Estadistica-Orange-solucion.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Librerías manejo de datos\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# Librerías de gráficos\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Carga de datos y ETL\n",
    "\n",
    "Vamos a cargar un dataset sobre el peso de los niños al nacer.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#birth_weight = pd.read_csv('birthweight.csv')\n",
    "birth_weight = pd.read_csv('https://github.com/calabozo/orange-stats/raw/master/birthweight.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>id</th>\n",
       "      <th>headcirumference</th>\n",
       "      <th>length</th>\n",
       "      <th>Birthweight</th>\n",
       "      <th>Gestation</th>\n",
       "      <th>smoker</th>\n",
       "      <th>motherage</th>\n",
       "      <th>mnocig</th>\n",
       "      <th>mheight</th>\n",
       "      <th>mppwt</th>\n",
       "      <th>fage</th>\n",
       "      <th>fedyrs</th>\n",
       "      <th>fnocig</th>\n",
       "      <th>fheight</th>\n",
       "      <th>lowbwt</th>\n",
       "      <th>mage35</th>\n",
       "      <th>LowBirthWeight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1313</td>\n",
       "      <td>12</td>\n",
       "      <td>17</td>\n",
       "      <td>5.8</td>\n",
       "      <td>33</td>\n",
       "      <td>0</td>\n",
       "      <td>24</td>\n",
       "      <td>0</td>\n",
       "      <td>58</td>\n",
       "      <td>99</td>\n",
       "      <td>26</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>66</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Low</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>431</td>\n",
       "      <td>12</td>\n",
       "      <td>19</td>\n",
       "      <td>4.2</td>\n",
       "      <td>33</td>\n",
       "      <td>1</td>\n",
       "      <td>20</td>\n",
       "      <td>7</td>\n",
       "      <td>63</td>\n",
       "      <td>109</td>\n",
       "      <td>20</td>\n",
       "      <td>10</td>\n",
       "      <td>35</td>\n",
       "      <td>71</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Low</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>808</td>\n",
       "      <td>13</td>\n",
       "      <td>19</td>\n",
       "      <td>6.4</td>\n",
       "      <td>34</td>\n",
       "      <td>0</td>\n",
       "      <td>26</td>\n",
       "      <td>0</td>\n",
       "      <td>65</td>\n",
       "      <td>140</td>\n",
       "      <td>25</td>\n",
       "      <td>12</td>\n",
       "      <td>25</td>\n",
       "      <td>69</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>Normal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>300</td>\n",
       "      <td>12</td>\n",
       "      <td>18</td>\n",
       "      <td>4.5</td>\n",
       "      <td>35</td>\n",
       "      <td>1</td>\n",
       "      <td>41</td>\n",
       "      <td>7</td>\n",
       "      <td>65</td>\n",
       "      <td>125</td>\n",
       "      <td>37</td>\n",
