],\n",
    "    [1, 0],\n",
    "    [1, 1]\n",
    "])\n",
    "# A vous !\n",
    "X = data[:,0]\n",
    "Y = data[:,1]\n",
    "mX = mean(X)\n",
    "mY = mean(Y)\n",
    "CXY = mean(X * Y) - (mX * mY)\n",
    "a = CXY / std(X)**2\n",
    "b = mY - a*mX\n",
    "scatter(X, Y)\n",
    "scatter([mX], [mY], color='red')\n",
    "plot(X, a*X + b, color='black')\n",
    "show()\n",
    "# Commentaire :\n",
    "# Le point (0, 0) supplémentaire 'tire' vers lui le centre de gravité et la droite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 2\n",
    "On va maintenant travailler avec les données Footprint. Le premier bloc ci-dessous contient les instructions pour importer les données et changer le nom des colonnes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  PAYS        SDG    LIFE    HDI      GDP  \\\n",
      "0          Afghanistan  51.847886  63.565  0.488  2439.68   \n",
      "1              Albania  71.486061  79.282   0.81  13862.6   \n",
      "2              Algeria  70.510917  76.474  0.748  11412.2   \n",
      "3               Angola  50.974803  62.448  0.595  7034.84   \n",
      "4  Antigua and Barbuda        NaN  78.691    0.8  22000.2   \n",
      "\n",
      "                         REG  IC     POP      PROD     CONSU      BCAP  \\\n",
      "0   Middle East/Central Asia  LI  38.042  0.750444  0.885011  0.578479   \n",
      "1               Other Europe  UM   2.881  1.566569  2.102276  1.124433   \n",
      "2                     Africa  UM  43.053  1.812774  2.367408  0.702314   \n",
      "3                     Africa  LM  31.825  0.686062  1.006983  1.738573   \n",
      "4  Central America/Caribbean  HI   0.097  1.541982  3.919553  0.931722   \n",
      "\n",
      "        ECO    NEARTH    NCOUNT  \n",
      "0 -0.306532  0.570763  1.529894  \n",
      "1 -0.977842  1.355804  1.869631  \n",
      "2 -1.665094  1.526794  3.370868  \n",
      "3  0.731590  0.649426  0.579201  \n",
      "4 -2.987832  2.527807  4.206785  \n"
     ]
    }
   ],
   "source": [
    "# Exécuter et observer !\n",
    "# Importation des données dans un dataframe\n",
    "df = read_excel('footprint.xlsx')\n",
    "# On renomme les colonnes. \n",
    "colonnes = [\n",
    "    \"PAYS\", \"SDG\", \"LIFE\", \"HDI\", \"GDP\", \"REG\", \"IC\", \"POP\",\n",
    "    \"PROD\", \"CONSU\", \"BCAP\", \"ECO\", \"NEARTH\", \"NCOUNT\"\n",
    "]\n",
    "df.columns = colonnes\n",
    "# Affichage de l'en-tête pour voir\n",
    "print(df.head()) \n",
    "# Noms des pays stockés dans \"pays\"\n",
    "pays = df.PAYS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1.**- On va étudier conjoitement les variables NEARTH et CONSU. En interprétant les informations contenues dans ces variables, stocker dans un dataframe (ou un array, au choix) nommé X la variable explicative et dans Y la variable expliquée."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# On choisit X = CONSU et Y = NEARTH car il est raisonnable (rationnel)\n",
    "# d'expliquer les ressources nécessaires à un pays, exprimées en \"nombre de\n",
    "# terres\", en fonction de sa consommation, et pas le contraire !\n",
    "X = df.CONSU\n",
    "Y = df.NEARTH"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2.** Écrire les instructions nécessaires pour effectuer les tâches demandées dans le bloc ci-dessous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corrélation entre X et Y : 1.0\n",
      "Équation de la droite de régression : y = 0.64 x + 0\n"
     ]
    }
   ],
   "source": [
    "# Calculer la moyenne de X et la moyenne de Y, la covariance de X et Y \n",
    "mX = mean(X)\n",
    "mY = mean(Y)\n",
    "CXY = mean(X * Y) - (mX * mY)\n",
    "# Calculer les coefficients a et b de la droite de régression de Y en fonction\n",
    "# de X (équation y=ax+b)\n",
    "a = CXY / std(X)**2\n",
    "b = mY - a*mX\n",
