P7_code_M3M4_Xuefei_NEW_14mars2022.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f651142f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np \n",
    "import seaborn as sns \n",
    "import matplotlib.pyplot as plt "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d75b2452",
   "metadata": {},
   "source": [
    "Maintenant qu'on a à disposition pour chaque pays, data sur le **revenu** et **indice de Gini** (2 variables explicatives) , pour il nous manque la **classe de revenu des parents** (3ème variable explicative). Pour avoir la classe de revenu des parents, il faut le **coefficient d'élasticité** de chaque pays \n",
    "\n",
    "*pj: coeff d'élasticité (propre à chaque pays) qui mesure la corrélation entre revenu d'enfant & revenu des parents - mobilité intergénérationnelle**\n",
    "\n",
    "Ainsi l'enjeu de cette mission consiste à sortir la distribution de probabilité la classe revenu des parents (**c_i_parent**) basé sur classe de revenu des enfants (**c_i_child**) et coeff d'élasticité (**pj**) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da5a21a9",
   "metadata": {},
   "source": [
    "### Ci-après les fonctions pour la Mission 3: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a5f55f7f",
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.135 0.103 0.115 0.09  0.095 0.1   0.093 0.11  0.083 0.076]\n",
      " [0.119 0.11  0.116 0.107 0.083 0.088 0.096 0.089 0.101 0.091]\n",
      " [0.113 0.116 0.101 0.102 0.11  0.112 0.096 0.086 0.086 0.078]\n",
      " [0.1   0.107 0.108 0.117 0.095 0.094 0.12  0.095 0.08  0.084]\n",
      " [0.094 0.109 0.112 0.106 0.109 0.091 0.094 0.094 0.085 0.106]\n",
      " [0.093 0.106 0.101 0.1   0.125 0.109 0.091 0.092 0.095 0.088]\n",
      " [0.088 0.093 0.096 0.111 0.109 0.101 0.092 0.102 0.107 0.101]\n",
      " [0.093 0.095 0.083 0.092 0.092 0.1   0.112 0.113 0.121 0.099]\n",
      " [0.086 0.085 0.077 0.088 0.088 0.102 0.105 0.118 0.124 0.127]\n",
      " [0.079 0.076 0.091 0.087 0.094 0.103 0.101 0.101 0.118 0.15 ]]\n",
      "\n",
      "P(c_i_parent = 8 | c_i_child = 5, pj = 0.1) = 0.095\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as st\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from collections import Counter\n",
    "\n",
    "def generate_incomes(n, pj):\n",
    "    # On génère les revenus des parents (exprimés en logs) selon une loi normale.\n",
    "    # La moyenne et variance n'ont aucune incidence sur le résultat final (ie. sur le caclul de la classe de revenu)\n",
    "    ln_y_parent = st.norm(0,1).rvs(size=n)\n",
    "    # Génération d'une réalisation du terme d'erreur epsilon\n",
    "    residues = st.norm(0,1).rvs(size=n)\n",
    "    return np.exp(pj*ln_y_parent + residues), np.exp(ln_y_parent)\n",
    "    \n",
    "def quantiles(l, nb_quantiles):\n",
    "    size = len(l)\n",
    "    l_sorted = l.copy()\n",
    "    l_sorted = l_sorted.sort_values()\n",
    "    quantiles = np.round(np.arange(1, nb_quantiles+1, nb_quantiles/size) -0.5 +1./size)\n",
    "    q_dict = {a:int(b) for a,b in zip(l_sorted,quantiles)}\n",
    "    return pd.Series([q_dict[e] for e in l])\n",
    "\n",
    "def compute_quantiles(y_child, y_parents, nb_quantiles):\n",
    "    y_child = pd.Series(y_child)\n",
    "    y_parents = pd.Series(y_parents)\n",
    "    c_i_child = quantiles(y_child, nb_quantiles)\n",
    "    c_i_parent = quantiles(y_parents, nb_quantiles)\n",
    "    sample = pd.concat([y_child, y_parents, c_i_child, c_i_parent], axis=1)\n",
    "    sample.columns = [\"y_child\", \"y_parents\", \"c_i_child\",\"c_i_parent\"]\n",
    "    return sample\n",
    "\n",
    "def distribution(counts, nb_quantiles):\n",
    "    distrib = []\n",
    "    total = counts[\"counts\"].sum()\n",
    "    \n",
    "    if total == 0 :\n",
    "        return [0] * nb_quantiles\n",
    "    \n",
    "    for q_p in range(1, nb_quantiles+1):\n",
    "        subset = counts[counts.c_i_parent == q_p]\n",
    "        if len(subset):\n",
    "            nb = subset[\"counts\"].values[0]\n",
    "            distrib += [nb / total]\n",
    "        else:\n",
    "            distrib += [0]\n",
    "    return distrib   \n",
    "\n",
    "def conditional_distributions(sample, nb_quantiles):\n",
    "    counts = sample.groupby([\"c_i_child\",\"c_i_parent\"]).apply(len)\n",
    "    counts = counts.reset_index()\n",
    "    counts.columns = [\"c_i_child\",\"c_i_parent\",\"counts\"]\n",
    "    \n",
    "    mat = []\n",
    "    for child_quantile in np.arange(nb_quantiles)+1:\n",
    "        subset = counts[counts.c_i_child == child_quantile]\n",
    "        mat += [distribution(subset, nb_quantiles)]\n",
    "    return np.array(mat) \n",
    "\n",
    "def plot_conditional_distributions(p, cd, nb_quantiles):\n",
    "    plt.figure()\n",
    "    \n",
    "    # La ligne suivante sert à afficher un graphique en \"stack bars\", sur ce modèle : https://matplotlib.org/gallery/lines_bars_and_markers/bar_stacked.html\n",
    "    cumul = np.array([0] * nb_quantiles)\n",
    "    \n",
    "    for i, child_quantile in enumerate(cd):\n",
    "        plt.bar(np.arange(nb_quantiles)+1, child_quantile, bottom=cumul, width=0.95, label = str(i+1) +\"e\")\n",
    "        cumul = cumul + np.array(child_quantile)\n",
    "\n",
    "    plt.axis([.5, nb_quantiles*1.3 ,0 ,1])\n",
    "    plt.title(\"p=\" + str(p))\n",
    "    plt.legend(fontsize= 9)\n",
    "    plt.xlabel(\"quantile parents\")\n",
    "    plt.ylabel(\"probabilité du quantile enfant\")\n",
    "    plt.show()\n",
    "    \n",
    "def proba_cond(c_i_parent, c_i_child, mat):\n",
    "    return mat[c_i_child, c_i_parent]\n",
    "\n",
    "pj = 0.1                             # coefficient d'élasticité du pays j\n",
    "nb_quantiles = 10           # nombre de quantiles (nombre de classes de revenu)\n",
    "n = 1000*nb_quantiles    # taille de l'échantillon\n",
    "\n",
    "y_child, y_parents = generate_incomes(n, pj)\n",
    "sample = compute_quantiles(y_child, y_parents, nb_quantiles)\n",
    "cd = conditional_distributions(sample, nb_quantiles)\n",
    "plot_conditional_distributions(pj, cd, nb_quantiles)              # Cette instruction prendra du temps si nb_quantiles > 10\n",
    "print(cd)\n",
    "\n",
    "c_i_child = 5\n",
    "c_i_parent = 8\n",
    "p = proba_cond(c_i_parent, c_i_child, cd)\n",
    "print(\"\\nP(c_i_parent = {} | c_i_child = {}, pj = {}) = {}\".format(c_i_parent, c_i_child,\n",
    "pj, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6994a17f",
   "metadata": {},
   "source": [
    "#### ici on suppose qu'on est dans le scenario à forte mobilité intergénérationnelle: pj=0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f86f0da6",
   "metadata": {},
   "source": [
    "#####  fonction *generate_incomes(n, pj)* arrive à répondre Q1 - Q3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "43772c2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0      -0.536694\n",
      "1      -0.164913\n",
      "2      -0.080303\n",
      "3       1.925688\n",
      "4       1.068600\n",
      "          ...   \n",
      "9995    1.238882\n",
      "9996   -0.904314\n",
      "9997   -1.335628\n",
      "9998   -0.021398\n",
      "9999    0.482564\n",
      "Length: 10000, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Q1. générer In_y_parent selon une loi normale.\n",
    "ln_y_parent = st.norm(0,1).rvs(size=n)  \n",
    "print(pd.Series(ln_y_parent))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a4b1761f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0      -0.622980\n",
      "1       0.541549\n",
      "2       0.066073\n",
      "3      -0.564668\n",
      "4       0.092650\n",
      "          ...   \n",
      "9995    1.400556\n",
      "9996    1.099306\n",
      "9997   -1.143759\n",
      "9998    0.053301\n",
      "9999    0.032380\n",
      "Length: 10000, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Q2. Générez réalisations du terme d'erreur selon une loi normale de moyenne 0 et d'écart-type 1\n",
    "residues = st.norm(0,1).rvs(size=n)\n",
    "print(pd.Series(residues))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "634eca28",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             0          1\n",
      "0     0.805640   1.493275\n",
      "1     1.170085   0.687710\n",
      "2     4.050742   1.289770\n",
      "3     1.131370   4.789738\n",
      "4     0.423556   5.114876\n",
      "...        ...        ...\n",
      "9995  3.033156   2.103701\n",
      "9996  0.498743  14.165651\n",
      "9997  2.497963   1.323000\n",
      "9998  4.014800   3.101153\n",
      "9999  4.412637   1.440211\n",
      "\n",
      "[10000 rows x 2 columns]\n",
      "                  0             1\n",
      "count  10000.000000  10000.000000\n",
      "mean       1.651012      1.648078\n",
      "std        1.981445      2.168341\n",
      "min        0.024423      0.024169\n",
      "25%        0.515035      0.518618\n",
      "50%        1.008804      1.002586\n",
      "75%        2.002001      1.934808\n",
      "max       28.116622     61.852199\n"
     ]
    },
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y_child</th>\n",
       "      <th>y_parents</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.805640</td>\n",
       "      <td>1.493275</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.170085</td>\n",
       "      <td>0.687710</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.050742</td>\n",
       "      <td>1.289770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.131370</td>\n",
       "      <td>4.789738</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.423556</td>\n",
       "      <td>5.114876</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    y_child  y_parents\n",
       "0  0.805640   1.493275\n",
       "1  1.170085   0.687710\n",
       "2  4.050742   1.289770\n",
       "3  1.131370   4.789738\n",
       "4  0.423556   5.114876"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Q1-3: générer les 10000 individus (pj = 0.1)\n",
    "\n",
    "Income= pd.DataFrame(generate_incomes(n, pj)).transpose()\n",
    "print(Income)\n",
    "print(Income.describe())\n",
    "\n",
    "Income= Income.rename(columns= {0: 'y_child', 1:'y_parents'})\n",
    "Income.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92b473aa",
   "metadata": {},
   "source": [
    "\n",
    "#### Q4.Pour chacun des individus générés, calculez la classe de revenu child (c_i_child) et celui de ses parents (c_i_parent) à partir de revenus child (y_child) et parents (y_parent) \n",
    "\n",
    "In_y_parent = (In_y_child - Epsilon)/pj \n",
    "y_parent = e (In_y_parent) = np.exp(In_y_parent)\n",
    "\n",
    "**fonctions: quantiles et compute_quantiles**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bd71f20d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y_child</th>\n",
       "      <th>y_parents</th>\n",
       "      <th>c_i_child</th>\n",
       "      <th>c_i_parent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.805640</td>\n",
       "      <td>1.493275</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.170085</td>\n",
       "      <td>0.687710</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.050742</td>\n",
       "      <td>1.289770</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.131370</td>\n",
       "      <td>4.789738</td>\n",
       "      <td>6</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.423556</td>\n",
       "      <td>5.114876</td>\n",
       "      <td>2</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>3.033156</td>\n",
       "      <td>2.103701</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>0.498743</td>\n",
       "      <td>14.165651</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>2.497963</td>\n",
       "      <td>1.323000</td>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>4.014800</td>\n",
       "      <td>3.101153</td>\n",
       "      <td>10</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>4.412637</td>\n",
       "      <td>1.440211</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10000 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       y_child  y_parents  c_i_child  c_i_parent\n",
       "0     0.805640   1.493275          5           7\n",
       "1     1.170085   0.687710          6           4\n",
       "2     4.050742   1.289770         10           7\n",
       "3     1.131370   4.789738          6          10\n",
       "4     0.423556   5.114876          2          10\n",
       "...        ...        ...        ...         ...\n",
       "9995  3.033156   2.103701          9           8\n",
       "9996  0.498743  14.165651          3          10\n",
       "9997  2.497963   1.323000          9           7\n",
       "9998  4.014800   3.101153         10           9\n",
       "9999  4.412637   1.440211         10           7\n",
       "\n",
       "[10000 rows x 4 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Q4 : calculation de classes revenu (\"c_i_child\",\"c_i_parent\") à partir de revenu (y_child et y_parents) \n",
    "\n",
    "nb_quantiles= 10\n",
    "n=nb_quantiles*1000\n",
    "\n",
    "# function Q4: income to class income\n",
    "\n",
    "def quantiles(l, nb_quantiles):\n",
    "    size = len(l)\n",
    "    l_sorted = l.copy()\n",
    "    l_sorted = l_sorted.sort_values()\n",
    "    quantiles = np.round(np.arange(1, nb_quantiles+1, nb_quantiles/size) -0.5 +1./size)\n",
    "    q_dict = {a:int(b) for a,b in zip(l_sorted,quantiles)}\n",
    "    return pd.Series([q_dict[e] for e in l])\n",
    "\n",
    "def compute_quantiles(y_child, y_parents, nb_quantiles):\n",
    "    y_child = pd.Series(Income['y_child'])\n",
    "    y_parents = pd.Series(Income['y_parents'])\n",
    "    c_i_child = quantiles(y_child, nb_quantiles)\n",
    "    c_i_parent = quantiles(y_parents, nb_quantiles)\n",
    "    sample = pd.concat([y_child, y_parents, c_i_child, c_i_parent], axis=1)\n",
    "    sample.columns = [\"y_child\", \"y_parents\", \"c_i_child\",\"c_i_parent\"]\n",
    "    return sample\n",
    "\n",
    "compute_quantiles(y_child, y_parents, nb_quantiles)\n",
    "\n",
    "# (proba conditionnelle n'est pas encore appliquée)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "321ccf69",
   "metadata": {},
   "source": [
    "#### Q5: estimez pour chaque c_i_child la distribution conditionnelle de c_i_parent\n",
    "\n",
    "#### fonction conditional_distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ab93561b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.135, 0.103, 0.115, 0.09 , 0.095, 0.1  , 0.093, 0.11 , 0.083,\n",
       "        0.076],\n",
       "       [0.119, 0.11 , 0.116, 0.107, 0.083, 0.088, 0.096, 0.089, 0.101,\n",
       "        0.091],\n",
       "       [0.113, 0.116, 0.101, 0.102, 0.11 , 0.112, 0.096, 0.086, 0.086,\n",
       "        0.078],\n",
       "       [0.1  , 0.107, 0.108, 0.117, 0.095, 0.094, 0.12 , 0.095, 0.08 ,\n",
       "        0.084],\n",
       "       [0.094, 0.109, 0.112, 0.106, 0.109, 0.091, 0.094, 0.094, 0.085,\n",
       "        0.106],\n",
       "       [0.093, 0.106, 0.101, 0.1  , 0.125, 0.109, 0.091, 0.092, 0.095,\n",
       "        0.088],\n",
       "       [0.088, 0.093, 0.096, 0.111, 0.109, 0.101, 0.092, 0.102, 0.107,\n",
       "        0.101],\n",
       "       [0.093, 0.095, 0.083, 0.092, 0.092, 0.1  , 0.112, 0.113, 0.121,\n",
       "        0.099],\n",
       "       [0.086, 0.085, 0.077, 0.088, 0.088, 0.102, 0.105, 0.118, 0.124,\n",
       "        0.127],\n",
       "       [0.079, 0.076, 0.091, 0.087, 0.094, 0.103, 0.101, 0.101, 0.118,\n",
       "        0.15 ]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Q5\n",
    "nb_quantiles= 10\n",
    "n=nb_quantiles*1000\n",
    "\n",
    "def distribution(counts, nb_quantiles):\n",
    "    distrib = []\n",
    "    total = counts[\"counts\"].sum()\n",
    "    \n",
    "    if total == 0 :\n",
    "        return [0] * nb_quantiles\n",
    "    \n",
    "    for q_p in range(1, nb_quantiles+1):\n",
    "        subset = counts[counts.c_i_parent == q_p]\n",
    "        if len(subset):\n",
    "            nb = subset[\"counts\"].values[0]\n",
    "            distrib += [nb / total]\n",
    "        else:\n",
    "            distrib += [0]\n",
    "    return distrib   \n",
    "\n",
    "def conditional_distributions(sample, nb_quantiles):\n",
    "    counts = sample.groupby([\"c_i_child\",\"c_i_parent\"]).apply(len)\n",
    "    counts = counts.reset_index()\n",
    "    counts.columns = [\"c_i_child\",\"c_i_parent\",\"counts\"]\n",
    "    \n",
    "    mat = []\n",
    "    for child_quantile in np.arange(nb_quantiles)+1:\n",
    "        subset = counts[counts.c_i_child == child_quantile]\n",
    "        mat += [distribution(subset, nb_quantiles)]\n",
    "    return np.array(mat) \n",
    "\n",
    "conditional_distributions(sample, nb_quantiles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "84650a44",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrice de distribution conditionnelle des probabilités c_i_child vs c_i_parent\n"
     ]
    },
    {
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       "      <th>quantile_enfant</th>\n",
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       "      <th>1</th>\n",
       "      <td>0.135</td>\n",
       "      <td>0.103</td>\n",
       "      <td>0.115</td>\n",
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       "      <td>0.107</td>\n",
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       "      <td>0.096</td>\n",
       "      <td>0.089</td>\n",
       "      <td>0.101</td>\n",
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       "      <td>0.086</td>\n",
       "      <td>0.086</td>\n",
       "      <td>0.078</td>\n",
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       "      <td>0.080</td>\n",
       "      <td>0.084</td>\n",
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       "      <td>0.112</td>\n",
       "      <td>0.106</td>\n",
       "      <td>0.109</td>\n",
       "      <td>0.091</td>\n",
       "      <td>0.094</td>\n",
       "      <td>0.094</td>\n",
       "      <td>0.085</td>\n",
       "      <td>0.106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.093</td>\n",
       "      <td>0.106</td>\n",
       "      <td>0.101</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.109</td>\n",
       "      <td>0.091</td>\n",
       "      <td>0.092</td>\n",
       "      <td>0.095</td>\n",
       "      <td>0.088</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.088</td>\n",
       "      <td>0.093</td>\n",
       "      <td>0.096</td>\n",
       "      <td>0.111</td>\n",
       "      <td>0.109</td>\n",
       "      <td>0.101</td>\n",
       "      <td>0.092</td>\n",
       "      <td>0.102</td>\n",
       "      <td>0.107</td>\n",
       "      <td>0.101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.093</td>\n",
       "      <td>0.095</td>\n",
       "      <td>0.083</td>\n",
       "      <td>0.092</td>\n",
       "      <td>0.092</td>\n",
       "      <td>0.100</td>\n",
       "      <td>0.112</td>\n",
       "      <td>0.113</td>\n",
       "      <td>0.121</td>\n",
       "      <td>0.099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.086</td>\n",
       "      <td>0.085</td>\n",