       "      <td>14</td>\n",
       "      <td>25</td>\n",
       "      <td>68</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Low</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>516</td>\n",
       "      <td>13</td>\n",
       "      <td>18</td>\n",
       "      <td>5.8</td>\n",
       "      <td>35</td>\n",
       "      <td>1</td>\n",
       "      <td>20</td>\n",
       "      <td>35</td>\n",
       "      <td>67</td>\n",
       "      <td>125</td>\n",
       "      <td>23</td>\n",
       "      <td>12</td>\n",
       "      <td>50</td>\n",
       "      <td>73</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Low</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     id  headcirumference  length  Birthweight  Gestation  smoker  motherage  \\\n",
       "0  1313                12      17          5.8         33       0         24   \n",
       "1   431                12      19          4.2         33       1         20   \n",
       "2   808                13      19          6.4         34       0         26   \n",
       "3   300                12      18          4.5         35       1         41   \n",
       "4   516                13      18          5.8         35       1         20   \n",
       "\n",
       "   mnocig  mheight  mppwt  fage  fedyrs  fnocig  fheight  lowbwt  mage35  \\\n",
       "0       0       58     99    26      16       0       66       1       0   \n",
       "1       7       63    109    20      10      35       71       1       0   \n",
       "2       0       65    140    25      12      25       69       0       0   \n",
       "3       7       65    125    37      14      25       68       1       1   \n",
       "4      35       67    125    23      12      50       73       1       0   \n",
       "\n",
       "  LowBirthWeight  \n",
       "0            Low  \n",
       "1            Low  \n",
       "2         Normal  \n",
       "3            Low  \n",
       "4            Low  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "birth_weight.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "birth_weight[\"Birthweight_kg\"]=birth_weight[\"Birthweight\"]*0.453592"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Media\n",
    "\n",
    "\\\\[ \\mu_{x} = E[x] =  \\frac{1}{N} \\sum _{i=1}^N x_i\\\\]\n",
    "\n",
    "Rellenar con formula y texto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.2950218857142866"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def mean(vector):\n",
    "    m = 0\n",
    "    for val in vector:\n",
    "        m = val+m\n",
    "    m = m/len(vector)\n",
    "    return m\n",
    "mean(birth_weight[\"Birthweight_kg\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.295021885714286"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(birth_weight[\"Birthweight_kg\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Varianza\n",
    "\n",
    "Es la esperanza del cuadrado de la desviación de dicha variable respecto a su media. Otra definición es la media de los residuos al cuadrado.\n",