    "# Tracer sur un graphique le nuage de points, le centre de gravité et la droite\n",
    "# de régression de Y en fonction de X. \n",
    "scatter(X, Y)\n",
    "scatter([mX], [mY], color='red')\n",
    "plot(X, a*X + b, color='black')\n",
    "show()\n",
    "# Afficher la valeur du coefficient de corrélation et l'équation de la droite\n",
    "# de régression.\n",
    "print(\"Corrélation entre X et Y :\", round(CXY / (std(X) * std(Y)), 2))\n",
    "print(\"Équation de la droite de régression : y =\", round(a, 2), \"x +\", round(b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3.** Commenter le graphique obtenu ! Quels sont les pays représentés par les deux points les plus extrêmes? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Les points sont parfaitement alignés, ce qui est cohérent avec la valeur 1 du coefficient de corrélation.\n",
      "98 130\n",
      "Les deux points extrêmes correspondent aux deux pays qui consomment le plus : Luxembourg et Qatar\n"
     ]
    }
   ],
   "source": [
    "# Commentaire\n",
    "print(\"Les points sont parfaitement alignés, ce qui est cohérent avec la valeur 1 du coefficient de corrélation.\")\n",
    "# Commentaire supplémentaire (Anne) : on peut aller étudier de plus près le\n",
    "# fichier footprint et le site  https://data.footprintnetwork.org/#/ pour\n",
    "# comprendre comment est calculé NEARTH \n",
    "\n",
    "# Les deux pays extrêmes (en haut à droite sur la droite) ?\n",
    "ind = argsort(df[\"CONSU\"]) # On trie CONSU par ordre croissant et on enregistre\n",
    "# les indices des pays ainsi triés.\n",
    "print(ind[180], ind[179]) # Les indices des deux pays qui consomment le plus\n",
    "print(\n",
    "    \"Les deux points extrêmes correspondent aux deux pays qui consomment le plus :\",\n",
    "    pays[ind[180]],\"et\", pays[ind[179]]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 4.** Reprendre avec variables BCAP et ECO."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corrélation entre X et Y:  0.98\n",
      "Équation de la droite de régression : y = 0.97 x + 3\n",
      "Les points extrêmes correspondent aux pays qui ont la plus grande biocapacité:\n",
      " French Guiana , Suriname et Guyana\n"
     ]
    }
   ],
   "source": [
    "X = df.ECO\n",
    "Y = df.BCAP\n",
    "# Calculer la moyenne de X et la moyenne de Y, la covariance de X et Y \n",
    "mX = mean(X)\n",
    "mY = mean(Y)\n",
    "CXY = mean(X * Y) - (mX * mY)\n",
    "# Calculer les coefficients a et b de la droite de régression de Y en fonction de X (équation y=ax+b)\n",
    "a = CXY / std(X)**2\n",
    "b= mY - a*mX\n",
    "# Tracer sur un graphique le nuage de points, le centre de gravité  et la\n",
    "# droite de régression de Y en fonction de X. \n",
    "scatter(X, Y)\n",
    "scatter([mX], [mY], color='red')\n",
    "plot(X, a*X + b, color='black')\n",
    "show()\n",
    "# Afficher la valeur du coefficient de corrélation et l'équation de la droite\n",
    "# de régression.\n",
    "print(\"Corrélation entre X et Y: \", round(CXY / (std(X) * std(Y)), 2))\n",
    "print(\"Équation de la droite de régression : y =\", round(a, 2), \"x +\", round(b))\n",
    "# Trois pays extrêmes (en haut à droite) ?\n",
    "ind = argsort(df[\"BCAP\"]) # On trie BCAP par ordre croissant et on enregistre\n",
    "# les indices des pays ainsi triés\n",
    "print(\n",
    "    \"Les points extrêmes correspondent aux pays qui ont la plus grande biocapacité:\\n\", \n",
    "    pays[ind[180]], \",\", pays[ind[179]], \"et\", pays[ind[178]]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 5.** Reprendre avec le couple de variables de votre choix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "iut",
   "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": "3.14.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}