       "      <td>0.077</td>\n",
       "      <td>0.088</td>\n",
       "      <td>0.088</td>\n",
       "      <td>0.102</td>\n",
       "      <td>0.105</td>\n",
       "      <td>0.118</td>\n",
       "      <td>0.124</td>\n",
       "      <td>0.127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.079</td>\n",
       "      <td>0.076</td>\n",
       "      <td>0.091</td>\n",
       "      <td>0.087</td>\n",
       "      <td>0.094</td>\n",
       "      <td>0.103</td>\n",
       "      <td>0.101</td>\n",
       "      <td>0.101</td>\n",
       "      <td>0.118</td>\n",
       "      <td>0.150</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    1      2      3      4      5      6      7      8   \\\n",
       "quantile_enfant                                                           \n",
       "1                0.135  0.103  0.115  0.090  0.095  0.100  0.093  0.110   \n",
       "2                0.119  0.110  0.116  0.107  0.083  0.088  0.096  0.089   \n",
       "3                0.113  0.116  0.101  0.102  0.110  0.112  0.096  0.086   \n",
       "4                0.100  0.107  0.108  0.117  0.095  0.094  0.120  0.095   \n",
       "5                0.094  0.109  0.112  0.106  0.109  0.091  0.094  0.094   \n",
       "6                0.093  0.106  0.101  0.100  0.125  0.109  0.091  0.092   \n",
       "7                0.088  0.093  0.096  0.111  0.109  0.101  0.092  0.102   \n",
       "8                0.093  0.095  0.083  0.092  0.092  0.100  0.112  0.113   \n",
       "9                0.086  0.085  0.077  0.088  0.088  0.102  0.105  0.118   \n",
       "10               0.079  0.076  0.091  0.087  0.094  0.103  0.101  0.101   \n",
       "\n",
       "                    9      10  \n",
       "quantile_enfant                \n",
       "1                0.083  0.076  \n",
       "2                0.101  0.091  \n",
       "3                0.086  0.078  \n",
       "4                0.080  0.084  \n",
       "5                0.085  0.106  \n",
       "6                0.095  0.088  \n",
       "7                0.107  0.101  \n",
       "8                0.121  0.099  \n",
       "9                0.124  0.127  \n",
       "10               0.118  0.150  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Q5 \n",
    "# pj=0.1\n",
    "Cond_distribution = pd.DataFrame(cd)\n",
    "Cond_distribution.columns = Cond_distribution.columns +1\n",
    "Cond_distribution['quantile_enfant'] =Cond_distribution.index +1\n",
    "Cond_distribution.set_index(['quantile_enfant'], inplace=True)\n",
    "\n",
    "print(\"Matrice de distribution conditionnelle des probabilités c_i_child vs c_i_parent\")\n",
    "Cond_distribution\n",
    "\n",
    "# ici les indexes 'quantile_enfant' sont les classes revenus enfants, les colonnes sont les classes revenus parents correspondants"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3135a4bd",
   "metadata": {},
   "source": [
    "ici l'échantillon est divisée en 10 classes de revenu, donc on a 10*10  estimations de ces probabilités conditionnelles, pour chaque pays\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "18103c5e",
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pj = 0.1                           # coefficient d'élasticité du pays j\n",
    "nb_quantiles = 10           # nombre de quantiles (nombre de classes de revenu) = 10 \n",
    "n  = 1000*nb_quantiles   # taille de l'échantillon = 1000*10\n",
    "\n",
    "def proba_cond(c_i_parent, c_i_child, mat):\n",
    "    return mat[c_i_child, c_i_parent]\n",
    "\n",
    "y_child, y_parents = generate_incomes(n, pj)\n",
    "sample = compute_quantiles(y_child, y_parents, nb_quantiles)\n",
    "cd = conditional_distributions(sample, nb_quantiles)\n",
    "plot_conditional_distributions(pj, cd, nb_quantiles)            \n",
    "\n",
    "\n",
    "plt.savefig('M3 Q123Q6_plot_conditional distribution_pj01.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a98d855",
   "metadata": {},
   "source": [
    "#### Q6. pour vérifier la cohérence de code - scénario à faible mobilité: pj = 0.9 \n",
    "idem que quand le coeff d'élasticité = 0.1, quand il = 0.9, on a "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2674d669",
   "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"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_incomes(n, pj):\n",
    "    # On génère les revenus des parents (exprimés en logs) selon une loi normale.\n",
    "    # La moyenne et variance n'ont aucune incidence sur le résultat final (ie. sur le caclul de la classe de revenu)\n",
    "    ln_y_parent = st.norm(0,1).rvs(size=n)\n",
    "    # Génération d'une réalisation du terme d'erreur epsilon\n",
    "    residues = st.norm(0,1).rvs(size=n)\n",
    "    return np.exp(pj*ln_y_parent + residues), np.exp(ln_y_parent)\n",
    "    \n",
    "def quantiles(l, nb_quantiles):\n",
    "    size = len(l)\n",
    "    l_sorted = l.copy()\n",
    "    l_sorted = l_sorted.sort_values()\n",
    "    quantiles = np.round(np.arange(1, nb_quantiles+1, nb_quantiles/size) -0.5 +1./size)\n",
    "    q_dict = {a:int(b) for a,b in zip(l_sorted,quantiles)}\n",
    "    return pd.Series([q_dict[e] for e in l])\n",
    "\n",
    "def compute_quantiles(y_child, y_parents, nb_quantiles):\n",
    "    y_child = pd.Series(y_child)\n",
    "    y_parents = pd.Series(y_parents)\n",
    "    c_i_child = quantiles(y_child, nb_quantiles)\n",
    "    c_i_parent = quantiles(y_parents, nb_quantiles)\n",
    "    sample = pd.concat([y_child, y_parents, c_i_child, c_i_parent], axis=1)\n",
    "    sample.columns = [\"y_child\", \"y_parents\", \"c_i_child\",\"c_i_parent\"]\n",
    "    return sample\n",
    "\n",
    "def distribution(counts, nb_quantiles):\n",
    "    distrib = []\n",
    "    total = counts[\"counts\"].sum()\n",
    "    \n",
    "    if total == 0 :\n",
    "        return [0] * nb_quantiles\n",
    "    \n",
    "    for q_p in range(1, nb_quantiles+1):\n",
    "        subset = counts[counts.c_i_parent == q_p]\n",
    "        if len(subset):\n",
    "            nb = subset[\"counts\"].values[0]\n",
    "            distrib += [nb / total]\n",
    "        else:\n",
    "            distrib += [0]\n",
    "    return distrib   \n",
    "\n",
    "def conditional_distributions(sample, nb_quantiles):\n",
    "    counts = sample.groupby([\"c_i_child\",\"c_i_parent\"]).apply(len)\n",
    "    counts = counts.reset_index()\n",
    "    counts.columns = [\"c_i_child\",\"c_i_parent\",\"counts\"]\n",
    "    \n",
    "    mat = []\n",
    "    for child_quantile in np.arange(nb_quantiles)+1:\n",
    "        subset = counts[counts.c_i_child == child_quantile]\n",
    "        mat += [distribution(subset, nb_quantiles)]\n",
    "    return np.array(mat) \n",
    "\n",
    "def plot_conditional_distributions(p, cd, nb_quantiles):\n",
    "    plt.figure()\n",
    "    \n",
    "    # La ligne suivante sert à afficher un graphique en \"stack bars\", sur ce modèle : https://matplotlib.org/gallery/lines_bars_and_markers/bar_stacked.html\n",
    "    cumul = np.array([0] * nb_quantiles)\n",
    "    \n",
    "    for i, child_quantile in enumerate(cd):\n",
    "        plt.bar(np.arange(nb_quantiles)+1, child_quantile, bottom=cumul, width=0.95, label = str(i+1) +\"e\")\n",
    "        cumul = cumul + np.array(child_quantile)\n",
    "\n",
    "    plt.axis([.5, nb_quantiles*1.3 ,0 ,1])\n",
    "    plt.title(\"p=\" + str(p))\n",
    "    plt.legend(fontsize= 9)\n",
    "    plt.xlabel(\"quantile parents\")\n",
    "    plt.ylabel(\"probabilité du quantile enfant\")\n",
    "    plt.show()\n",
    "    \n",
    "def proba_cond(c_i_parent, c_i_child, mat):\n",
    "    return mat[c_i_child, c_i_parent]\n",
    "\n",
    "pj = 0.9                             # coefficient d'élasticité du pays j\n",
    "nb_quantiles = 10           # nombre de quantiles (nombre de classes de revenu)\n",
    "n = 1000*nb_quantiles    # taille de l'échantillon\n",
    "\n",
    "y_child, y_parents = generate_incomes(n, pj)\n",
    "sample = compute_quantiles(y_child, y_parents, nb_quantiles)\n",
    "cd = conditional_distributions(sample, nb_quantiles)\n",
    "plot_conditional_distributions(pj, cd, nb_quantiles)              # Cette instruction prendra du temps si nb_quantiles > 10\n",
    "\n",
    "plt.savefig('M3Q1236_plot_conditionaldistribution_pj09.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4567dc8e",
   "metadata": {},
   "source": [
    "#### Q8: Nous allons maintenant travailler sur un nouvel échantillon. Celui-ci sera créé à partir de laWID. Pour chaque individu de la Wold Income Distribution, créez-en 499 \"clones\". La taille devotre nouvel échantillon sera donc 500 fois plus grand que celui de la Wold Income Distribution. \n",
    "- 1. Build up the dataframe including info on 114 countries client + corresponding coeff (pj) + Gini indexes: merge gini & coeff & dataWID\n",
    "- 2. clone 500 times  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "83d3a6c7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 11600 entries, 0 to 11599\n",
      "Data columns (total 6 columns):\n",
      " #   Column        Non-Null Count  Dtype  \n",
      "---  ------        --------------  -----  \n",
      " 0   country       11600 non-null  object \n",
      " 1   year_survey   11600 non-null  int64  \n",
      " 2   quantile      11600 non-null  int64  \n",
      " 3   nb_quantiles  11600 non-null  int64  \n",
      " 4   income        11600 non-null  float64\n",
      " 5   gdpppp        11600 non-null  float64\n",
      "dtypes: float64(2), int64(3), object(1)\n",
      "memory usage: 543.9+ KB\n",
      "None\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>year_survey</th>\n",
       "      <th>quantile</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income</th>\n",
       "      <th>gdpppp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ALB</td>\n",
       "      <td>2008</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ALB</td>\n",
       "      <td>2008</td>\n",
       "      <td>2</td>\n",
       "      <td>100</td>\n",
       "      <td>916.66235</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ALB</td>\n",
       "      <td>2008</td>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>1010.91600</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ALB</td>\n",
       "      <td>2008</td>\n",
       "      <td>4</td>\n",
       "      <td>100</td>\n",
       "      <td>1086.90780</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ALB</td>\n",
       "      <td>2008</td>\n",
       "      <td>5</td>\n",
       "      <td>100</td>\n",
       "      <td>1132.69970</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  country  year_survey  quantile  nb_quantiles      income  gdpppp\n",
       "0     ALB         2008         1           100   728.89795  7297.0\n",
       "1     ALB         2008         2           100   916.66235  7297.0\n",
       "2     ALB         2008         3           100  1010.91600  7297.0\n",
       "3     ALB         2008         4           100  1086.90780  7297.0\n",
       "4     ALB         2008         5           100  1132.69970  7297.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Q8 : dataframe dataWID\n",
    "dataWID = pd.read_csv('data_cleaned_WID.csv')\n",
    "dataWID= dataWID.drop(columns=['Unnamed: 0'])\n",
    "dataWID.describe()\n",
    "print(dataWID.info())\n",
    "dataWID.head()\n",
    "# data_cleaned_WID is the cleaned dataframe 'world_income_distribution.csv' for client countries on 2008"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8d6325e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 75 entries, 0 to 74\n",
      "Data columns (total 2 columns):\n",
      " #   Column     Non-Null Count  Dtype  \n",
      "---  ------     --------------  -----  \n",
      " 0   wbcode     75 non-null     object \n",
      " 1   IGEincome  75 non-null     float64\n",
      "dtypes: float64(1), object(1)\n",
      "memory usage: 1.3+ KB\n",
      "None\n"
     ]
    },
    {
     "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",
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       "    }\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>wbcode</th>\n",
       "      <th>IGEincome</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ALB</td>\n",
       "      <td>0.815874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AUS</td>\n",
       "      <td>0.275000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>AUT</td>\n",
       "      <td>0.245267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BEL</td>\n",
       "      <td>0.183176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>BEN</td>\n",
       "      <td>0.855116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>USA</td>\n",
       "      <td>0.537666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>UZB</td>\n",
       "      <td>0.496764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>VNM</td>\n",
       "      <td>0.480000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>ZAF</td>\n",
       "      <td>0.677000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>ZAR</td>\n",
       "      <td>0.707703</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>75 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   wbcode  IGEincome\n",
       "0     ALB   0.815874\n",
       "1     AUS   0.275000\n",
       "2     AUT   0.245267\n",
       "3     BEL   0.183176\n",
       "4     BEN   0.855116\n",
       "..    ...        ...\n",
       "70    USA   0.537666\n",
       "71    UZB   0.496764\n",
       "72    VNM   0.480000\n",
       "73    ZAF   0.677000\n",
       "74    ZAR   0.707703\n",
       "\n",
       "[75 rows x 2 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Q8_dataframe Coeff_coeffcient d'électricité \n",
    "coeff= pd.read_csv('coeff_pj.csv')\n",
    "Coeff= coeff.drop(columns=['Unnamed: 0','year'])                  # here all the year 1960-1980\n",
    "print(Coeff.info())\n",
    "Coeff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "75553fcf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 id          year          gini\n",
      "count  20592.000000  20592.000000  20592.000000\n",
      "mean   10630.988782   2001.319542     37.281548\n",
      "std     6145.293483     14.517767      9.416913\n",
      "min        1.000000   1867.000000     12.100000\n",
      "25%     5293.750000   1995.000000     30.300000\n",
      "50%    10639.500000   2005.000000     35.570000\n",
      "75%    15971.250000   2012.000000     43.462500\n",
      "max    21253.000000   2020.000000     78.600000\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>c3</th>\n",
       "      <th>gini</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>AFG</td>\n",
       "      <td>31.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AGO</td>\n",
       "      <td>47.095000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ALB</td>\n",
       "      <td>31.408889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>AND</td>\n",
       "      <td>27.097500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ARE</td>\n",
       "      <td>35.405000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    c3       gini\n",
       "0  AFG  31.000000\n",
       "1  AGO  47.095000\n",
       "2  ALB  31.408889\n",
       "3  AND  27.097500\n",
       "4  ARE  35.405000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Q8_dataframe ginidata\n",
    "ginidata= pd.read_csv('ginidata.csv', index_col=None).sort_values('country')\n",
    "print(ginidata.describe())\n",
    "ginidata_mean=ginidata[['c3','gini']].groupby('c3').mean('gini').reset_index()         # aggfunc by the mean of 'gini' data over years \n",
    "ginidata_mean.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8feb4de2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>c3</th>\n",
       "      <th>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ALB</td>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AUS</td>\n",
       "      <td>33.017782</td>\n",
       "      <td>0.275000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>AUT</td>\n",
       "      <td>30.632243</td>\n",
       "      <td>0.245267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BEL</td>\n",
       "      <td>30.698808</td>\n",
       "      <td>0.183176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>BEN</td>\n",
       "      <td>41.796667</td>\n",
       "      <td>0.855116</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>67</th>\n",
       "      <td>UGA</td>\n",
       "      <td>40.748387</td>\n",
       "      <td>1.029195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>68</th>\n",
       "      <td>USA</td>\n",
       "      <td>40.205324</td>\n",
       "      <td>0.537666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>UZB</td>\n",
       "      <td>33.486250</td>\n",
       "      <td>0.496764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>VNM</td>\n",
       "      <td>36.275400</td>\n",
       "      <td>0.480000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>ZAF</td>\n",
       "      <td>64.490000</td>\n",
       "      <td>0.677000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>72 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     c3       gini  IGEincome\n",
       "0   ALB  31.408889   0.815874\n",
       "1   AUS  33.017782   0.275000\n",
       "2   AUT  30.632243   0.245267\n",
       "3   BEL  30.698808   0.183176\n",
       "4   BEN  41.796667   0.855116\n",
       "..  ...        ...        ...\n",
       "67  UGA  40.748387   1.029195\n",
       "68  USA  40.205324   0.537666\n",
       "69  UZB  33.486250   0.496764\n",
       "70  VNM  36.275400   0.480000\n",
       "71  ZAF  64.490000   0.677000\n",
       "\n",
       "[72 rows x 3 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Q8 Step1: jointure de 2 df\n",
    "gini_coeff = ginidata_mean.merge(Coeff, left_on='c3', right_on= 'wbcode').drop(columns=['wbcode'])\n",
    "gini_coeff \n",
    "# inclut pj et gini \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bae412bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 11600 entries, 0 to 11599\n",
      "Data columns (total 7 columns):\n",
      " #   Column        Non-Null Count  Dtype  \n",
      "---  ------        --------------  -----  \n",
      " 0   gini          6300 non-null   float64\n",
      " 1   IGEincome     6300 non-null   float64\n",
      " 2   country       11600 non-null  object \n",
      " 3   quantile      11600 non-null  int64  \n",
      " 4   nb_quantiles  11600 non-null  int64  \n",
      " 5   income        11600 non-null  float64\n",
      " 6   gdpppp        11600 non-null  float64\n",
      "dtypes: float64(4), int64(2), object(1)\n",
      "memory usage: 725.0+ KB\n",
      "None\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>country</th>\n",
       "      <th>quantile</th>\n",
       "      <th>nb_quantiles</th>\n",
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       "      <th>gdpppp</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
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       "      <td>1</td>\n",
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       "      <td>7297.0</td>\n",
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       "      <th>2</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>3</td>\n",