    "\n",
    "Su formula es:\n",
    "\n",
    "\\\\[ Var[x] =  \\frac{1}{N} \\sum _{i=1}^N \\left( x_i-\\bar{x} \\right)^2 \\\\]\n",
    "\n",
    "Pero como no sabremos $\\bar{x}$ sino que siempre tendremoso que estimar la media E[x] la formula del estimador insesgado de la varianza para una muestra de la población es:\n",
    "\n",
    "\\\\[ Var[x] =  \\frac{1}{N-1} \\sum _{i=1}^N \\left( x_i-E[x] \\right)^2 \\\\]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.363800698111214"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def var(vector):\n",
    "    m = mean(vector)\n",
    "    v = 0\n",
    "    for val in vector:\n",
    "        v = (val-m)**2 + v\n",
    "    v = v/(len(vector)-1)\n",
    "    return v\n",
    "var(birth_weight[\"Birthweight_kg\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36380069811121396"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(birth_weight[\"Birthweight_kg\"],ddof=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mediana\n",
    "\n",
    "La mediana es el valor de una distribución tal que la mitad de los elementos son superiores y la mitad son inferiores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.25\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "def median(vector: pd.Series) -> float:\n",
    "    vector = vector.sort_values()\n",
    "    idx=(len(vector)-1)/2\n",
    "    if idx==int(idx):\n",
    "        return vector.iloc[int(idx)]\n",
    "    else:\n",
    "        return (vector.iloc[int(np.floor(idx))]+vector.iloc[int(np.ceil(idx))])/2\n",
    "    \n",
    "print(median(pd.Series([1,2,3,3.5,4,6])))\n",
    "print(median(pd.Series([1,2,3,4,6])))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.288542"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median(birth_weight[\"Birthweight_kg\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.288542"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(birth_weight[\"Birthweight_kg\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cuantiles\n",
    "\n",
    "Los cuantiles suelen usarse por grupos que dividen la distribución en partes iguales; entendidas estas como intervalos que comprenden la misma proporción de valores. Los más usados son:\n",
    "\n",
    "* Los cuartiles, que dividen a la distribución en cuatro partes (corresponden a los cuantiles 0,25; 0,50 y 0,75);\n",
    "* Los quintiles, que dividen a la distribución en cinco partes (corresponden a los cuantiles 0,20; 0,40; 0,60 y 0,80);\n",
    "* Los deciles, que dividen a la distribución en diez partes;\n",
    "* Los percentiles, que dividen a la distribución en cien partes.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.9256684, 3.288542 , 3.628736 ])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(birth_weight[\"Birthweight_kg\"],[0.25,0.5,0.75])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boxplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Birthweight_kg'>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.boxplot(x=birth_weight[\"Birthweight_kg\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histograma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f0fecb90e80>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEGCAYAAACD7ClEAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAbVElEQVR4nO3de3TU9Z3/8eeLi0QKXgrRAgkGC0sJSCkGqqD8UMqWosKvys+7i1WX/rTd2qsHd8+xv+4524Nu6632ItUu2nrBrRfQrbZ0K1XASgOiKHhpFU2ACoWK4IqKff/+mIHGMCQzSWa+mXxfj3NyMvO9zOf9ySTzyvf2+SoiMDOzdOqWdAFmZpYch4CZWYo5BMzMUswhYGaWYg4BM7MU65F0Afno379/1NTUJF2GmVlZWbVq1Z8jorKlZcoiBGpqaqivr0+6DDOzsiLp1daW8e4gM7MUcwiYmaWYQ8DMLMXK4piAmXVe7733Ho2NjezevTvpUlKroqKCqqoqevbsWfC6DgEza5fGxkb69u1LTU0NkpIuJ3Uigm3bttHY2MiQIUMKXt+7g8ysXXbv3k2/fv0cAAmRRL9+/dq8JeYQMLN2cwAkqz0/f4eAmVmKOQTMrEMNqh6MpA77GlQ9uNU2H3nkEYYPH87QoUOZN29ezmUWLFhAZWUlY8aMYcyYMdxyyy37LbNhwwZGjRqVc/1LLrmEdevWFfbDaGbx4sUHrK9Pnz77arjzzjs/UPcXv/jFdrXbEh8YtkQMqh7MpsaGpMtot4FV1WxseC3pMjqVTY0NnHXzig57vYWfn9Di/Pfff58vfOELLFmyhKqqKsaNG8eMGTOora3db9mzzjqLm266qU115AqNQs2YMYMZM2a0uMzeEDj33HPb3V4+HAKWiI7+oEhKax9QVnwrV65k6NChHH300QCcffbZLFq0KGcI5GPPnj2cd955rF69mpEjR3L77bfTu3dvJk+ezHe+8x3q6uro06cPl19+OQ899BAHH3wwixYton///gwdOpSXX36ZHTt20K9fPx599FEmTZrEpEmTuPXWW1m+fDn19fXcdNNNvPLKK5x77rns2rWLmTNn7mt/7ty5rF+/njFjxjB79mwOP/xwNm3axLRp0/jjH//IZz/7Wa655poO+dmBdweZWZnbuHEj1dXV+55XVVWxcePGnMvee++9jB49mlmzZtHQkHtL9IUXXuCyyy5j/fr1HHLIIfzgBz/Yb5m33nqL4447jqeffppJkybx4x//mO7duzN8+HDWrVvHsmXLGDt2LI8//jjvvPMODQ0NDBs27AOvcfnll3PppZeydu1aBgwYsG/6vHnzOPHEE1mzZg1f+cpXAFizZg0LFy5k7dq1LFy48IC1t4VDwMxS4bTTTmPDhg0888wzTJ06ldmzZ+dcrrq6mokTJwJw/vnns2zZsv2WOeiggzj11FMBOPbYY9mwYQMAJ554Io899hiPPfYYV155JcuWLeP3v/8948aN2+81li9fzjnnnAPABRdc0GLtU6ZM4dBDD6WiooLa2lpefbXVceHy5hAws7I2aNCgD/xn3NjYyKBBg/Zbrl+/fvTq1QvIHORdtWpVztdrfrplrtMve/bsuW969+7d2bNnDwCTJk3i8ccfZ+XKlUyfPp033niDpUuXcuKJJ+bV1oHsrbt5ex3BIWBmZW3cuHG89NJLvPLKK7z77rvcfffdOQ++bt68ed/jxYsXM2LEiJyv99prr/HEE08AcOedd3LCCSfkXcv48eNZsWIF3bp1o6KigjFjxnDzzTczadKk/ZadOHEid999NwB33HHHvul9+/Zl586debfZXj4wbGYdamBVdYceMB9YVd3i/B49enDTTTfx6U9/mvfff5+LLrqIkSNHAnDVVVdRV1fHjBkzuPHGG1m8eDE9evTgwx/+MAsWLMj5esOHD+f73/8+F110EbW1tVx66aV519qrVy+qq6s57rjjgMzuobvuuotjjjlmv2VvuOEGzj33XK6++uoPHBgePXo03bt35+Mf/zgXXnghhx9+eN7tt4UioqgNdIS6urrwTWW6Fkld5uygcvgbKqb169cf8L9qK51c74OkVRFR19J63h1kZpZiDgEzsxQrWghI+omkLZKezTHva5JCUv9itW9mZq0r5pbAAmBa84mSqoG/B3ytvZlZwooWAhHxGLA9x6zrgCuAdB9NMzPrBEp6TEDSTGBjRDxdynbNzCy3koWApN7APwNX5bn8HEn1kuq3bt1a3OLMrMPUDBzYoUNJ1wwc2GJ7DQ0NnHTSSdTW1jJy5EhuuOGGffO2b9/O1KlTGTZsGFOnTuUvf/nLfuu3NFTzhAldf4DAUl4s9lFgCPB09lLpKmC1pPER8afmC0fEfGA+ZK4TKGGdZtYOr27eTEye3GGvp6VLW5zfo0cPvvvd7zJ27Fh27tzJsccey9SpU6mtrWXevHlMmTKFuXPnMm/ePObNm8fVV1+dd9srVpT/tSytKdmWQESsjYgjIqImImqARmBsrgAwM8vXgAEDGDt2LJAZcmHEiBH7RhFdtGjRvoHiZs+ezQMPPJDzNRoaGpg8eTLDhg3jW9/61r7pe2/0snTpUiZPnsysWbP42Mc+xnnnnbfvIsG5c+dSW1vL6NGj+frXv16sbhZN0bYEJN0FTAb6S2oEvhkRtxarPTOzDRs28NRTT/HJT34SgNdff33fMM0f+chHeP3113Out3LlSp599ll69+7NuHHjOOWUU6ir++CFtk899RTPPfccAwcOZOLEiSxfvpwRI0Zw//338/zzzyOJN954o6j9K4Zinh10TkQMiIieEVHVPACyWwR/Llb