       "      <td>100</td>\n",
       "      <td>1010.91600</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>4</td>\n",
       "      <td>100</td>\n",
       "      <td>1086.90780</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>5</td>\n",
       "      <td>100</td>\n",
       "      <td>1132.69970</td>\n",
       "      <td>7297.0</td>\n",
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       "      <th>11494</th>\n",
       "      <td>64.490000</td>\n",
       "      <td>0.677000</td>\n",
       "      <td>ZAF</td>\n",
       "      <td>96</td>\n",
       "      <td>100</td>\n",
       "      <td>24553.56800</td>\n",
       "      <td>9602.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11495</th>\n",
       "      <td>64.490000</td>\n",
       "      <td>0.677000</td>\n",
       "      <td>ZAF</td>\n",
       "      <td>97</td>\n",
       "      <td>100</td>\n",
       "      <td>28858.03100</td>\n",
       "      <td>9602.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11496</th>\n",
       "      <td>64.490000</td>\n",
       "      <td>0.677000</td>\n",
       "      <td>ZAF</td>\n",
       "      <td>98</td>\n",
       "      <td>100</td>\n",
       "      <td>35750.29000</td>\n",
       "      <td>9602.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11497</th>\n",
       "      <td>64.490000</td>\n",
       "      <td>0.677000</td>\n",
       "      <td>ZAF</td>\n",
       "      <td>99</td>\n",
       "      <td>100</td>\n",
       "      <td>46297.31600</td>\n",
       "      <td>9602.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11498</th>\n",
       "      <td>64.490000</td>\n",
       "      <td>0.677000</td>\n",
       "      <td>ZAF</td>\n",
       "      <td>100</td>\n",
       "      <td>100</td>\n",
       "      <td>82408.55000</td>\n",
       "      <td>9602.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6300 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            gini  IGEincome country  quantile  nb_quantiles       income  \\\n",
       "0      31.408889   0.815874     ALB         1           100    728.89795   \n",
       "1      31.408889   0.815874     ALB         2           100    916.66235   \n",
       "2      31.408889   0.815874     ALB         3           100   1010.91600   \n",
       "3      31.408889   0.815874     ALB         4           100   1086.90780   \n",
       "4      31.408889   0.815874     ALB         5           100   1132.69970   \n",
       "...          ...        ...     ...       ...           ...          ...   \n",
       "11494  64.490000   0.677000     ZAF        96           100  24553.56800   \n",
       "11495  64.490000   0.677000     ZAF        97           100  28858.03100   \n",
       "11496  64.490000   0.677000     ZAF        98           100  35750.29000   \n",
       "11497  64.490000   0.677000     ZAF        99           100  46297.31600   \n",
       "11498  64.490000   0.677000     ZAF       100           100  82408.55000   \n",
       "\n",
       "       gdpppp  \n",
       "0      7297.0  \n",
       "1      7297.0  \n",
       "2      7297.0  \n",
       "3      7297.0  \n",
       "4      7297.0  \n",
       "...       ...  \n",
       "11494  9602.0  \n",
       "11495  9602.0  \n",
       "11496  9602.0  \n",
       "11497  9602.0  \n",
       "11498  9602.0  \n",
       "\n",
       "[6300 rows x 7 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Q8\n",
    "# step2: jointure de tous ces 3 dataframes \n",
    "\n",
    "Co = pd.merge(gini_coeff, dataWID, left_on= 'c3', right_on ='country', how='right').drop(['year_survey', 'c3'], axis=1)  \n",
    "print(Co.info())\n",
    "Co=Co.dropna(how='any')\n",
    "Co\n",
    "\n",
    "#income: revenu des parents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9b6066f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 3150000 entries, 0 to 3149999\n",
      "Data columns (total 7 columns):\n",
      " #   Column        Dtype  \n",
      "---  ------        -----  \n",
      " 0   gini          float64\n",
      " 1   IGEincome     float64\n",
      " 2   country       object \n",
      " 3   quantile      int64  \n",
      " 4   nb_quantiles  int64  \n",
      " 5   income        float64\n",
      " 6   gdpppp        float64\n",
      "dtypes: float64(4), int64(2), object(1)\n",
      "memory usage: 192.3+ MB\n",
      "None\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>country</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income</th>\n",
       "      <th>gdpppp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6300</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12600</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18900</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25200</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            gini  IGEincome country  quantile_child  nb_quantiles     income  \\\n",
       "0      31.408889   0.815874     ALB               1           100  728.89795   \n",
       "6300   31.408889   0.815874     ALB               1           100  728.89795   \n",
       "12600  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "18900  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "25200  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "\n",
       "       gdpppp  \n",
       "0      7297.0  \n",
       "6300   7297.0  \n",
       "12600  7297.0  \n",
       "18900  7297.0  \n",
       "25200  7297.0  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Q8 \n",
    "#Step 3: cloner tous les individus (pays clientèle) par 500 fois : on a 500 pour chaque c_i_child et chaque country \n",
    "\n",
    "Co500 = pd.concat([Co]*500, ignore_index=True)                 # cloner en 500 fois les individus \n",
    "Co500= Co500.sort_values(by=['country','quantile'])\n",
    "print(Co500.info())\n",
    "Co500=Co500.rename({'quantile': 'quantile_child'}, axis=1)      #here quantile is changed to quantile_child \n",
    "Co500.head()\n",
    "\n",
    "# 500 individus pour chaque c_i_child de chaque pays , donc y a 100*500 individus pour chaque pays \n",
    "# 6300*500 = 3150000 rows\n",
    "# Q8 fini"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5e7cb28",
   "metadata": {},
   "source": [
    "#### Q9: Vous attribuerez aux 500 individus leurs classes c_i_parent conformément aux distributions trouvées précédemment. Ctd. attribution de c_i_parent à chaque observation selon fonctions données\n",
    "\n",
    "- 1.  Calculate corresponding **conditional distribution (P)** of class income parents based on the class income child that we have in the dataframe of Q8.\n",
    "- 2. then add onto the dataframe **quantities of every possibility** for class income parents with regard to every class income child "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "de386da5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 50000 entries, 0 to 3143799\n",
      "Data columns (total 7 columns):\n",
      " #   Column          Non-Null Count  Dtype  \n",
      "---  ------          --------------  -----  \n",
      " 0   gini            50000 non-null  float64\n",
      " 1   IGEincome       50000 non-null  float64\n",
      " 2   country         50000 non-null  object \n",
      " 3   quantile_child  50000 non-null  int64  \n",
      " 4   nb_quantiles    50000 non-null  int64  \n",
      " 5   income          50000 non-null  float64\n",
      " 6   gdpppp          50000 non-null  float64\n",
      "dtypes: float64(4), int64(2), object(1)\n",
      "memory usage: 3.1+ MB\n",
      "None\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>country</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income</th>\n",
       "      <th>gdpppp</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6300</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
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       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
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       "    <tr>\n",
       "      <th>12600</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18900</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25200</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            gini  IGEincome country  quantile_child  nb_quantiles     income  \\\n",
       "0      31.408889   0.815874     ALB               1           100  728.89795   \n",
       "6300   31.408889   0.815874     ALB               1           100  728.89795   \n",
       "12600  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "18900  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "25200  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "\n",
       "       gdpppp  \n",
       "0      7297.0  \n",
       "6300   7297.0  \n",
       "12600  7297.0  \n",
       "18900  7297.0  \n",
       "25200  7297.0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Q9: attribution de c_i_parent à chaque observation selon fonctions ('counts')\n",
    "\n",
    "# pour faciliter la vitesse de calcul, ici on prend ALB pour exemple illustratif\n",
    "\n",
    "ALB = Co500[Co500['country']=='ALB']\n",
    "print(ALB.info())\n",
    "ALB.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7b033745",
   "metadata": {},
   "outputs": [],
   "source": [
    "ALB_proba=[]\n",
    "\n",
    "pj=Co500.loc[Co500['country']=='ALB','IGEincome'].iloc[0]            # coefficient d'élasticité du pays j\n",
    "nb_quantiles = 100                                                                              # nombre de quantiles (nombre de classes de revenu)\n",
    "n = 500*nb_quantiles                                                                       # taille de l'échantillon\n",
    "    \n",
    "y_child, y_parents = generate_incomes(n, pj)\n",
    "sample = compute_quantiles(y_child, y_parents, nb_quantiles)\n",
    "cd = conditional_distributions(sample, nb_quantiles)\n",
    "for c_i_child in range(100):\n",
    "    for c_i_parent in range(100):\n",
    "        p = proba_cond(c_i_parent, c_i_child, cd)\n",
    "        ALB_proba.extend([c_i_parent+1]*(int(p*500)))        \n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "bf7c8162",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50000"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ALB_proba)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2b583048",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-20-049235bb7fc6>:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  ALB['proba_quantile_parent']=ALB_proba\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 50000 entries, 0 to 3143799\n",
      "Data columns (total 8 columns):\n",
      " #   Column                 Non-Null Count  Dtype  \n",
      "---  ------                 --------------  -----  \n",
      " 0   gini                   50000 non-null  float64\n",
      " 1   IGEincome              50000 non-null  float64\n",
      " 2   country                50000 non-null  object \n",
      " 3   quantile_child         50000 non-null  int64  \n",
      " 4   nb_quantiles           50000 non-null  int64  \n",
      " 5   income                 50000 non-null  float64\n",
      " 6   gdpppp                 50000 non-null  float64\n",
      " 7   proba_quantile_parent  50000 non-null  int64  \n",
      "dtypes: float64(4), int64(3), object(1)\n",
      "memory usage: 3.4+ MB\n",
      "None\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th>gini</th>\n",
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       "      <th>country</th>\n",
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       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
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       "      <td>100</td>\n",
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       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
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       "      <th>6300</th>\n",
       "      <td>31.408889</td>\n",
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       "      <td>7297.0</td>\n",
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       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            gini  IGEincome country  quantile_child  nb_quantiles     income  \\\n",
       "0      31.408889   0.815874     ALB               1           100  728.89795   \n",
       "6300   31.408889   0.815874     ALB               1           100  728.89795   \n",
       "12600  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "18900  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "25200  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "\n",
       "       gdpppp  proba_quantile_parent  \n",
       "0      7297.0                      1  \n",
       "6300   7297.0                      1  \n",
       "12600  7297.0                      1  \n",
       "18900  7297.0                      1  \n",
       "25200  7297.0                      1  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ALB['proba_quantile_parent']=ALB_proba\n",
    "\n",
    "ALB.to_csv('M3_final_ex_ALB.csv')\n",
    "print(ALB.info())\n",
    "ALB.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f166038c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8158745"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Co500.loc[Co500['country']=='ALB','IGEincome'].iloc[0]   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "18a38061",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "P(c_i_parent = 12 | c_i_child = 16, pj = 0.8158745) = 0.028\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# un exemple d'Albania: ALB\n",
    "\n",
    "pj=Co500.loc[Co500['country']=='ALB','IGEincome'].iloc[0]   \n",
    "nb_quantiles = 100                       # classes de revenu = 100                                                       \n",
    "n = 500*nb_quantiles\n",
    "\n",
    "def plot_conditional_distributions(p, cd, nb_quantiles):\n",
    "    plt.figure(figsize= (15,15))\n",
    "    cumul = np.array([0] * nb_quantiles)\n",
    "    \n",
    "    for i, child_quantile in enumerate(cd):\n",
    "        plt.bar(np.arange(nb_quantiles)+1, child_quantile, bottom=cumul, width=0.95, label = str(i+1) +\"e\")\n",
    "        cumul = cumul + np.array(child_quantile)\n",
    "\n",
    "    plt.axis([.5, nb_quantiles*1.3 ,0 ,1])\n",
    "    plt.title(\"p=\" + str(p))\n",
    "    plt.legend(fontsize= 5)\n",
    "    plt.xlabel(\"quantile parents\")\n",
    "    plt.ylabel(\"probabilité du quantile enfant\")\n",
    "    plt.show()\n",
    "    \n",
    "plot_conditional_distributions(pj, cd, nb_quantiles)            \n",
    "\n",
    "plt.savefig('M3 ALB_plot_conditional distribution.jpg')\n",
    "\n",
    "# cas illustrative: Albania \n",
    "c_i_child = 16\n",
    "c_i_parent = 12\n",
    "p = proba_cond(c_i_parent, c_i_child, cd)\n",
    "print(\"\\nP(c_i_parent = {} | c_i_child = {}, pj = {}) = {}\".format(c_i_parent, c_i_child,\n",
    "pj, p))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37eabda1",
   "metadata": {},
   "source": [
    "<font color=\"1E1EE9\"> Pour le pays Albania qui a pour coeff d'élasticité 0.8158745 à faible mobilité, la probabilité pour que la classe revenu parents se situe à la 12ème est 2.8% sachant la classe revenu d'enfant se situe à 16ème/100 classes </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a10c0d98",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the number of countries in Co500:  63\n"
     ]
    }
   ],
   "source": [
    "print('the number of countries in Co500: ', len(Co500['IGEincome'].unique()))\n",
    "#Co500['IGEincome'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "3551cb9a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "63\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array(['ALB', 'AUT', 'BEL', 'BGD', 'BIH', 'BLR', 'BOL', 'BRA', 'CAN',\n",
       "       'CHL', 'CHN', 'COL', 'CYP', 'CZE', 'DEU', 'DNK', 'ECU', 'EGY',\n",
       "       'ESP', 'FIN', 'FRA', 'GBR', 'GHA', 'GIN', 'GRC', 'GTM', 'HRV',\n",
       "       'IND', 'IRL', 'ITA', 'JOR', 'JPN', 'KAZ', 'KEN', 'KGZ', 'KOR',\n",
       "       'LUX', 'LVA', 'MAR', 'MDG', 'MKD', 'MLI', 'MNG', 'MWI', 'MYS',\n",
       "       'NGA', 'NLD', 'NOR', 'NPL', 'PAK', 'PAN', 'PER', 'PRT', 'RUS',\n",
       "       'SVK', 'SVN', 'SWE', 'TWN', 'TZA', 'UGA', 'USA', 'VNM', 'ZAF'],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "country_list=Co500['country'].unique()\n",
    "print(len(country_list))\n",
    "country_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4c08f3f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Q9\n",
    "\n",
    "list_prob=[]\n",
    "\n",
    "for country in country_list:\n",
    "    pj=Co500.loc[Co500['country']==country,'IGEincome'].iloc[0]             # coefficient d'élasticité du pays j\n",
    "    nb_quantiles = 100                                                                              # nombre de quantiles (nombre de classes de revenu)=100\n",
    "    n = 500*nb_quantiles                                                                           # taille de l'échantillon=500*100 vu qu'on a 500 fois le même individu \n",
    "    y_child, y_parents = generate_incomes(n, pj)\n",
    "    sample = compute_quantiles(y_child, y_parents, nb_quantiles)\n",
    "    cd = conditional_distributions(sample, nb_quantiles)\n",
    "    for c_i_child in range(100):\n",
    "        for c_i_parent in range(100):\n",
    "            p = proba_cond(c_i_parent, c_i_child, cd)\n",
    "            list_prob.extend([c_i_parent+1]*(int(p*500)))        \n",
    "            \n",
    "            # p is the probability (in %) for every individual c_i_parent I c_i_child I pj = coeffs, \n",
    "            # now that we have 500 clones for every individual, thus p*500 = the number of (c_i_parent) in every probability             \n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "de469592",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3150000"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(list_prob)     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "78ec2b8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3150000, 7)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Co500.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "833d19fc",
   "metadata": {},
   "source": [
    "len(list_prob) = len(Co500), so we can add list_prob onto the Co500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "cbcd6336",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 3150000 entries, 0 to 3149999\n",
      "Data columns (total 8 columns):\n",
      " #   Column                 Dtype  \n",
      "---  ------                 -----  \n",
      " 0   gini                   float64\n",
      " 1   IGEincome              float64\n",
      " 2   country                object \n",
      " 3   quantile_child         int64  \n",
      " 4   nb_quantiles           int64  \n",
      " 5   income                 float64\n",
      " 6   gdpppp                 float64\n",
      " 7   proba_quantile_parent  int64  \n",
      "dtypes: float64(4), int64(3), object(1)\n",
      "memory usage: 216.3+ MB\n",
      "None\n"
     ]
    },
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>country</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income</th>\n",