7ZpYuu3bt4owzzuD666/nkEMO2W/+3mMMuUydOpV+/fpx8MEHc/rpp+ccPnr8+PFUVVXRrVs3xowZw4YNG/YN73zxxRdz33330bt37w7vV7H5imEzK3vvvfceZ5xxBueddx6nn376vulHHnnkvtFDN2/ezBFHHJFz/XyGj841nHOPHj1YuXIls2bN4qGHHmLatP0ujer0HAJmVtYigosvvpgRI0bw1a9+9QPzZsyYwW233QbAbbfd9oHROptasmQJ27dv5+233+aBBx7Yd1OZ1uzatYsdO3Ywffp0rrvuOp5+uvzOfvdQ0mbWoY4aMKDVM3oKfb2WLF++nJ/+9Kccc8wxjBkzBoBvf/vbTJ8+nblz53LmmWdy6623ctRRR3HPPffkfI3x48dzxhln0NjYyPnnn7/f8YAD2blzJzNnzmT37t1EBNdee21BfesMPJS0JcJDSXcdHkq6c/BQ0mZmVjCHgJlZijkEzKzd0r5LLGnt+fk7BMysXSoqKti2bZuDICERwbZt26ioqGjT+j47yMzapaqqisbGRjzQY3IqKiqoqqpq07oOATNrl549ezJkyJCky7A28u4gM7MUcwiYmaWYQ8DMLMUcAmZmKeYQMDNLMYeAmVmKOQTMzFLMIWBmlmIOATOzFCtaCEj6iaQtkp5tMu3fJT0v6RlJ90s6rFjtm5lZ64q5JbAAaH7DzSXAqIgYDbwIXFnE9s3MrBVFC4GIeAzY3mzaryJiT/bp74C2jXhkZmYdIsljAhcBDx9opqQ5kuol1Xt0QjOz4kgkBCT9C7AHuONAy0TE/Iioi4i6ysrK0hVnZpYiJR9KWtKFwKnAlPBdKMzMElXSEJA0DbgC+F8R8T+lbNvMzPZXzFNE7wKeAIZLapR0MXAT0BdYImmNpB8Vq30zM2td0bYEIuKcHJNvLVZ7ZmZWOF8xbGaWYg4BM7MUcwiYmaWYQ8DMLMUcAmZmKeYQMDNLMYeAmVmKOQTMzFKs5GMHmXUp3XogKekqOsTAqmo2NryWdBlWYg4Bs/b46x7OunlF0lV0iIWfn5B0CZYA7w4yM0sxh4CZWYo5BMzMUswhYGaWYg4BM7MUcwiYmaWYQ8DMLMUcAmZmKeYQMDNLsWLeaP4nkrZIerbJtA9LWiLppez3w4vVvpmZta6YWwILgGnNps0F/jsihgH/nX1uZmYJKVoIRMRjwPZmk2cCt2Uf3wb872K1b2ZmrSv1MYEjI2Jz9vGfgCMPtKCkOZLqJdVv3bq1NNWZmaVMYgeGIyKAaGH+/Iioi4i6ysrKElZmZpYepQ6B1yUNAMh+31Li9s3MrIlSh8BiYHb28WxgUYnbNzOzJop5iuhdwBPAcEmNki4G5gFTJb0EfCr73MzMElK0O4tFxDkHmDWlWG2amVlhfMWwmVmKOQTMzFLMIWBmlmIOATOzFHMImJmlmEPAzCzFHAJmZinmEDAzSzGHgJlZijkEzMxSzCFgZpZieYWApIn5TDMzs/KS75bA9/KcZmZmZaTFUUQlHQ9MAColfbXJrEOA7sUszMzMiq+1oaQPAvpkl+vbZPqbwKxiFWVmZqXRYghExG+B30paEBGvlqgmMzMrkXxvKtNL0nygpuk6EXFyMYoyM7PSyDcE/hP4EXAL8H7xyjEzs1LKNwT2RMQPO6pRSV8BLgECWAt8LiJ2d9Trm5lZfvI9RfRBSZdJGiDpw3u/2tKgpEHAl4C6iBhF5iyjs9vyWmZm1j75bgnMzn7/RpNpARzdjnYPlvQe0BvY1MbXMTOzdsgrBCJiSEc1GBEbJX0HeA14G/hVRPyq+XKS5gBzAAYPHtxRzZe1QdWD2dTYkHQZZtaF5BUCkv4h1/SIuL3QBiUdDswEhgBvAP8p6fyI+Fmz154PzAeoq6uLQtvpijY1NnDWzSuSLqNDLPz8hKRLMDPy3x00rsnjCmAKsBooOASATwGvRMRWAEn3kbkq+WctrmVmZh0u391B/9T0uaTDgLvb2OZrwHGSepPZHTQFqG/ja5mZWTu0dSjpt8jszilYRDwJ/JzMlsTabA3z21iHmZm1Q77HBB4kczYQZE7pHAHc09ZGI+KbwDfbur6ZmXWMfI8JfKfJ4z3AqxHRWIR6zMyshPLaHZQdSO55MiOJHg68W8yizMysNPK9s9iZwErg/wBnAk9K8lDSZmZlLt/dQf8CjIuILQCSKoFfkznAa2ZmZSrfs4O67Q2ArG0FrGtmZp1UvlsCj0j6JXBX9vlZwC+KU5KZmZVKa/cYHgocGRHfkHQ6cEJ21hPAHcUuzszMiqu1LYHrgSsBIuI+4D4AScdk551WxNrMzKzIWtuvf2RErG0+MTutpigVmZlZybQWAoe1MO/gDqzDzMwS0FoI1Ev6x+YTJV0CrCpOSWZmViqtHRP4MnC/pPP424d+HXAQ8Nki1mVmZiXQYghExOvABEknAaOyk/8rIn5T9MrMzKzo8r2fwKPAo0WuxczMSsxX/ZqZpZhDwMwsxRwCZmYp5hAwM0sxh4CZWYolEgKSDpP0c0nPS1ov6fgk6jAzS7t8h5LuaDcAj0TELEkHAb0TqsPMLNVKHgKSDgUmARcCRMS7+J7FZmaJSGJ30BBgK/Afkp6SdIukDzVfSNIcSfWS6rdu3Vr6Ks3MUiCJEOgBjAV+GBGfAN4C5jZfKCLmR0RdRNRVVlaWukYzs1RIIgQagcaIeDL7/OdkQsHMzEqs5CEQEX8CGiQNz06aAqwrdR1mZpbc2UH/BNyRPTPoZeBzCdVhZpZqiYRARKwhc18CMzNLkK8YNjNLMYeAmVmKOQTMzFLMIWBmlmIOATOzFHMImJmlmEPAzCzFHAJmZimW1BXDZh3i4StO480d2wper5fEOxEFrXPIof34zDUPFtyWWWfmELCy9uaObTz7d4WPPzjqxdUFrzfqxdUFt2PW2Xl3kJlZijkEzMxSzCFgZpZiDgEzsxRzCJiZpZhDwMwsxRwCZmYp5hAwM0uxxEJAUndJT0l6KKkazMzSLsktgcuB9Qm2b2aWeomEgKQq4BTgliTaNzOzjKS2BK4HrgD+mlD7ZmZGAiEg6VRgS0SsamW5OZLqJdVv3bq1RNWZmaVLElsCE4EZkjYAdwMnS/pZ84UiYn5E1EVEXWVlZalrNDNLhZKHQERcGRFVEVEDnA38JiLOL3UdZmbm6wTMzFIt0ZvKRMRSYGmSNZiZpZm3BMzMUswhYGaWYg4BM7MUcwiYmaWYQ8DMLMUcAmZmKeYQMDNLMYeAmVmKJXqxWCkMqh7MpsaGpMsoWw9fcRpv7thW8HqHHNqPz1zzYEna6sza2qdeEu9EFH2dD7xP3XogqaD1O6uBVdVsbHgt6TLKQpcPgU2NDZx184qky+gQCz8/oeRtvrljG8/+3diC1xv14uqStNWWdkqpPT+/tvws2vXz++se/62kkHcHmZmlmEPAzCzFHAJmZinmEDAzSzGHgJlZijkEzMxSzCFgZpZiDgEzsxRzCJiZpVjJQ0BStaRHJa2T9Jyky0tdg5mZZSQxbMQe4GsRsVpSX2CVpCURsS6BWszMUq3kWwIRsTkiVmcf7wTWA4NKXYeZmSU8gJykGuATwJM55s0B5gAMHjy4tIV1UaUcpbMnrQ/iVW6DfB2oT+XWj6aa9ynfvrR7xNIi6wkFj4jaE3ivKNW0T7FHRE0sBCT1Ae4FvhwRbzafHxHzgfkAdXV1hf22WU6lHKXzPWixrS0vruaIZvM7+4igufqUqx9NlVOfWutLU+0esbTIWvv9y2XUi6s75Siqxf4nI5GzgyT1JBMAd0TEfUnUYGZmyZwdJOBWYH1EXFvq9s3M7G+S2BKYCFwAnCxpTfZregJ1mJmlXsmPCUTEMqBr3MPOzKzM+YphM7MUcwiYmaWYQ8DMLMUcAmZmKeYQMDNLMYeAmVmKOQTMzFLMIWBmlmKJjiJaCvmMZplLqUZJLHRkz719aUt9ZuWmlCPfplWXD4G2jCYIpRslsZCRPZuO8tjZR3E06whtGfkW/LteCO8OMjNLMYeAmVmKOQTMzFLMIWBmlmIOATOzFHMImJmlmEPAzCzFHAJmZinmEDAzS7FEQkDSNEkvSPqDpLlJ1GBmZgmEgKTuwPeBzwC1wDmSaktdh5mZJbMlMB74Q0S8HBHvAncDMxOow8ws9RQlHolS0ixgWkRckn1+AfDJiPhis+XmAHOyT4cDLxS5tP7An4vcRql0lb50lX6A+9IZdZV+wIH7clREVLa0YqcdRTQi5gPzS9WepPqIqCtVe8XUVfrSVfoB7ktn1FX6Ae3rSxK7gzYC1U2eV2WnmZlZiSURAr8HhkkaIukg4GxgcQJ1mJmlXsl3B0XEHklfBH4JdAd+EhHPlbqOHEq266kEukpfuko/wH3pjLpKP6AdfSn5gWEzM+s8fMWwmVmKOQTMzFIsVSEgqVrSo5LWSXpO0uU5lpGkG7NDWjwjqfC7XBdZnv2YLGmHpDXZr6uSqLU1kiokrZT0dLYv38qxTC9JC7PvyZOSahIotVV59uVCSVubvC+XJFFrPiR1l/SUpIdyzCuL92SvVvpSTu/JBklrs3XW55hf8OdXp71OoEj2AF+LiNWS+gKrJC2JiHVNlvkMMCz79Ungh9nvnUk+/QB4PCJOTaC+QrwDnBwRuyT1BJZJejgiftdkmYuBv0TEUElnA1cDZyVRbCvy6QvAwuYXR3ZSlwPrgUNyzCuX92SvlvoC5fOeAJwUEQe6yK3gz69UbQlExOaIWJ19vJPML8WgZovNBG6PjN8Bh0kaUOJSW5RnP8pC9ue8K/u0Z/ar+dkKM4Hbso9/DkyRpBKVmLc8+1IWJFUBpwC3HGCRsnhPIK++dCUFf36lKgSaym6+fgJ4stmsQUBDk+eNdOIP2Bb6AXB8dtfEw5JGlray/GU31dcAW4AlEXHA9yQi9gA7gH4lLTJPefQF4IzspvrPJVXnmN8ZXA9cAfz1APPL5j2h9b5AebwnkPmn4leSVmWH1mmu4M+vVIaApD7AvcCXI+LNpOtpq1b6sZrMuCEfB74HPFDi8vIWEe9HxBgyV4+PlzQq4ZLaLI++PAjURMRoYAl/+2+605B0KrAlIlYlXUt75dmXTv+eNHFCRIwls9vnC5ImtfcFUxcC2X219wJ3RMR9ORYpi2EtWutHRLy5d9dERPwC6Cmpf4nLLEhEvAE8CkxrNmvfeyKpB3AosK2kxRXoQH2JiG0R8U726S3AsSUuLR8TgRmSNpAZ5fdkST9rtky5vCet9qVM3hMAImJj9vsW4H4yozI3VfDnV6pCILvP8lZgfURce4DFFgP/kD3KfhywIyI2l6zIPOTTD0kf2buPVtJ4Mu91p/sjlVQp6bDs44OBqcDzzRZbDMzOPp4F/CY64VWO+fSl2f7ZGWSO53QqEXFlRFRFRA2ZYV1+ExHnN1usLN6TfPpSDu8JgKQPZU8EQdKHgL8Hnm22WMGfX2k7O2gicAGwNrvfFuCfgcEAEfEj4BfAdOAPwP8Anyt9ma3Kpx+zgEsl7QHeBs7ujH+kwADgNmVuNtQNuCciHpL0r0B9RCwmE3g/lfQHYDuZP+bOKJ++fEnSDDJneG0HLkys2gKV6XuSU5m+J0cC92f/t+sB3BkRj0j6v9D2zy8PG2FmlmKp2h1kZmYf5BAwM0sxh4CZWYo5BMzMUswhYGaWYg4B6zIkXSfpy02e/1LSLU2ef1fSV1tY/18lfaqVNv6fpK/nmH6YpMsOsE6NpLf3ns6bfd78/O4WKTNq7C5JXeLG6NZ5OASsK1kOTACQ1A3oDzQdM2kCsOJAK0fEVRHx6za2fRiQMwSy/pgdTqJNIuIkYL+hg83ayyFgXckK4Pjs45FkrqbcKelwSb2AEcBqScdK+m12EK5f7r1iVNICSbOyj6dLej67zI364Dj0tZKWSnpZ0pey0+YBH1VmnPd/z7dgSUcrM879OEm9Jd2jzH0i7ldmnH7/529FlbYrhq0Li4hNkvZIGkzmv/4nyIygeDyZUS7XkhmF8XvAzIjYKuks4N+Ai/a+jqQK4GZgUkS8IumuZk19DDgJ6Au8IOmHwFxgVCH/7UsaTmY8mwsj4unsbqa/RERtduC5NQX/EMwK5BCwrmYFmQCYAFxLJgQmkAmB5cBwYBSwJHv5fXeg+dgqHwNejohXss/vApoO2/tf2QHH3pG0hczl/IWqBBYBpze5GdAJwA0AEfGspGfa8LpmBXEIWFez97jAMWR2BzUAXwPeBP4DEPBcRBx/wFdo3TtNHr9P2/6OdgCvkfngb35HOLOS8TEB62pWAKcC27Nj+28nc9D2+Oy8F4BKScdDZkhu7X/DnReAo/W3++bmc9vEnWR2D+XrXeCzZEZ8PDc7bTlwZrauWjJBZlZU3hKwrmYtmbOC7mw2rc/e+7JmD/7eKOlQMn8D1wPP7V04It7Onu75iKS3gN+31mhEbJO0PHvq58MR8Y081nlLmZueLJG0C/gBmVFI15EZgvo5MlsMZkXjUUTNcpDUJ3vDeAHfB16KiOva+Fo1wEMR0eId07JDUPeMiN2SPgr8GhgeEe9m5y8Fvh4RPlXUOoy3BMxy+0dJs4GDgKfInC3UVu8Dh0pa08rZQ72BR5W5a5yAy5oEwKPA0cB77ajDbD/eEjAzSzEfGDYzSzGHgJlZijkEzMxSzCFgZpZiDgEzsxT7/+0Bpsm949kyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(birth_weight[\"Birthweight_kg\"], binwidth=0.5,label=\"0.5 binwidth\")\n",
    "sns.histplot(birth_weight[\"Birthweight_kg\"], bins=20,color=\"red\",label=\"20 bins\")\n",
    "plt.xlabel(\"Weight [kg]\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Curva de densidad (kernel density estimation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f0fecaaa5f8>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.kdeplot(birth_weight[\"Birthweight_kg\"], bw_adjust=0.5,label=\"bw_adjust=0.5\")\n",
    "sns.kdeplot(birth_weight[\"Birthweight_kg\"], bw_adjust=2,color=\"red\",label=\"bw_adjust=1\")\n",
    "plt.xlabel(\"Weight [kg]\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Violin plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Birthweight_kg'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.violinplot(data=birth_weight,x=\"Birthweight_kg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tests estadísticos\n",
    "\n",
    "¿Es la media de estas dos poblaciones iguales?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "weight_NO_smoke = birth_weight.loc[birth_weight[\"smoker\"]==0,\"Birthweight_kg\"]\n",
    "weight_YES_smoke = birth_weight.loc[birth_weight[\"smoker\"]==1,\"Birthweight_kg\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    20.000000\n",
       "mean      3.488122\n",
       "std       0.520701\n",
       "min       2.630834\n",
       "25%       3.118445\n",
       "50%       3.356581\n",
       "75%       3.900891\n",
       "max       4.535920\n",
       "Name: Birthweight_kg, dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight_NO_smoke.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    22.000000\n",
       "mean      3.119476\n",
       "std       0.630217\n",
       "min       1.905086\n",
       "25%       2.721552\n",
       "50%       3.175144\n",
       "75%       3.526678\n",
       "max       4.535920\n",