       "      <th>gdpppp</th>\n",
       "      <th>proba_quantile_parent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6300</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
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       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>12600</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18900</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25200</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            gini  IGEincome country  quantile_child  nb_quantiles     income  \\\n",
       "0      31.408889   0.815874     ALB               1           100  728.89795   \n",
       "6300   31.408889   0.815874     ALB               1           100  728.89795   \n",
       "12600  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "18900  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "25200  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "\n",
       "       gdpppp  proba_quantile_parent  \n",
       "0      7297.0                      1  \n",
       "6300   7297.0                      1  \n",
       "12600  7297.0                      1  \n",
       "18900  7297.0                      1  \n",
       "25200  7297.0                      1  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Q9\n",
    "Co500['proba_quantile_parent']=list_prob\n",
    "print(Co500.info())\n",
    "#Co500= Co500.drop('log_gdpppp', axis=1) \n",
    "Co500.to_csv('M3_final_Co500.csv')\n",
    "Co500.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1913ce29",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Q10: remove the quantile_child (c_i_child) for further use in M4\n",
    "Co500_2= Co500.drop(columns= ['quantile_child'])\n",
    "Co500_2.to_csv('M3_final_Co500_2_droped.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "722bfd9e",
   "metadata": {},
   "source": [
    "<font color=\"1E1EE9\"> \n",
    "    approach retrospective: \n",
    "     we know the c_i_child (quantile) and income of child , retrospect to find out the c_i_parent (the revenue classes of their parents) via functions of cd </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12b211f2",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## M4.1\n",
    "Appliquez une **ANOVA** sur vos données, en n’incluant comme variable explicative que **le pays** de l’individu. et Analysez la performance du modèle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "ae8a37a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "from statsmodels.formula.api import ols\n",
    "import statsmodels.formula.api as smf\n",
    "import statsmodels.stats.api as sms\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb84ae37",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Co500_2['log_gdpppp']=np.log(Co500_2['gdpppp'])  \n",
    "#Co500_2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "084195cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Co500['log_gdpppp']=np.log(Co500['gdpppp'])        # log of natural number \n",
    "Co500.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65213abb",
   "metadata": {},
   "source": [
    "<font color=\"#342EF3\"> \n",
    "*Why logarithm and why natural logarithm?*\n",
    "    \n",
    "Logarithm is the inverse of exponential , that means it's able to transform exponential series into additional series. This makes the calculus easier when it refers to complex situation with multiple variables. \n",
    "\n",
    "Natural logarithm is the logarithm to the base of the mathematical constant e, which is approximately 2.718281. Apart from natural log, we can also use log on the base of 10. But natural log is more commonly used in practice. </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "66b2f925",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>country</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income</th>\n",
       "      <th>gdpppp</th>\n",
       "      <th>proba_quantile_parent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815875</td>\n",
       "      <td>100.0</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>9.276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ALB</td>\n",
       "      <td>2</td>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815875</td>\n",
       "      <td>100.0</td>\n",
       "      <td>916.66235</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>13.972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ALB</td>\n",
       "      <td>3</td>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815875</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1010.91600</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>16.064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ALB</td>\n",
       "      <td>4</td>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815875</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1086.90780</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>18.616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ALB</td>\n",
       "      <td>5</td>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815875</td>\n",
       "      <td>100.0</td>\n",
       "      <td>1132.69970</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>19.760</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  country  quantile_child       gini  IGEincome  nb_quantiles      income  \\\n",
       "0     ALB               1  31.408889   0.815875         100.0   728.89795   \n",
       "1     ALB               2  31.408889   0.815875         100.0   916.66235   \n",
       "2     ALB               3  31.408889   0.815875         100.0  1010.91600   \n",
       "3     ALB               4  31.408889   0.815875         100.0  1086.90780   \n",
       "4     ALB               5  31.408889   0.815875         100.0  1132.69970   \n",
       "\n",
       "   gdpppp  proba_quantile_parent  \n",
       "0  7297.0                  9.276  \n",
       "1  7297.0                 13.972  \n",
       "2  7297.0                 16.064  \n",
       "3  7297.0                 18.616  \n",
       "4  7297.0                 19.760  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1_ANOVA=Co500.groupby(['country','quantile_child']).mean().reset_index()\n",
    "Q1_ANOVA.head()\n",
    "\n",
    "                                                                                                                                                # income représente revenu enfants"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "138f76b2",
   "metadata": {},
   "source": [
    "## ANOVA (analysis of variance) \n",
    "\n",
    "On teste la variable pays de l'individu [country] sur le revenu [income] \n",
    "\n",
    "Dans notre cas, c'est un One-way ANOVA car il n'y a qu'une seule variable explicative. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9c5ca2f",
   "metadata": {},
   "source": [
    "\n",
    "R2 is the percentage of variation in the response that is explained by the model. The higher the R2 value, the better the model fits your data. R2 is always between 0% and 100%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "7207876c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>income</td>      <th>  R-squared:         </th> <td>   0.456</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.451</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   84.42</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 11 Mar 2022</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>21:36:52</td>     <th>  Log-Likelihood:    </th> <td> -65714.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  6300</td>      <th>  AIC:               </th> <td>1.316e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  6237</td>      <th>  BIC:               </th> <td>1.320e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>    62</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "         <td></td>           <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>      <td> 2994.8299</td> <td>  824.141</td> <td>    3.634</td> <td> 0.000</td> <td> 1379.229</td> <td> 4610.431</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.AUT]</th> <td> 1.364e+04</td> <td> 1165.512</td> <td>   11.705</td> <td> 0.000</td> <td> 1.14e+04</td> <td> 1.59e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.BEL]</th> <td> 1.203e+04</td> <td> 1165.512</td> <td>   10.321</td> <td> 0.000</td> <td> 9744.979</td> <td> 1.43e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.BGD]</th> <td>-1996.1375</td> <td> 1165.512</td> <td>   -1.713</td> <td> 0.087</td> <td>-4280.942</td> <td>  288.667</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.BIH]</th> <td> 3339.8574</td> <td> 1165.512</td> <td>    2.866</td> <td> 0.004</td> <td> 1055.052</td> <td> 5624.662</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.BLR]</th> <td>  926.3336</td> <td> 1165.512</td> <td>    0.795</td> <td> 0.427</td> <td>-1358.471</td> <td> 3211.139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.BOL]</th> <td>   21.4339</td> <td> 1165.512</td> <td>    0.018</td> <td> 0.985</td> <td>-2263.371</td> <td> 2306.239</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.BRA]</th> <td> 1812.6547</td> <td> 1165.512</td> <td>    1.555</td> <td> 0.120</td> <td> -472.150</td> <td> 4097.460</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.CAN]</th> <td> 2.074e+04</td> <td> 1165.512</td> <td>   17.799</td> <td> 0.000</td> <td> 1.85e+04</td> <td>  2.3e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.CHL]</th> <td> 4056.7801</td> <td> 1165.512</td> <td>    3.481</td> <td> 0.001</td> <td> 1771.975</td> <td> 6341.585</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.CHN]</th> <td> -472.0712</td> <td> 1165.512</td> <td>   -0.405</td> <td> 0.685</td> <td>-2756.876</td> <td> 1812.734</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.COL]</th> <td>  552.1754</td> <td> 1165.512</td> <td>    0.474</td> <td> 0.636</td> <td>-1732.630</td> <td> 2836.980</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.CYP]</th> <td> 1.435e+04</td> <td> 1165.512</td> <td>   12.313</td> <td> 0.000</td> <td> 1.21e+04</td> <td> 1.66e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.CZE]</th> <td> 5240.4635</td> <td> 1165.512</td> <td>    4.496</td> <td> 0.000</td> <td> 2955.659</td> <td> 7525.268</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.DEU]</th> <td> 1.507e+04</td> <td> 1165.512</td> <td>   12.927</td> <td> 0.000</td> <td> 1.28e+04</td> <td> 1.74e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.DNK]</th> <td> 1.405e+04</td> <td> 1165.512</td> <td>   12.053</td> <td> 0.000</td> <td> 1.18e+04</td> <td> 1.63e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.ECU]</th> <td>  388.9111</td> <td> 1165.512</td> <td>    0.334</td> <td> 0.739</td> <td>-1895.894</td> <td> 2673.716</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.EGY]</th> <td>-1025.2525</td> <td> 1165.512</td> <td>   -0.880</td> <td> 0.379</td> <td>-3310.057</td> <td> 1259.552</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.ESP]</th> <td> 1.012e+04</td> <td> 1165.512</td> <td>    8.685</td> <td> 0.000</td> <td> 7837.358</td> <td> 1.24e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.FIN]</th> <td> 1.331e+04</td> <td> 1165.512</td> <td>   11.421</td> <td> 0.000</td> <td>  1.1e+04</td> <td> 1.56e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.FRA]</th> <td> 1.531e+04</td> <td> 1165.512</td> <td>   13.140</td> <td> 0.000</td> <td>  1.3e+04</td> <td> 1.76e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.GBR]</th> <td> 1.871e+04</td> <td> 1165.512</td> <td>   16.057</td> <td> 0.000</td> <td> 1.64e+04</td> <td>  2.1e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.GHA]</th> <td>-2258.2274</td> <td> 1165.512</td> <td>   -1.938</td> <td> 0.053</td> <td>-4543.032</td> <td>   26.578</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.GIN]</th> <td>-2298.8179</td> <td> 1165.512</td> <td>   -1.972</td> <td> 0.049</td> <td>-4583.623</td> <td>  -14.013</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.GRC]</th> <td> 8732.4444</td> <td> 1165.512</td> <td>    7.492</td> <td> 0.000</td> <td> 6447.639</td> <td>  1.1e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.GTM]</th> <td> -852.3551</td> <td> 1165.512</td> <td>   -0.731</td> <td> 0.465</td> <td>-3137.160</td> <td> 1432.450</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.HRV]</th> <td> 4721.6359</td> <td> 1165.512</td> <td>    4.051</td> <td> 0.000</td> <td> 2436.831</td> <td> 7006.441</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.IND]</th> <td>-2070.5604</td> <td> 1165.512</td> <td>   -1.777</td> <td> 0.076</td> <td>-4355.365</td> <td>  214.244</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.IRL]</th> <td> 1.472e+04</td> <td> 1165.512</td> <td>   12.626</td> <td> 0.000</td> <td> 1.24e+04</td> <td>  1.7e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.ITA]</th> <td> 1.193e+04</td> <td> 1165.512</td> <td>   10.236</td> <td> 0.000</td> <td> 9645.580</td> <td> 1.42e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.JOR]</th> <td>   53.8011</td> <td> 1165.512</td> <td>    0.046</td> <td> 0.963</td> <td>-2231.004</td> <td> 2338.606</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.JPN]</th> <td> 1.444e+04</td> <td> 1165.512</td> <td>   12.388</td> <td> 0.000</td> <td> 1.22e+04</td> <td> 1.67e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.KAZ]</th> <td> -755.6801</td> <td> 1165.512</td> <td>   -0.648</td> <td> 0.517</td> <td>-3040.485</td> <td> 1529.125</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.KEN]</th> <td>-2475.5099</td> <td> 1165.512</td> <td>   -2.124</td> <td> 0.034</td> <td>-4760.315</td> <td> -190.705</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.KGZ]</th> <td>-1221.6107</td> <td> 1165.512</td> <td>   -1.048</td> <td> 0.295</td> <td>-3506.416</td> <td> 1063.194</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.KOR]</th> <td> 1.223e+04</td> <td> 1165.512</td> <td>   10.496</td> <td> 0.000</td> <td> 9947.935</td> <td> 1.45e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.LUX]</th> <td> 2.222e+04</td> <td> 1165.512</td> <td>   19.067</td> <td> 0.000</td> <td> 1.99e+04</td> <td> 2.45e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.LVA]</th> <td> 3769.6447</td> <td> 1165.512</td> <td>    3.234</td> <td> 0.001</td> <td> 1484.840</td> <td> 6054.450</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.MAR]</th> <td> -657.2293</td> <td> 1165.512</td> <td>   -0.564</td> <td> 0.573</td> <td>-2942.034</td> <td> 1627.576</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.MDG]</th> <td>-2649.5928</td> <td> 1165.512</td> <td>   -2.273</td> <td> 0.023</td> <td>-4934.398</td> <td> -364.788</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.MKD]</th> <td> 1604.5664</td> <td> 1165.512</td> <td>    1.377</td> <td> 0.169</td> <td> -680.239</td> <td> 3889.371</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.MLI]</th> <td>-2313.7549</td> <td> 1165.512</td> <td>   -1.985</td> <td> 0.047</td> <td>-4598.560</td> <td>  -28.950</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.MNG]</th> <td> -656.7425</td> <td> 1165.512</td> <td>   -0.563</td> <td> 0.573</td> <td>-2941.547</td> <td> 1628.062</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.MWI]</th> <td>-2080.5645</td> <td> 1165.512</td> <td>   -1.785</td> <td> 0.074</td> <td>-4365.369</td> <td>  204.240</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.MYS]</th> <td> 3011.5125</td> <td> 1165.512</td> <td>    2.584</td> <td> 0.010</td> <td>  726.708</td> <td> 5296.317</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.NGA]</th> <td>-2302.9745</td> <td> 1165.512</td> <td>   -1.976</td> <td> 0.048</td> <td>-4587.779</td> <td>  -18.170</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.NLD]</th> <td> 1.473e+04</td> <td> 1165.512</td> <td>   12.641</td> <td> 0.000</td> <td> 1.24e+04</td> <td>  1.7e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.NOR]</th> <td> 1.949e+04</td> <td> 1165.512</td> <td>   16.721</td> <td> 0.000</td> <td> 1.72e+04</td> <td> 2.18e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.NPL]</th> <td>-2080.4383</td> <td> 1165.512</td> <td>   -1.785</td> <td> 0.074</td> <td>-4365.243</td> <td>  204.367</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.PAK]</th> <td>-2106.9906</td> <td> 1165.512</td> <td>   -1.808</td> <td> 0.071</td> <td>-4391.796</td> <td>  177.814</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.PAN]</th> <td> 2140.3095</td> <td> 1165.512</td> <td>    1.836</td> <td> 0.066</td> <td> -144.495</td> <td> 4425.114</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.PER]</th> <td>  335.7034</td> <td> 1165.512</td> <td>    0.288</td> <td> 0.773</td> <td>-1949.101</td> <td> 2620.508</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.PRT]</th> <td> 7103.8455</td> <td> 1165.512</td> <td>    6.095</td> <td> 0.000</td> <td> 4819.041</td> <td> 9388.650</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.RUS]</th> <td> 4161.9408</td> <td> 1165.512</td> <td>    3.571</td> <td> 0.000</td> <td> 1877.136</td> <td> 6446.746</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.SVK]</th> <td> 3101.7500</td> <td> 1165.512</td> <td>    2.661</td> <td> 0.008</td> <td>  816.945</td> <td> 5386.555</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.SVN]</th> <td> 9111.1776</td> <td> 1165.512</td> <td>    7.817</td> <td> 0.000</td> <td> 6826.373</td> <td> 1.14e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.SWE]</th> <td> 1.319e+04</td> <td> 1165.512</td> <td>   11.316</td> <td> 0.000</td> <td> 1.09e+04</td> <td> 1.55e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.TWN]</th> <td> 1.351e+04</td> <td> 1165.512</td> <td>   11.588</td> <td> 0.000</td> <td> 1.12e+04</td> <td> 1.58e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.TZA]</th> <td>-2406.0629</td> <td> 1165.512</td> <td>   -2.064</td> <td> 0.039</td> <td>-4690.868</td> <td> -121.258</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.UGA]</th> <td>-2007.6236</td> <td> 1165.512</td> <td>   -1.723</td> <td> 0.085</td> <td>-4292.429</td> <td>  277.181</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.USA]</th> <td> 2.251e+04</td> <td> 1165.512</td> <td>   19.312</td> <td> 0.000</td> <td> 2.02e+04</td> <td> 2.48e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.VNM]</th> <td>-1617.0559</td> <td> 1165.512</td> <td>   -1.387</td> <td> 0.165</td> <td>-3901.861</td> <td>  667.749</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>country[T.ZAF]</th> <td> 2623.0750</td> <td> 1165.512</td> <td>    2.251</td> <td> 0.024</td> <td>  338.270</td> <td> 4907.880</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>7040.441</td> <th>  Durbin-Watson:     </th>  <td>   0.666</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>999879.108</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 5.574</td>  <th>  Prob(JB):          </th>  <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>63.703</td>  <th>  Cond. No.          </th>  <td>    64.0</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                 income   R-squared:                       0.456\n",
       "Model:                            OLS   Adj. R-squared:                  0.451\n",
       "Method:                 Least Squares   F-statistic:                     84.42\n",
       "Date:                Fri, 11 Mar 2022   Prob (F-statistic):               0.00\n",
       "Time:                        21:36:52   Log-Likelihood:                -65714.\n",
       "No. Observations:                6300   AIC:                         1.316e+05\n",
       "Df Residuals:                    6237   BIC:                         1.320e+05\n",
       "Df Model:                          62                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==================================================================================\n",
       "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------\n",
       "Intercept       2994.8299    824.141      3.634      0.000    1379.229    4610.431\n",
       "country[T.AUT]  1.364e+04   1165.512     11.705      0.000    1.14e+04    1.59e+04\n",
       "country[T.BEL]  1.203e+04   1165.512     10.321      0.000    9744.979    1.43e+04\n",
       "country[T.BGD] -1996.1375   1165.512     -1.713      0.087   -4280.942     288.667\n",
       "country[T.BIH]  3339.8574   1165.512      2.866      0.004    1055.052    5624.662\n",
       "country[T.BLR]   926.3336   1165.512      0.795      0.427   -1358.471    3211.139\n",
       "country[T.BOL]    21.4339   1165.512      0.018      0.985   -2263.371    2306.239\n",
       "country[T.BRA]  1812.6547   1165.512      1.555      0.120    -472.150    4097.460\n",
       "country[T.CAN]  2.074e+04   1165.512     17.799      0.000    1.85e+04     2.3e+04\n",
       "country[T.CHL]  4056.7801   1165.512      3.481      0.001    1771.975    6341.585\n",
       "country[T.CHN]  -472.0712   1165.512     -0.405      0.685   -2756.876    1812.734\n",
       "country[T.COL]   552.1754   1165.512      0.474      0.636   -1732.630    2836.980\n",
       "country[T.CYP]  1.435e+04   1165.512     12.313      0.000    1.21e+04    1.66e+04\n",
       "country[T.CZE]  5240.4635   1165.512      4.496      0.000    2955.659    7525.268\n",
       "country[T.DEU]  1.507e+04   1165.512     12.927      0.000    1.28e+04    1.74e+04\n",
       "country[T.DNK]  1.405e+04   1165.512     12.053      0.000    1.18e+04    1.63e+04\n",
       "country[T.ECU]   388.9111   1165.512      0.334      0.739   -1895.894    2673.716\n",
       "country[T.EGY] -1025.2525   1165.512     -0.880      0.379   -3310.057    1259.552\n",
       "country[T.ESP]  1.012e+04   1165.512      8.685      0.000    7837.358    1.24e+04\n",
       "country[T.FIN]  1.331e+04   1165.512     11.421      0.000     1.1e+04    1.56e+04\n",
       "country[T.FRA]  1.531e+04   1165.512     13.140      0.000     1.3e+04    1.76e+04\n",
       "country[T.GBR]  1.871e+04   1165.512     16.057      0.000    1.64e+04     2.1e+04\n",
       "country[T.GHA] -2258.2274   1165.512     -1.938      0.053   -4543.032      26.578\n",
       "country[T.GIN] -2298.8179   1165.512     -1.972      0.049   -4583.623     -14.013\n",
       "country[T.GRC]  8732.4444   1165.512      7.492      0.000    6447.639     1.1e+04\n",
       "country[T.GTM]  -852.3551   1165.512     -0.731      0.465   -3137.160    1432.450\n",
       "country[T.HRV]  4721.6359   1165.512      4.051      0.000    2436.831    7006.441\n",
       "country[T.IND] -2070.5604   1165.512     -1.777      0.076   -4355.365     214.244\n",
       "country[T.IRL]  1.472e+04   1165.512     12.626      0.000    1.24e+04     1.7e+04\n",
       "country[T.ITA]  1.193e+04   1165.512     10.236      0.000    9645.580    1.42e+04\n",
       "country[T.JOR]    53.8011   1165.512      0.046      0.963   -2231.004    2338.606\n",
       "country[T.JPN]  1.444e+04   1165.512     12.388      0.000    1.22e+04    1.67e+04\n",
       "country[T.KAZ]  -755.6801   1165.512     -0.648      0.517   -3040.485    1529.125\n",
       "country[T.KEN] -2475.5099   1165.512     -2.124      0.034   -4760.315    -190.705\n",
       "country[T.KGZ] -1221.6107   1165.512     -1.048      0.295   -3506.416    1063.194\n",
       "country[T.KOR]  1.223e+04   1165.512     10.496      0.000    9947.935    1.45e+04\n",
       "country[T.LUX]  2.222e+04   1165.512     19.067      0.000    1.99e+04    2.45e+04\n",
       "country[T.LVA]  3769.6447   1165.512      3.234      0.001    1484.840    6054.450\n",
       "country[T.MAR]  -657.2293   1165.512     -0.564      0.573   -2942.034    1627.576\n",
       "country[T.MDG] -2649.5928   1165.512     -2.273      0.023   -4934.398    -364.788\n",
       "country[T.MKD]  1604.5664   1165.512      1.377      0.169    -680.239    3889.371\n",
       "country[T.MLI] -2313.7549   1165.512     -1.985      0.047   -4598.560     -28.950\n",
       "country[T.MNG]  -656.7425   1165.512     -0.563      0.573   -2941.547    1628.062\n",
       "country[T.MWI] -2080.5645   1165.512     -1.785      0.074   -4365.369     204.240\n",
       "country[T.MYS]  3011.5125   1165.512      2.584      0.010     726.708    5296.317\n",
       "country[T.NGA] -2302.9745   1165.512     -1.976      0.048   -4587.779     -18.170\n",
       "country[T.NLD]  1.473e+04   1165.512     12.641      0.000    1.24e+04     1.7e+04\n",
       "country[T.NOR]  1.949e+04   1165.512     16.721      0.000    1.72e+04    2.18e+04\n",
       "country[T.NPL] -2080.4383   1165.512     -1.785      0.074   -4365.243     204.367\n",
       "country[T.PAK] -2106.9906   1165.512     -1.808      0.071   -4391.796     177.814\n",
       "country[T.PAN]  2140.3095   1165.512      1.836      0.066    -144.495    4425.114\n",
       "country[T.PER]   335.7034   1165.512      0.288      0.773   -1949.101    2620.508\n",
       "country[T.PRT]  7103.8455   1165.512      6.095      0.000    4819.041    9388.650\n",
       "country[T.RUS]  4161.9408   1165.512      3.571      0.000    1877.136    6446.746\n",
       "country[T.SVK]  3101.7500   1165.512      2.661      0.008     816.945    5386.555\n",
       "country[T.SVN]  9111.1776   1165.512      7.817      0.000    6826.373    1.14e+04\n",
       "country[T.SWE]  1.319e+04   1165.512     11.316      0.000    1.09e+04    1.55e+04\n",
       "country[T.TWN]  1.351e+04   1165.512     11.588      0.000    1.12e+04    1.58e+04\n",
       "country[T.TZA] -2406.0629   1165.512     -2.064      0.039   -4690.868    -121.258\n",
       "country[T.UGA] -2007.6236   1165.512     -1.723      0.085   -4292.429     277.181\n",
       "country[T.USA]  2.251e+04   1165.512     19.312      0.000    2.02e+04    2.48e+04\n",
       "country[T.VNM] -1617.0559   1165.512     -1.387      0.165   -3901.861     667.749\n",
       "country[T.ZAF]  2623.0750   1165.512      2.251      0.024     338.270    4907.880\n",
       "==============================================================================\n",
       "Omnibus:                     7040.441   Durbin-Watson:                   0.666\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           999879.108\n",
       "Skew:                           5.574   Prob(JB):                         0.00\n",
       "Kurtosis:                      63.703   Cond. No.                         64.0\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anova_Q1 = ols('income~country', data=Q1_ANOVA).fit()\n",
    "anova_Q1.summary()\n",
    "\n",
    "# why income~country ?  income is the dependent variable Y, country is the X "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d66a5889",
   "metadata": {},
   "source": [
    "#### H0 pour ce modèle: le pays (country) n'a pas d'impact sur les revenus (income), ctd. les variances de income de ces différents pays sont similaires / qui que ce soit le pays, les vairances de income sont identiques. \n",
    "\n",
    "##### F-stat est petite et La Prob(F-statistic)  - est 0.00, largement inférieure à 5 %. \n",
    "##### On rejette donc l'hypothèse H0 (égalité des variances), il existe de grande diversité en terme de variance de différents pays, donc le pays a de l'impact sur les revenus. \n",
    "\n",
    "-----\n",
    "\n",
    "##### R-squared = 0.45 => la variance expliquée par ce modèle est 45%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8593e02d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>df</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>country</th>\n",
       "      <td>3.554930e+11</td>\n",
       "      <td>62.0</td>\n",
       "      <td>84.418151</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>4.236227e+11</td>\n",
       "      <td>6237.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                sum_sq      df          F  PR(>F)\n",
       "country   3.554930e+11    62.0  84.418151     0.0\n",
       "Residual  4.236227e+11  6237.0        NaN     NaN"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analyse_country=sm.stats.anova_lm(anova_Q1, typ=2) \n",
    "analyse_country"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "a60afb97",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sur les revenus, la variance expliquée par pays est: 45.627751738907044 %\n"
     ]
    }
   ],
   "source": [
    "SCE_country=analyse_country.iloc[0,0]\n",
    "SCR=analyse_country.iloc[1,0]\n",
    "R2_country=SCE_country/(SCE_country+SCR)\n",
    "print('sur les revenus, la variance expliquée par pays est:', R2_country*100, '%')        \n",
    "\n",
    "#the calculation result resonate with the anova_Q1.summary() "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23b9b2d0",
   "metadata": {},
   "source": [
    "## M4.2  Linear regression - multi variable\n",
    "\n",
    "Régression linéaire avec 3 variables :\n",
    "\n",
    "- le revenu des parents ;\n",
    "- le revenu moyen du pays dans lequel habite le prospect ;\n",
    "- l'indice de Gini calculé sur les revenus des habitants du pays en question\n",
    "\n",
    "Pour chacune des régressions suivantes, vous testerez 2 version : l'une en exprimant **le revenu moyen (mean of income by country)** du pays et **les revenus (parents & enfants) en logarithme (In of incomes)**, l'autre en les laissant tels quels. \n",
    "Vous choisirez la version la plus performante pour répondre aux question.\n",
    "Pour chaque version: \n",
    "\n",
    "Appliquez une **régression linéaire** multi variables sur vos données, en n’incluant comme variables explicatives\n",
    "uniquement **le revenu moyen** du pays de l’individu et l’indice de **Gini** du pays de l’individu. Quel est le pourcentage de variance expliquée par votre modèle ?\n",
    "Selon ce modèle, donnez la décomposition de variance totale expliquée par :\n",
    "- le **pays de naissance (ie. le revenu moyen et l’indice de Gini)**  --- facteur fixe\n",
    "- les autres facteurs non considérés dans le modèle (efforts, chance, etc.) --- facteurs aléatoires\n",
    "\n",
    "- Améliorez le modèle précédent en incluant maintenant la **classe de revenu des parents**/c_i_parent/proba_quantile_parents. Quel est le pourcentage de variance expliquée par ce nouveau modèle ?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a6d4576",
   "metadata": {},
   "source": [
    "# Multi-linear regressions\n",
    "## Verification of the assumptions (conditions de validité) for linear regression\n",
    "- il n'existe pas grande colinéarité des variables explicatives  \n",
    "- normalité des résidus  \n",
    "- homosétasticité des résidus: ctd les résidus ont la même variance quel que soit le groupe considéré, ou quelle que soit la valeur de la variable explicative considérée\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "8f54a7ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        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>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>country</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income</th>\n",
       "      <th>gdpppp</th>\n",
       "      <th>proba_quantile_parent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6300</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12600</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18900</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25200</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            gini  IGEincome country  quantile_child  nb_quantiles     income  \\\n",
       "0      31.408889   0.815874     ALB               1           100  728.89795   \n",
       "6300   31.408889   0.815874     ALB               1           100  728.89795   \n",
       "12600  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "18900  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "25200  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "\n",
       "       gdpppp  proba_quantile_parent  \n",
       "0      7297.0                      1  \n",
       "6300   7297.0                      1  \n",
       "12600  7297.0                      1  \n",
       "18900  7297.0                      1  \n",
       "25200  7297.0                      1  "
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2 = Co500.copy()\n",
    "Q2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7c48ec58",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. vérifiez la collinéarité des variables explicatives\n",
    "Q2.corr()\n",
    "sns.heatmap(Q2.corr(),linewidths=0.1)\n",
    "plt.savefig('bi_heatmap_colinearity_Q2.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f06ad64",
   "metadata": {},
   "source": [
    "Parmi les variables explicatives qu'on va employer [income, gdpppp, gini], on constate qu'il existe la forte colinéarité entre gdpppp et gini, gdpppp et income, ainsi on enlève gdpppp dans ce cas. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "0e8d076c",
   "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>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income</th>\n",
       "      <th>proba_quantile_parent</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>gini</th>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>6.158294e-01</td>\n",
       "      <td>1.039667e-14</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.314331</td>\n",
       "      <td>-1.052292e-14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IGEincome</th>\n",
       "      <td>6.158294e-01</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>-2.289996e-16</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.382558</td>\n",
       "      <td>-1.404345e-15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>quantile_child</th>\n",
       "      <td>1.039667e-14</td>\n",
       "      <td>-2.289996e-16</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.433898</td>\n",
       "      <td>4.182193e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nb_quantiles</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>income</th>\n",
       "      <td>-3.143313e-01</td>\n",
       "      <td>-3.825577e-01</td>\n",
       "      <td>4.338985e-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.675381e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>proba_quantile_parent</th>\n",
       "      <td>-1.052292e-14</td>\n",
       "      <td>-1.404345e-15</td>\n",
       "      <td>4.182193e-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.167538</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                               gini     IGEincome  quantile_child  \\\n",
       "gini                   1.000000e+00  6.158294e-01    1.039667e-14   \n",
       "IGEincome              6.158294e-01  1.000000e+00   -2.289996e-16   \n",
       "quantile_child         1.039667e-14 -2.289996e-16    1.000000e+00   \n",
       "nb_quantiles                    NaN           NaN             NaN   \n",
       "income                -3.143313e-01 -3.825577e-01    4.338985e-01   \n",
       "proba_quantile_parent -1.052292e-14 -1.404345e-15    4.182193e-01   \n",
       "\n",
       "                       nb_quantiles    income  proba_quantile_parent  \n",
       "gini                            NaN -0.314331          -1.052292e-14  \n",
       "IGEincome                       NaN -0.382558          -1.404345e-15  \n",
       "quantile_child                  NaN  0.433898           4.182193e-01  \n",
       "nb_quantiles                    NaN       NaN                    NaN  \n",
       "income                          NaN  1.000000           1.675381e-01  \n",
       "proba_quantile_parent           NaN  0.167538           1.000000e+00  "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2=Q2.drop('gdpppp',axis=1)\n",
    "Q2.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "42aa43bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 63 entries, 0 to 62\n",
      "Data columns (total 2 columns):\n",
      " #   Column   Non-Null Count  Dtype  \n",
      "---  ------   --------------  -----  \n",
      " 0   country  63 non-null     object \n",
      " 1   income   63 non-null     float64\n",
      "dtypes: float64(1), object(1)\n",
      "memory usage: 1.1+ KB\n",
      "None\n"
     ]
    },
    {
     "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>country</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ALB</td>\n",
       "      <td>2994.829902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>AUT</td>\n",
       "      <td>16637.600204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>BEL</td>\n",
       "      <td>15024.614176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>BGD</td>\n",
       "      <td>998.692409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>BIH</td>\n",
       "      <td>6334.687311</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  country        income\n",
       "0     ALB   2994.829902\n",
       "1     AUT  16637.600204\n",
       "2     BEL  15024.614176\n",
       "3     BGD    998.692409\n",
       "4     BIH   6334.687311"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "income_mean_country = Q2.groupby(['country']).mean().reset_index()[['country','income']]\n",
    "print(income_mean_country.info())\n",
    "income_mean_country.head()\n",
    "\n",
    "# overall mean income for the 100 quantiles as a whole country by country"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "de8c1d6a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 3150000 entries, 0 to 3149999\n",
      "Data columns (total 8 columns):\n",
      " #   Column                 Dtype  \n",
      "---  ------                 -----  \n",
      " 0   gini                   float64\n",
      " 1   IGEincome              float64\n",
      " 2   country                object \n",
      " 3   quantile_child         int64  \n",
      " 4   nb_quantiles           int64  \n",
      " 5   income_normal          float64\n",
      " 6   proba_quantile_parent  int64  \n",
      " 7   income_mean            float64\n",
      "dtypes: float64(4), int64(3), object(1)\n",
      "memory usage: 216.3+ MB\n",
      "None\n"
     ]
    },
    {
     "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>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>country</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income_normal</th>\n",
       "      <th>proba_quantile_parent</th>\n",
       "      <th>income_mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        gini  IGEincome country  quantile_child  nb_quantiles  income_normal  \\\n",
       "0  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "1  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "2  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "3  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "4  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "\n",
       "   proba_quantile_parent  income_mean  \n",
       "0                      1  2994.829902  \n",
       "1                      1  2994.829902  \n",
       "2                      1  2994.829902  \n",
       "3                      1  2994.829902  \n",
       "4                      1  2994.829902  "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Linear_reg=Q2.merge(income_mean_country, \n",
    "                         left_on=['country'], \n",
    "                         right_on=['country'],\n",
    "                        suffixes=('_normal', '_mean'))\n",
    "\n",
    "print(Linear_reg.info())\n",
    "Linear_reg.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab8d1646",
   "metadata": {},
   "source": [
    "## Multi linear regression_2 variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "cad7ae7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>income_normal</td>  <th>  R-squared:         </th>  <td>   0.456</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.456</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>1.322e+06</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 11 Mar 2022</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>21:37:33</td>     <th>  Log-Likelihood:    </th> <td>-3.2857e+07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>3150000</td>     <th>  AIC:               </th>  <td>6.571e+07</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>3149997</td>     <th>  BIC:               </th>  <td>6.571e+07</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>   <td>-9.976e-09</td> <td>   27.758</td> <td>-3.59e-10</td> <td> 1.000</td> <td>  -54.406</td> <td>   54.406</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>income_mean</th> <td>    1.0000</td> <td>    0.001</td> <td> 1439.091</td> <td> 0.000</td> <td>    0.999</td> <td>    1.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>gini</th>        <td> 7.773e-11</td> <td>    0.631</td> <td> 1.23e-10</td> <td> 1.000</td> <td>   -1.237</td> <td>    1.237</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>3495810.153</td> <th>  Durbin-Watson:     </th>   <td>   0.001</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>   <td> 0.000</td>    <th>  Jarque-Bera (JB):  </th> <td>499939554.028</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>            <td> 5.574</td>    <th>  Prob(JB):          </th>   <td>    0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>        <td>63.703</td>    <th>  Cond. No.          </th>   <td>6.75e+04</td>   \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 6.75e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:          income_normal   R-squared:                       0.456\n",
       "Model:                            OLS   Adj. R-squared:                  0.456\n",
       "Method:                 Least Squares   F-statistic:                 1.322e+06\n",
       "Date:                Fri, 11 Mar 2022   Prob (F-statistic):               0.00\n",
       "Time:                        21:37:33   Log-Likelihood:            -3.2857e+07\n",
       "No. Observations:             3150000   AIC:                         6.571e+07\n",
       "Df Residuals:                 3149997   BIC:                         6.571e+07\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================\n",
       "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "Intercept   -9.976e-09     27.758  -3.59e-10      1.000     -54.406      54.406\n",
       "income_mean     1.0000      0.001   1439.091      0.000       0.999       1.001\n",
       "gini         7.773e-11      0.631   1.23e-10      1.000      -1.237       1.237\n",
       "==============================================================================\n",
       "Omnibus:                  3495810.153   Durbin-Watson:                   0.001\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):        499939554.028\n",
       "Skew:                           5.574   Prob(JB):                         0.00\n",
       "Kurtosis:                      63.703   Cond. No.                     6.75e+04\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 6.75e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_multi = smf.ols('income_normal~income_mean+gini', data=Linear_reg).fit()\n",
    "reg_multi.summary()\n",
    "\n",
    "# linear reg with multiple explicative variables : 'income_mean+gini' explain income_normal of every quantile"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "426c50f9",
   "metadata": {},
   "source": [
    "##### - P-value of income_mean is 0, thus we reject H0, therefore we conclude that income_mean has impact on income_normal (income quantile by quantile) \n",
    "##### - P-value of gini is 1 (100%), thus we don't reject H0, therefore we conclude that gini has NO impact on income_normal (income quantile by quantile) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "409b2cce",
   "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": [
    "# 1. vérifier la normalité des résidus du model reg_multi \n",
    "\n",
    "stats.probplot(reg_multi.resid, dist=\"norm\", plot= plt)\n",
    "plt.title(\"reg_multi residuals Q-Q Plot\")\n",
    "plt.savefig(\"reg_multi_Residus_qqplot.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f910b590",
   "metadata": {},
   "source": [
    "#### Grande superposition de bleue avec ligne rouge => condition normalité est valide. \n",
    "\n",
    "A noter qu'ici on ne stipule pas une normalité au sense stricte des résidus "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "ccc80dbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Lagrange multiplier statistic', 81352.84092300001),\n",
       " ('p-value', 0.0),\n",
       " ('f-value', 41754.75243071066),\n",
       " ('f p-value', 0.0)]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#2. vérifier homosétasticité des résidus par statsmodels -  reg_multi\n",
    "from statsmodels.compat import lzip\n",
    "import statsmodels\n",
    "\n",
    "name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value']\n",
    "\n",
    "test = sms.het_breuschpagan(reg_multi.resid, reg_multi.model.exog)\n",
    "\n",
    "lzip(name, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "742f7b35",
   "metadata": {},
   "source": [
    "#### H0: présence de l'homoscétasticité des résidus\n",
    "#### Lagrange multiplier statistic = 81352 très grand et le correspondant P-value = 0.0, <0.5%, rejet de H0 au niveau de test 0.5%, donc au niveau de test 0.5%, il n'existe pas de l'homoscétasticité (présence de hétéroscétasticité) pour les résidus de ce modèle reg_multi\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "89f1f14a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "389557848791378.1\n"
     ]
    },
    {
     "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>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>income_mean</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.777465e+14</td>\n",
       "      <td>1.777465e+14</td>\n",
       "      <td>2.643394e+06</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gini</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5.456975e-13</td>\n",
       "      <td>5.456975e-13</td>\n",
       "      <td>8.115455e-21</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>3149997.0</td>\n",
       "      <td>2.118114e+14</td>\n",
       "      <td>6.724177e+07</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    df        sum_sq       mean_sq             F  PR(>F)\n",
       "income_mean        1.0  1.777465e+14  1.777465e+14  2.643394e+06     0.0\n",
       "gini               1.0  5.456975e-13  5.456975e-13  8.115455e-21     1.0\n",
       "Residual     3149997.0  2.118114e+14  6.724177e+07           NaN     NaN"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analyse1=sm.stats.anova_lm(reg_multi, typ=1)\n",
    "print(sum(analyse1['sum_sq']) )                          #SCT\n",
    "analyse1\n",
    "\n",
    "# type 1 suppose that there's interaction effects among independant variables , and the first-order variable is more important than the following variables "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "75a75113",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La variance expliquée par income_mean (soit le revenu moyen) du pays est 45.63 %\n"
     ]
    }
   ],
   "source": [
    "SCE_income=analyse1.iloc[0,1]                                                 #SCR (Somme des Carrés des Résidus) \n",
    "SCE_gini=analyse1.iloc[1,1]\n",
    "SCR=analyse1.iloc[2,1]                                                                 #SCR (Somme des Carrés Expliquées) \n",
    "\n",
    "R2_income_mean=SCE_income/sum(analyse1['sum_sq'])                # sum(analyse1['sum_sq']) = SCT  = SCE (variance expliquée par toutes les variables du modèle ou seulement par la variable en question) + SCR \n",
    "\n",
    "print(\"La variance expliquée par income_mean (soit le revenu moyen) du pays est\", round(R2_income_mean*100, 2), '%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "89546b03",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La variance expliquée par indice Gini du pays: 0.0 %\n"
     ]
    }
   ],
   "source": [
    "R2_gini=SCE_gini/sum(analyse1['sum_sq']) \n",
    "print('La variance expliquée par indice Gini du pays:', round( R2_gini*100, 2), '%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "aeadee31",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La variance expliquée par les autres facteurs non-considérées dans modèle: 54.37 %\n"
     ]
    }
   ],
   "source": [
    "R2_R=SCR/sum(analyse1['sum_sq'])\n",
    "print('La variance expliquée par les autres facteurs non-considérées dans modèle:', round(R2_R*100, 2), '%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "6c40f558",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4562775173896536"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R2_income_mean + R2_gini\n",
    "\n",
    "#verification ok"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c24d38a0",
   "metadata": {},
   "source": [
    "\n",
    "    On en conclut que:\n",
    "    la variance expliquée par le revenu moyen est environ 45.6%;   \n",
    "    quasi zéro par indice de Gini; \n",
    "    et par les autres facteurs non-incluses dans ce modèle est 54.4%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "210c3556",
   "metadata": {},
   "source": [
    "<font color = \"#343EE4\">\n",
    "      - Comment réduire hétéroscédasticité ? \n",
    "      - Ici dans notre cas on peut transformer les variables en logarithme. </font>\n",
    "https://www.statology.org/breusch-pagan-test-python/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c52d0ddb",
   "metadata": {},
   "source": [
    "## Multi linear regression_2_log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "e5080403",
   "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>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>country</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income_normal</th>\n",
       "      <th>proba_quantile_parent</th>\n",
       "      <th>income_mean</th>\n",
       "      <th>log_income</th>\n",
       "      <th>log_income_mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        gini  IGEincome country  quantile_child  nb_quantiles  income_normal  \\\n",
       "0  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "1  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "2  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "3  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "4  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "\n",
       "   proba_quantile_parent  income_mean  log_income  log_income_mean  \n",
       "0                      1  2994.829902    6.591534         8.004643  \n",
       "1                      1  2994.829902    6.591534         8.004643  \n",
       "2                      1  2994.829902    6.591534         8.004643  \n",
       "3                      1  2994.829902    6.591534         8.004643  \n",
       "4                      1  2994.829902    6.591534         8.004643  "
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Linear_reg_log=Linear_reg.copy()\n",
    "Linear_reg_log['log_income']=np.log(Linear_reg_log['income_normal'])\n",
    "Linear_reg_log['log_income_mean']=np.log(Linear_reg_log['income_mean'])\n",
    "Linear_reg_log.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47250e0a",
   "metadata": {},
   "source": [
    "Multicollinearity is a statistical concept where several independent variables in a model are correlated.\n",
    "\n",
    "Two variables are considered to be perfectly collinear if their correlation coefficient is +/- 1.0.\n",
    "\n",
    "Multicollinearity among independent variables will result in less reliable statistical inferences.\n",
    "\n",
    "It is better to use independent variables that are not correlated or repetitive when building multiple regression models that use two or more variables.\n",
    "\n",
    "The existence of multicollinearity in a data set can lead to less reliable results due to larger standard errors.\n",
    "https://www.investopedia.com/terms/m/multicollinearity.asp#:~:text=Multicollinearity%20is%20a%20statistical%20concept,in%20less%20reliable%20statistical%20inferences\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "3dd27e5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Linear_reg.corr()\n",
    "sns.heatmap(Linear_reg.corr(),linewidths=.1)\n",
    "plt.savefig('bi_heatmap_colinearity.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "d0befa24",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# . vérifiez la multicolinéarité des variables explicatives\n",
    "Linear_reg_log.corr()\n",
    "sns.heatmap(Linear_reg_log.corr(),linewidths=.1)\n",
    "plt.savefig('bi_heatmap_colinearity_log.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "ba8f5507",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>log_income</td>    <th>  R-squared:         </th>  <td>   0.754</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.754</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>4.834e+06</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 11 Mar 2022</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>21:49:06</td>     <th>  Log-Likelihood:    </th> <td>-3.4190e+06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>3150000</td>     <th>  AIC:               </th>  <td>6.838e+06</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>3149997</td>     <th>  BIC:               </th>  <td>6.838e+06</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "         <td></td>            <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>       <td>    0.6782</td> <td>    0.005</td> <td>  149.201</td> <td> 0.000</td> <td>    0.669</td> <td>    0.687</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_income_mean</th> <td>    0.9707</td> <td>    0.000</td> <td> 2597.477</td> <td> 0.000</td> <td>    0.970</td> <td>    0.971</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>gini</th>            <td>   -0.0180</td> <td> 5.49e-05</td> <td> -326.925</td> <td> 0.000</td> <td>   -0.018</td> <td>   -0.018</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>320818.887</td> <th>  Durbin-Watson:     </th>  <td>   0.001</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>   <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>1914508.355</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>            <td>-0.308</td>   <th>  Prob(JB):          </th>  <td>    0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>        <td> 6.769</td>   <th>  Cond. No.          </th>  <td>    452.</td>  \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:             log_income   R-squared:                       0.754\n",
       "Model:                            OLS   Adj. R-squared:                  0.754\n",
       "Method:                 Least Squares   F-statistic:                 4.834e+06\n",
       "Date:                Fri, 11 Mar 2022   Prob (F-statistic):               0.00\n",
       "Time:                        21:49:06   Log-Likelihood:            -3.4190e+06\n",
       "No. Observations:             3150000   AIC:                         6.838e+06\n",
       "Df Residuals:                 3149997   BIC:                         6.838e+06\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "===================================================================================\n",
       "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------\n",
       "Intercept           0.6782      0.005    149.201      0.000       0.669       0.687\n",
       "log_income_mean     0.9707      0.000   2597.477      0.000       0.970       0.971\n",
       "gini               -0.0180   5.49e-05   -326.925      0.000      -0.018      -0.018\n",
       "==============================================================================\n",
       "Omnibus:                   320818.887   Durbin-Watson:                   0.001\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1914508.355\n",
       "Skew:                          -0.308   Prob(JB):                         0.00\n",
       "Kurtosis:                       6.769   Cond. No.                         452.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_multi_2 = smf.ols('log_income~log_income_mean+gini', data=Linear_reg_log).fit()\n",
    "reg_multi_2.summary()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "26d10c3f",
   "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": [
    "# 1. vérifier la normalité des résidus du model reg_multi_2\n",
    "\n",
    "stats.probplot(reg_multi_2.resid, dist=\"norm\", plot= plt)\n",
    "plt.title(\"reg_multi_2 Residuals Q-Q Plot\")\n",
    "\n",
    "plt.savefig(\"reg_multi_2_Residus_qqplot.png\")\n",
    "\n",
    "# normalité des résidus valide "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "8a239abb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Lagrange multiplier statistic', 145979.22385892624),\n",
       " ('p-value', 0.0),\n",
       " ('f-value', 76536.44090448711),\n",
       " ('f p-value', 0.0)]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2. vérifier homosétasticité des résidus par statsmodels -  reg_multi_2\n",
    "name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value']\n",
    "test = sms.het_breuschpagan(reg_multi_2.resid, reg_multi_2.model.exog)\n",
    "lzip(name, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d80cc04e",
   "metadata": {},
   "source": [
    "#### P-value est 0, <0.5%, rejet de H0, donc il n'existe pas de l'homosétasticité (présence de l'hétéroscétasticité) pour les résidus de ce modèle reg_multi_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "7cce1117",
   "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>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>log_income_mean</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.907014e+06</td>\n",
       "      <td>4.907014e+06</td>\n",
       "      <td>9.561381e+06</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gini</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5.485212e+04</td>\n",
       "      <td>5.485212e+04</td>\n",
       "      <td>1.068801e+05</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>3149997.0</td>\n",
       "      <td>1.616616e+06</td>\n",
       "      <td>5.132119e-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        df        sum_sq       mean_sq             F  PR(>F)\n",
       "log_income_mean        1.0  4.907014e+06  4.907014e+06  9.561381e+06     0.0\n",
       "gini                   1.0  5.485212e+04  5.485212e+04  1.068801e+05     0.0\n",
       "Residual         3149997.0  1.616616e+06  5.132119e-01           NaN     NaN"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analyse_2=sm.stats.anova_lm(reg_multi_2, typ=1)\n",
    "analyse_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "331df505",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La variance expliquée par revenue moyen en log (log_income_mean) est de : 74.59189072396639 %\n"
     ]
    }
   ],
   "source": [
    "SCE_log_income_mean=analyse_2.iloc[0,1]\n",
    "SCE_gini=analyse_2.iloc[1,1]\n",
    "SCR_log=analyse_2.iloc[2,1]\n",
    "\n",
    "R2_log_income_mean=SCE_log_income_mean/sum(analyse_2['sum_sq'])\n",
    "print(\"La variance expliquée par revenue moyen en log (log_income_mean) est de :\", R2_log_income_mean*100,'%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "6a211b88",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La variance expliquée par Gini du pays: 0.833811129197848 %\n"
     ]
    }
   ],
   "source": [
    "R2_gini2=SCE_gini/sum(analyse_2['sum_sq'])\n",
    "print('La variance expliquée par Gini du pays:', R2_gini2*100, '%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "5b571287",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La variance expliquée par les résiduels:  24.57429814683577 %\n"
     ]
    }
   ],
   "source": [
    "R2_SCR2 = SCR_log/sum(analyse_2['sum_sq'])\n",
    "print('La variance expliquée par les résiduels: ', R2_SCR2*100, '%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "71c8953d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7542570185316423"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#verification \n",
    "\n",
    "R2_log_income_mean+ R2_gini2                    # result equals to the R-squared, ok "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "441ddb97",
   "metadata": {},
   "source": [
    "    On en conclut que la variance expliquée par le revenu moyen en log est environ 74.6%; \n",
    "    0.8 % par indice de Gini; \n",
    "    et par les autres facteurs non-incluses dans ce modèle est 24.6%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ec197b3",
   "metadata": {},
   "source": [
    "### En incluant les classes de revenus des parents dans les variables explicatives:\n",
    "\n",
    "## Multi linear regression_3 variables explicatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "167da579",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>      <td>income_normal</td>  <th>  R-squared:         </th>  <td>   0.484</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.484</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>9.862e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 14 Mar 2022</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:38:31</td>     <th>  Log-Likelihood:    </th> <td>-3.2774e+07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>3150000</td>     <th>  AIC:               </th>  <td>6.555e+07</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>3149996</td>     <th>  BIC:               </th>  <td>6.555e+07</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>Intercept</th>             <td>-3259.4773</td> <td>   28.155</td> <td> -115.768</td> <td> 0.000</td> <td>-3314.661</td> <td>-3204.294</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>income_mean</th>           <td>    1.0000</td> <td>    0.001</td> <td> 1477.739</td> <td> 0.000</td> <td>    0.999</td> <td>    1.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>gini</th>                  <td> 7.824e-11</td> <td>    0.614</td> <td> 1.27e-10</td> <td> 1.000</td> <td>   -1.204</td> <td>    1.204</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>proba_quantile_parent</th> <td>   64.5441</td> <td>    0.156</td> <td>  414.085</td> <td> 0.000</td> <td>   64.239</td> <td>   64.850</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>3537135.379</td> <th>  Durbin-Watson:     </th>   <td>   0.003</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>   <td> 0.000</td>    <th>  Jarque-Bera (JB):  </th> <td>540107613.415</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>            <td> 5.668</td>    <th>  Prob(JB):          </th>   <td>    0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>        <td>66.140</td>    <th>  Cond. No.          </th>   <td>7.03e+04</td>   \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 7.03e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:          income_normal   R-squared:                       0.484\n",
       "Model:                            OLS   Adj. R-squared:                  0.484\n",
       "Method:                 Least Squares   F-statistic:                 9.862e+05\n",
       "Date:                Mon, 14 Mar 2022   Prob (F-statistic):               0.00\n",
       "Time:                        13:38:31   Log-Likelihood:            -3.2774e+07\n",
       "No. Observations:             3150000   AIC:                         6.555e+07\n",
       "Df Residuals:                 3149996   BIC:                         6.555e+07\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=========================================================================================\n",
       "                            coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------------\n",
       "Intercept             -3259.4773     28.155   -115.768      0.000   -3314.661   -3204.294\n",
       "income_mean               1.0000      0.001   1477.739      0.000       0.999       1.001\n",
       "gini                   7.824e-11      0.614   1.27e-10      1.000      -1.204       1.204\n",
       "proba_quantile_parent    64.5441      0.156    414.085      0.000      64.239      64.850\n",
       "==============================================================================\n",
       "Omnibus:                  3537135.379   Durbin-Watson:                   0.003\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):        540107613.415\n",
       "Skew:                           5.668   Prob(JB):                         0.00\n",
       "Kurtosis:                      66.140   Cond. No.                     7.03e+04\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 7.03e+04. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_multi_3 = smf.ols('income_normal~income_mean+gini+proba_quantile_parent', data=Linear_reg_log).fit()\n",
    "reg_multi_3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "cffbc190",
   "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": [
    "# 1. vérifier la normalité des résidus du model reg_multi_3\n",
    "\n",
    "stats.probplot(reg_multi_3.resid, dist=\"norm\", plot= plt)\n",
    "plt.title(\"reg_multi_3 Residuals Q-Q Plot\")\n",
    "plt.savefig(\"reg_multi_3 Residus_qqplot.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "79dbe12d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Lagrange multiplier statistic', 90355.6983633005),\n",
       " ('p-value', 0.0),\n",
       " ('f-value', 31007.971337207444),\n",
       " ('f p-value', 0.0)]"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2. vérifier homosétasticité des résidus par statsmodels -  reg_multi_3\n",
    "name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value']\n",
    "test = sms.het_breuschpagan(reg_multi_3.resid, reg_multi_3.model.exog)\n",
    "lzip(name, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3a776cc",
   "metadata": {},
   "source": [
    "#### P-value est 0, <0.5%, rejet de H0, donc il n'existe pas de l'homosétasticité (présence de l'hétéroscétasticité) pour les résidus de ce modèle reg_multi_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "1cc1a08e",
   "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>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>income_mean</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.777465e+14</td>\n",
       "      <td>1.777465e+14</td>\n",
       "      <td>2.787283e+06</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gini</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5.456975e-13</td>\n",
       "      <td>5.456975e-13</td>\n",
       "      <td>8.557208e-21</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>proba_quantile_parent</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.093450e+13</td>\n",
       "      <td>1.093450e+13</td>\n",
       "      <td>1.714664e+05</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>3149996.0</td>\n",
       "      <td>2.008769e+14</td>\n",
       "      <td>6.377051e+07</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              df        sum_sq       mean_sq             F  \\\n",
       "income_mean                  1.0  1.777465e+14  1.777465e+14  2.787283e+06   \n",
       "gini                         1.0  5.456975e-13  5.456975e-13  8.557208e-21   \n",
       "proba_quantile_parent        1.0  1.093450e+13  1.093450e+13  1.714664e+05   \n",
       "Residual               3149996.0  2.008769e+14  6.377051e+07           NaN   \n",
       "\n",
       "                       PR(>F)  \n",
       "income_mean               0.0  \n",
       "gini                      1.0  \n",
       "proba_quantile_parent     0.0  \n",
       "Residual                  NaN  "
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analyse3=sm.stats.anova_lm(reg_multi_3, typ=1)\n",
    "analyse3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "76d71b67",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La variance expliquée par la classe de revenu des parents est de : 2.81 %\n",
      "La variance expliquée par le revenu moyen du pays est de : 45.63 %\n",
      "La variance expliquée par Gini du pays: 0.0 %\n",
      "La variance expliquée par les autres facteurs est de : 51.57 %\n"
     ]
    }
   ],
   "source": [
    "SCE_income_mean=analyse3.iloc[0,1]\n",
    "SCE_gini=analyse3.iloc[1,1]\n",
    "SCE_class_p=analyse3.iloc[2,1]\n",
    "SCR_3=analyse3.iloc[3,1]\n",
    "\n",
    "R2_classe_parent=SCE_class_p/sum(analyse3['sum_sq'])\n",
    "R2_income_mean = SCE_income_mean/sum(analyse3['sum_sq'])\n",
    "R2_SCR3 = SCR_3/sum(analyse3['sum_sq'])\n",
    "R2_gini3= SCE_gini/sum(analyse3['sum_sq'])\n",
    "\n",
    "print('La variance expliquée par la classe de revenu des parents est de :', round(R2_classe_parent*100,2), '%')\n",
    "print('La variance expliquée par le revenu moyen du pays est de :', round(R2_income_mean*100,2),'%')\n",
    "print('La variance expliquée par Gini du pays:', round(R2_gini3*100,2), '%')\n",
    "print('La variance expliquée par les autres facteurs est de :', round(R2_SCR3*100,2), '%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "abefd3b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4843465270857672"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R2_classe_parent + R2_income_mean  +  R2_gini3\n",
    "\n",
    "# verification ok"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5598c2ec",
   "metadata": {},
   "source": [
    "## Multi linear regression_3_log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "093b13a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>log_income</td>    <th>  R-squared:         </th>  <td>   0.798</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.798</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>4.141e+06</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 16 Mar 2022</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:00:02</td>     <th>  Log-Likelihood:    </th> <td>-3.1124e+06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>3150000</td>     <th>  AIC:               </th>  <td>6.225e+06</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>3149996</td>     <th>  BIC:               </th>  <td>6.225e+06</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>Intercept</th>             <td>    0.1511</td> <td>    0.004</td> <td>   36.195</td> <td> 0.000</td> <td>    0.143</td> <td>    0.159</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_income_mean</th>       <td>    0.9707</td> <td>    0.000</td> <td> 2863.028</td> <td> 0.000</td> <td>    0.970</td> <td>    0.971</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>gini</th>                  <td>   -0.0180</td> <td> 4.98e-05</td> <td> -360.348</td> <td> 0.000</td> <td>   -0.018</td> <td>   -0.018</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>proba_quantile_parent</th> <td>    0.0104</td> <td> 1.27e-05</td> <td>  822.800</td> <td> 0.000</td> <td>    0.010</td> <td>    0.010</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>348378.084</td> <th>  Durbin-Watson:     </th>  <td>   0.006</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>   <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>2099750.184</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>            <td>-0.363</td>   <th>  Prob(JB):          </th>  <td>    0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>        <td> 6.933</td>   <th>  Cond. No.          </th>  <td>    781.</td>  \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:             log_income   R-squared:                       0.798\n",
       "Model:                            OLS   Adj. R-squared:                  0.798\n",
       "Method:                 Least Squares   F-statistic:                 4.141e+06\n",
       "Date:                Wed, 16 Mar 2022   Prob (F-statistic):               0.00\n",
       "Time:                        11:00:02   Log-Likelihood:            -3.1124e+06\n",
       "No. Observations:             3150000   AIC:                         6.225e+06\n",
       "Df Residuals:                 3149996   BIC:                         6.225e+06\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "=========================================================================================\n",
       "                            coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------------\n",
       "Intercept                 0.1511      0.004     36.195      0.000       0.143       0.159\n",
       "log_income_mean           0.9707      0.000   2863.028      0.000       0.970       0.971\n",
       "gini                     -0.0180   4.98e-05   -360.348      0.000      -0.018      -0.018\n",
       "proba_quantile_parent     0.0104   1.27e-05    822.800      0.000       0.010       0.010\n",
       "==============================================================================\n",
       "Omnibus:                   348378.084   Durbin-Watson:                   0.006\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          2099750.184\n",
       "Skew:                          -0.363   Prob(JB):                         0.00\n",
       "Kurtosis:                       6.933   Cond. No.                         781.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_multi_3_log= smf.ols('log_income~log_income_mean+gini+proba_quantile_parent', data=Linear_reg_log).fit()\n",
    "reg_multi_3_log.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "a7ace2c0",
   "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": [
    "# 1. vérifier la normalité des résidus du model reg_multi_3_log\n",
    "\n",
    "stats.probplot(reg_multi_3_log.resid, dist=\"norm\", plot= plt)\n",
    "plt.title(\"reg_multi_3_log Residuals Q-Q Plot\")\n",
    "plt.savefig(\"reg_multi_3_log Residus_qqplot.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "91ca8f1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Lagrange multiplier statistic', 101338.99782132792),\n",
       " ('p-value', 0.0),\n",
       " ('f-value', 34902.474403579006),\n",
       " ('f p-value', 0.0)]"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2. vérifier homosétasticité des résidus par statsmodels -  reg_multi_3_log\n",
    "name = ['Lagrange multiplier statistic', 'p-value', 'f-value', 'f p-value']\n",
    "test = sms.het_breuschpagan(reg_multi_3_log.resid, reg_multi_3_log.model.exog)\n",
    "lzip(name, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f44a4eef",
   "metadata": {},
   "source": [
    "#### P-value = 0.0, <0.5%, rejet de H0 au niveau de test 0.5%, il n'existe pas de l'homosétasticité pour les résidus de ce modèle reg_multi_3_log"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "6bd6372d",
   "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>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>log_income_mean</th>\n",
       "      <td>1.0</td>\n",
       "      <td>4.907014e+06</td>\n",
       "      <td>4.907014e+06</td>\n",
       "      <td>1.161632e+07</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gini</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5.485212e+04</td>\n",
       "      <td>5.485212e+04</td>\n",
       "      <td>1.298508e+05</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>proba_quantile_parent</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.859814e+05</td>\n",
       "      <td>2.859814e+05</td>\n",
       "      <td>6.770005e+05</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>3149996.0</td>\n",
       "      <td>1.330634e+06</td>\n",
       "      <td>4.224242e-01</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              df        sum_sq       mean_sq             F  \\\n",
       "log_income_mean              1.0  4.907014e+06  4.907014e+06  1.161632e+07   \n",
       "gini                         1.0  5.485212e+04  5.485212e+04  1.298508e+05   \n",
       "proba_quantile_parent        1.0  2.859814e+05  2.859814e+05  6.770005e+05   \n",
       "Residual               3149996.0  1.330634e+06  4.224242e-01           NaN   \n",
       "\n",
       "                       PR(>F)  \n",
       "log_income_mean           0.0  \n",
       "gini                      0.0  \n",
       "proba_quantile_parent     0.0  \n",
       "Residual                  NaN  "
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analyse4=sm.stats.anova_lm(reg_multi_3_log, typ=1)\n",
    "analyse4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "506f3b5b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La variance expliquée par la classe de revenu des parents est de : 4.35 %\n",
      "La variance expliquée par le revenu moyen en log est de : 74.59 %\n",
      "La variance expliquée par lindice Gini est de : 0.83 %\n",
      "La variance expliquée par les autres facteurs est de : 20.23 %\n"
     ]
    }
   ],
   "source": [
    "SCE_income_mean_log=analyse4.iloc[0,1]\n",
    "SCE_gini4=analyse4.iloc[1,1]\n",
    "SCE_class_p=analyse4.iloc[2,1]\n",
    "SCR_4=analyse4.iloc[3,1]\n",
    "\n",
    "R2_classe_p=SCE_class_p/sum(analyse4['sum_sq'])\n",
    "R2_incomemean_log= SCE_income_mean_log/sum(analyse4['sum_sq'])\n",
    "R2_gini4 = SCE_gini4/sum(analyse4['sum_sq'])\n",
    "R2_SCR4 = SCR_4/sum(analyse4['sum_sq']) \n",
    "\n",
    "print('La variance expliquée par la classe de revenu des parents est de :', round(R2_classe_p*100,2), '%')\n",
    "print('La variance expliquée par le revenu moyen en log est de :', round(R2_incomemean_log*100,2), '%')\n",
    "print('La variance expliquée par lindice Gini est de :', round(R2_gini4*100,2), '%')\n",
    "print('La variance expliquée par les autres facteurs est de :', round(R2_SCR4*100,2), '%')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06e949e7",
   "metadata": {},
   "source": [
    "Autrement dit, en terme de logarithme, sur le revenu des enfants (log_income): \n",
    "\n",
    "    - la classe de revenu des parents a 4.35 % d'influence\n",
    "    - le revenu moyen du pays (en log) a 74.59 % d'influence\n",
    "    - indice Gini du pays en joue 0.83 % \n",
    "    - les autres facteurs aléatoires en jouent 20.23 % "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "f6b7bfeb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7977292596010751"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R2_gini4 +  R2_incomemean_log + R2_classe_p\n",
    "\n",
    "#verification ok "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "2cf8aaab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>log_income</td>    <th>  R-squared:         </th>  <td>   0.798</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.798</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>4.733e+06</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 16 Mar 2022</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:05:30</td>     <th>  Log-Likelihood:    </th> <td>-3.1124e+06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>3150000</td>     <th>  AIC:               </th>  <td>6.225e+06</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>3149996</td>     <th>  BIC:               </th>  <td>6.225e+06</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>HC3</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>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>             <td>    0.1511</td> <td>    0.005</td> <td>   31.607</td> <td> 0.000</td> <td>    0.142</td> <td>    0.160</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_income_mean</th>       <td>    0.9707</td> <td>    0.000</td> <td> 2777.395</td> <td> 0.000</td> <td>    0.970</td> <td>    0.971</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>gini</th>                  <td>   -0.0180</td> <td> 6.52e-05</td> <td> -275.243</td> <td> 0.000</td> <td>   -0.018</td> <td>   -0.018</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>proba_quantile_parent</th> <td>    0.0104</td> <td> 1.36e-05</td> <td>  767.066</td> <td> 0.000</td> <td>    0.010</td> <td>    0.010</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>348378.084</td> <th>  Durbin-Watson:     </th>  <td>   0.006</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>   <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>2099750.184</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>            <td>-0.363</td>   <th>  Prob(JB):          </th>  <td>    0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>        <td> 6.933</td>   <th>  Cond. No.          </th>  <td>    781.</td>  \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors are heteroscedasticity robust (HC3)"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             log_income   R-squared:                       0.798\n",
       "Model:                            OLS   Adj. R-squared:                  0.798\n",
       "Method:                 Least Squares   F-statistic:                 4.733e+06\n",
       "Date:                Wed, 16 Mar 2022   Prob (F-statistic):               0.00\n",
       "Time:                        11:05:30   Log-Likelihood:            -3.1124e+06\n",
       "No. Observations:             3150000   AIC:                         6.225e+06\n",
       "Df Residuals:                 3149996   BIC:                         6.225e+06\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:                  HC3                                         \n",
       "=========================================================================================\n",
       "                            coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------------\n",
       "Intercept                 0.1511      0.005     31.607      0.000       0.142       0.160\n",
       "log_income_mean           0.9707      0.000   2777.395      0.000       0.970       0.971\n",
       "gini                     -0.0180   6.52e-05   -275.243      0.000      -0.018      -0.018\n",
       "proba_quantile_parent     0.0104   1.36e-05    767.066      0.000       0.010       0.010\n",
       "==============================================================================\n",
       "Omnibus:                   348378.084   Durbin-Watson:                   0.006\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):          2099750.184\n",
       "Skew:                          -0.363   Prob(JB):                         0.00\n",
       "Kurtosis:                       6.933   Cond. No.                         781.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors are heteroscedasticity robust (HC3)\n",
       "\"\"\""
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# méthode fit() pour prendre en compte l'impact de hétéroscétasticité \n",
    "reg_multi_3_logfit= smf.ols('log_income~log_income_mean+gini+proba_quantile_parent', data=Linear_reg_log).fit(cov_type='HC3')\n",
    "reg_multi_3_logfit.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b3dfd42",
   "metadata": {},
   "source": [
    "<font color=\"purple\"> Le coefficient de régression indique dans quelle mesure la valeur d'une variable dépendante varie avec la variation de la valeur de la variable indépendante (aussi appelée variable explicative). \n",
    "\n",
    "L'intercept (= ordonnée à l'origine) est la valeur obtenue lorsque la variable indépendante vaut zéro (voir figure 1). </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "c6d069a4",
   "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>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>country</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income_normal</th>\n",
       "      <th>proba_quantile_parent</th>\n",
       "      <th>income_mean</th>\n",
       "      <th>log_income</th>\n",
       "      <th>log_income_mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        gini  IGEincome country  quantile_child  nb_quantiles  income_normal  \\\n",
       "0  31.408889   0.815874     ALB               1           100      728.89795   \n",
       "\n",
       "   proba_quantile_parent  income_mean  log_income  log_income_mean  \n",
       "0                      1  2994.829902    6.591534         8.004643  "
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Linear_reg_log.head(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "7cc81044",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize= (10,5))\n",
    "sns.scatterplot(data=Linear_reg_log, x=\"income_mean\", y=\"income_normal\")\n",
    "plt.title(\"scatter plot_assumption homoscetasticity check\")\n",
    "plt.savefig('P7M4_scatter plot_assumption homoscetasticity check.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd4629ed",
   "metadata": {},
   "source": [
    "## Si l'on fait linear regression sur l'échantillon d'un pays?\n",
    "Ici on prend l'exemple ALB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "c4f57cce",
   "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>gini</th>\n",
       "      <th>IGEincome</th>\n",
       "      <th>country</th>\n",
       "      <th>quantile_child</th>\n",
       "      <th>nb_quantiles</th>\n",
       "      <th>income</th>\n",
       "      <th>gdpppp</th>\n",
       "      <th>proba_quantile_parent</th>\n",
       "      <th>income_mean</th>\n",
       "      <th>log_income</th>\n",
       "      <th>log_income_mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6300</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12600</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18900</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25200</th>\n",
       "      <td>31.408889</td>\n",
       "      <td>0.815874</td>\n",
       "      <td>ALB</td>\n",
       "      <td>1</td>\n",
       "      <td>100</td>\n",
       "      <td>728.89795</td>\n",
       "      <td>7297.0</td>\n",
       "      <td>1</td>\n",
       "      <td>2994.829902</td>\n",
       "      <td>6.591534</td>\n",
       "      <td>8.004643</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            gini  IGEincome country  quantile_child  nb_quantiles     income  \\\n",
       "0      31.408889   0.815874     ALB               1           100  728.89795   \n",
       "6300   31.408889   0.815874     ALB               1           100  728.89795   \n",
       "12600  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "18900  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "25200  31.408889   0.815874     ALB               1           100  728.89795   \n",
       "\n",
       "       gdpppp  proba_quantile_parent  income_mean  log_income  log_income_mean  \n",
       "0      7297.0                      1  2994.829902    6.591534         8.004643  \n",
       "6300   7297.0                      1  2994.829902    6.591534         8.004643  \n",
       "12600  7297.0                      1  2994.829902    6.591534         8.004643  \n",
       "18900  7297.0                      1  2994.829902    6.591534         8.004643  \n",
       "25200  7297.0                      1  2994.829902    6.591534         8.004643  "
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ALB.head()\n",
    "ALB_reg= ALB.copy()\n",
    "ALB_reg['income_mean']= ALB_reg['income'].mean()\n",
    "ALB_reg['log_income'] =np.log(ALB_reg['income'])\n",
    "ALB_reg['log_income_mean'] =np.log(ALB_reg['income_mean'])\n",
    "ALB_reg.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "53c6a694",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ZoeyZhang/opt/anaconda3/lib/python3.8/site-packages/statsmodels/base/model.py:1832: ValueWarning: covariance of constraints does not have full rank. The number of constraints is 3, but rank is 1\n",
      "  warnings.warn('covariance of constraints does not have full '\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>log_income</td>    <th>  R-squared:         </th> <td>   0.370</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.370</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>1.151e+15</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 14 Mar 2022</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>12:41:18</td>     <th>  Log-Likelihood:    </th> <td> -27059.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 50000</td>      <th>  AIC:               </th> <td>5.412e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 49997</td>      <th>  BIC:               </th> <td>5.415e+04</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>HC3</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>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>             <td> 3.291e+08</td> <td>    9.703</td> <td> 3.39e+07</td> <td> 0.000</td> <td> 3.29e+08</td> <td> 3.29e+08</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_income_mean</th>       <td> 5.637e+09</td> <td>  166.163</td> <td> 3.39e+07</td> <td> 0.000</td> <td> 5.64e+09</td> <td> 5.64e+09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>gini</th>                  <td>-1.447e+09</td> <td>   42.656</td> <td>-3.39e+07</td> <td> 0.000</td> <td>-1.45e+09</td> <td>-1.45e+09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>proba_quantile_parent</th> <td>    0.0110</td> <td>    2e-12</td> <td> 5.53e+09</td> <td> 0.000</td> <td>    0.011</td> <td>    0.011</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>2778.436</td> <th>  Durbin-Watson:     </th> <td>   0.014</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>  <th>  Jarque-Bera (JB):  </th> <td>4262.285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.479</td>  <th>  Prob(JB):          </th> <td>    0.00</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td> 4.062</td>  <th>  Cond. No.          </th> <td>7.86e+19</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors are heteroscedasticity robust (HC3)<br/>[2] The smallest eigenvalue is 3.42e-32. This might indicate that there are<br/>strong multicollinearity problems or that the design matrix is singular."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:             log_income   R-squared:                       0.370\n",
       "Model:                            OLS   Adj. R-squared:                  0.370\n",
       "Method:                 Least Squares   F-statistic:                 1.151e+15\n",
       "Date:                Mon, 14 Mar 2022   Prob (F-statistic):               0.00\n",
       "Time:                        12:41:18   Log-Likelihood:                -27059.\n",
       "No. Observations:               50000   AIC:                         5.412e+04\n",
       "Df Residuals:                   49997   BIC:                         5.415e+04\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:                  HC3                                         \n",
       "=========================================================================================\n",
       "                            coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------------\n",
       "Intercept              3.291e+08      9.703   3.39e+07      0.000    3.29e+08    3.29e+08\n",
       "log_income_mean        5.637e+09    166.163   3.39e+07      0.000    5.64e+09    5.64e+09\n",
       "gini                  -1.447e+09     42.656  -3.39e+07      0.000   -1.45e+09   -1.45e+09\n",
       "proba_quantile_parent     0.0110      2e-12   5.53e+09      0.000       0.011       0.011\n",
       "==============================================================================\n",
       "Omnibus:                     2778.436   Durbin-Watson:                   0.014\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             4262.285\n",
       "Skew:                           0.479   Prob(JB):                         0.00\n",
       "Kurtosis:                       4.062   Cond. No.                     7.86e+19\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors are heteroscedasticity robust (HC3)\n",
       "[2] The smallest eigenvalue is 3.42e-32. This might indicate that there are\n",
       "strong multicollinearity problems or that the design matrix is singular.\n",
       "\"\"\""
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_ALB =  smf.ols('log_income~log_income_mean+gini+proba_quantile_parent', data=ALB_reg).fit(cov_type='HC3')\n",
    "reg_ALB.summary()\n",
    "\n",
    "# méthode .fit(cov_type='HC3') aide à réduire l'effect de l'hétéroscétasticité "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "a182d4ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. vérifier la normalité des résidus du model reg_ALB\n",
    "stats.probplot(reg_ALB.resid, dist=\"norm\", plot= plt)\n",
    "plt.title(\"reg_ALB Residuals Q-Q Plot\")\n",
    "plt.savefig(\"reg_ALB Residus_qqplot.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44a9c3dd",
   "metadata": {},
   "source": [
    "=> normalité quasi parfaite pour les résidus du modèle reg_ALB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "0f6814e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Lagrange multiplier statistic', 649.0151053177129),\n",
       " ('p-value', 2.38174700496322e-140),\n",
       " ('f-value', 328.7554269668309),\n",
       " ('f p-value', 1.4256401060724296e-142)]"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2. vérifier homosétasticité des résidus par statsmodels reg_ALB\n",
    "\n",
    "test = sms.het_breuschpagan(reg_ALB.resid, reg_ALB.model.exog)\n",
    "lzip(name, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f2f1197",
   "metadata": {},
   "source": [
    "#### Lagrange multiplier statistic est petit et sa P-value = 2.38 > 5%, non-rejet de H0 au niveau de test 5%, il existe de l'homosétasticité pour les résidus de ce modèle reg_ALB\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "d8650ba8",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>df</th>\n",
       "      <th>sum_sq</th>\n",
       "      <th>mean_sq</th>\n",
       "      <th>F</th>\n",
       "      <th>PR(&gt;F)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>log_income_mean</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.588086</td>\n",
       "      <td>1.588086</td>\n",
       "      <td>9.188968</td>\n",
       "      <td>0.002436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gini</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.588150</td>\n",
       "      <td>1.588150</td>\n",
       "      <td>9.189336</td>\n",
       "      <td>0.002436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>proba_quantile_parent</th>\n",
       "      <td>1.0</td>\n",
       "      <td>5081.766626</td>\n",
       "      <td>5081.766626</td>\n",
       "      <td>29404.060971</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Residual</th>\n",
       "      <td>49997.0</td>\n",
       "      <td>8640.748168</td>\n",
       "      <td>0.172825</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            df       sum_sq      mean_sq             F  \\\n",
       "log_income_mean            1.0     1.588086     1.588086      9.188968   \n",
       "gini                       1.0     1.588150     1.588150      9.189336   \n",
       "proba_quantile_parent      1.0  5081.766626  5081.766626  29404.060971   \n",
       "Residual               49997.0  8640.748168     0.172825           NaN   \n",
       "\n",
       "                         PR(>F)  \n",
       "log_income_mean        0.002436  \n",
       "gini                   0.002436  \n",
       "proba_quantile_parent  0.000000  \n",
       "Residual                    NaN  "
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analyse_ALB=sm.stats.anova_lm(reg_ALB, typ=1)\n",
    "analyse_ALB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "5b4966d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Décomposition de variance totale expliquée_pays ALB: \n",
      "La variance expliquée par la classe de revenu des parents est de : 37.02 %\n",
      "La variance expliquée par le revenu moyen en log est de : 0.01 %\n",
      "La variance expliquée par lindice Gini est de : 0.01 %\n",
      "La variance expliquée par les autres facteurs est de : 62.95 %\n"
     ]
    }
   ],
   "source": [
    "SCE_income_mean_log5=analyse_ALB.iloc[0,1]\n",
    "SCE_gini5=analyse_ALB.iloc[1,1]\n",
    "SCE_class_p5=analyse_ALB.iloc[2,1]\n",
    "SCR_5=analyse_ALB.iloc[3,1]\n",
    "\n",
    "R2_classe_p5=SCE_class_p5/sum(analyse_ALB['sum_sq'])\n",
    "R2_incomemean_log5= SCE_income_mean_log5/sum(analyse_ALB['sum_sq'])\n",
    "R2_gini5 = SCE_gini5/sum(analyse_ALB['sum_sq'])\n",
    "R2_SCR5 = SCR_5/sum(analyse_ALB['sum_sq']) \n",
    "\n",
    "print('Décomposition de variance totale expliquée_pays ALB: ')\n",
    "print('La variance expliquée par la classe de revenu des parents est de :', round(R2_classe_p5*100,2), '%')\n",
    "print('La variance expliquée par le revenu moyen en log est de :', round(R2_incomemean_log5*100,2), '%')\n",
    "print('La variance expliquée par lindice Gini est de :', round(R2_gini5*100,2), '%')\n",
    "print('La variance expliquée par les autres facteurs est de :', round(R2_SCR5*100,2), '%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "cfce0dbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# End"
   ]
  }
 ],
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