       "Name: Birthweight_kg, dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight_YES_smoke.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7efef9d80710>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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yDb0Lmyj++GP497/hwQfhjjvKL6gmTeCxx+wdiOvwk4LqhwTz/i09SM/M4faP4zialVt+salKSxOB8lmLtqYSFOBHt2a1T30hPh7uvBP69bOf0Mvbww/b4nVPPVVocbr2jUJ547qurN+TzuhP4sjM0ZVEqmw0ESif9ce2VGKa1SY4sMDpVampcPXVUK8eTJ1qh2nKW7Vq8OSTdtfyvHmFXnJR+wZMuCaKP7amct8X8eTmnbm8tVJF0USgfNLhYzls3JvOOc0LDAvl59vCcLt32zMF6pewEqk73XGH3aswbtwZS1Zf0z2c8YM78N/1+7j/y5XkaDJQpaSJQPmkFUmHMAZ6NC8wLPTyy/Djj/Dqq9Czp8diAyA42BanW7TIHmhzBrec15wnL2vHD6v3cO/n8WTnajJQJaeJQPmkZYkHCfATuka4EsHSpXY45ppr7PxARTBqlB2iKmKeYnTfloy7ogM/rdvLmM+W6+5jVWKaCJRPiks8RKcmNaka5G/PFbj2Wrti59137U7fiqBaNRg7FmbPtmcXnMWt5zfnH1d25OcN+xk9ZblOIKsS0USgfE5Wbh4rk9PoEVnbjr+PHg07d8IXX9haQhXJmDFQtSq88UaRl97YK5J/Xd2Z37akcPvHcRzP1mSgikcTgfI5a3cdJjs3n5jIOvDee/DVV/D889Crl6dD+6s6dexu488+O+PRlgVd27MpLw3twh/bDnDbx8s0Gahi0USgfM6f2+0hMOcc22NPFhswoNCdvBXGXXfB8eN2k1sxDO0ezsvDurA4IZVbP9JkoIrmaCIQkYEisklEtorI44W8fouIpIjIStfjdifjUQogLvEgbWoHUeuOUbbY2yeflPyEsfLUrRuce66tUFrMk8qu7hbOK8O7sHS7TQbHsnUHsjozx/71i4g/MBkYBHQArhORwqp2fWmMiXY93nMqHqUA8vMNcTsO8fjSL2HVKjs53LChp8Mq2pgxsHnzGTeYFeaqruG8MjyapdtTuWNKnK4mUmfk5MegnsBWY0yCMSYbmApc6WB/ShVpa0oGLbespt93H8Ktt8KVXvJPctgwu5R08uQSvW1I1yZ2zmBrKg9OW0V+vp59rP7KyUTQBCh40Gqy67nTXSMiq0XkaxGJKKwhERktInEiEpeSkuJErMpHxK/fyaRZL5MXHgGTJnk6nOILDobbboPvvoPk5BK99Zru4Tx5WTtmrd7Dcz+sxxRzeEn5Dk8PjH4PRBpjooC5QKGzYcaYd4wxMcaYmLCwYhwwrtQZRLwwjojD+/D/ZAqEhno6nJL529/sHMH775f4raP7tuR218E2ny5NciA45c2cTAS7gIKf8MNdz51kjEk1xpw4l+89oLuD8ShfN2sWvX+Zzi+XjUT69vV0NCXXvLmtiDplSrEnjQt68rL2XNSuPs/OXMfShFQHAlTeyslEsAxoLSLNRSQIuBaYWfACEWlU4MtYYIOD8ShfduAAebfeyoawSHY9+KSnoym9m26ChIS/HHJfHH5+wqRro2latxpjPlvB7rTjDgSovJFjicAYkwvcA8zB/oKfZoxZJyLPiUis67L7RGSdiKwC7gNucSoe5cOMgTvvRA4e4sErHiSmbaOi31NRXX21LT0xZUqp3h4aHMi7N8WQlZvP/VNXkqeTxwqH5wiMMbONMW2MMS2NMS+4nhtnjJnp+vsTxpiOxpguxph+xpiNTsajfNTnn8P06fxy/T3sCG9Nu4Yhno6o9EJCbDKYNg0yS3dUZcuwGjx3ZUf+TDzIW79uc3OAyht5erJYKWft3Qv33gu9e/NmzBCiwmsS4O/l/+xvusmWm/jhh1I3cVXXJlwR1YhJczezOjnNbaEp7+TlPxFKFeGee+DYMbLeeoe1ezOIjqhgReVKo39/aNy41MNDACLCC0M6ExZShfu/XKmbzXycJgJVeX39tT1p7NlnWRvamJw8Q9emtTwdVdn5+8PIkfYQnf37S91MzWqB/N/VnUlIOcpbCxLcGKDyNpoIVOWUmgp33w3du8NDD7FyZxoAXSNqeTQst7nxRsjNtecql8GFbetzRVQjJi/YSkJKhpuCU95GE4GqnO6/Hw4dgg8/hIAA4pMO0aRWVeqHBns6Mvfo1Am6dIEvvyxzU+Ou6ECVAD+e+nat7jr2UZoIVOUzaxZ8+qk9erJzZwDik9KIrgzDQgUNH273E+zcWfS1Z1E/NJhHB7Zj0bZUZq/Z66bglDfRRKAql/R0W4qhUyebCID9RzLZlXa88gwLnTBsmP3z66/L3NT1PZvStkEIL/60kezc/DK3p7yLJgJVuTz1FOzeDR98AEFBAKxMSgOoHBPFBbVuDV272hPWysjfT3jisnYkHTzGJ0t2uCE45U00EajKIy4O/v1vO0nco8fJp+N3phHoL3RsXNODwTlk+HBYvBiSyl5I7oI2YfRpXY835m3h8LEcNwSnvIUmAlU55ObaIaGGDe35wwWsTEqjfaNQggP9PRScg9w4PCQiPDGoPYeP5/Dmr1vL3J7yHpoIVOUweTKsWAGvvQY1//fJPy/fsCo5rfLND5zQsqU9ynLaNLc016FxKFd2acyURTtIzcgq+g2qUtBEoLxfcrKdGxg0CIYOPeWlzfuOcCw7j65NK8GO4jMZPhyWLoXERLc0d0//1mTm5vHOQt1k5is0ESjvN3asHRqaPBlETnnpxEay6Mp6RwD/Gx5yw6QxQKv6NRgc1ZhPFutdga/QRKC82w8/wIwZMG6cPbjlNPFJh6hdLZBmdat5ILhy0qKFHR765hu3NXnfRa04npPHuwu3u61NVXFpIlDeKzMT7rsPOnSAhx4q9JL4pDS6Nq2NnHanUOkMGQJLlthqq27Qqn4IV0Q1ZsriRF1B5AM0ESjv9fLLsH07vPHGyT0DBaVn5rA1JaNyDwudMGSIPYDn++/d1uRdF7TkWHYeny7VfQWVnSYC5Z2Sk+Gf/7SHtPTvX+glq3cexphKuJGsMJ062SGib791W5MdGofSp3U9PlqUqGWqKzlNBMo7Pfoo5Ofbu4IziE86hAh08YU7AhG48kr4+Wc4csRtzY7u24KUI1l8F7/bbW2qikcTgfI+CxfCF1/AI49AZOQZL1u5M42WYTUIDQ4sv9g8acgQyM6Gn35yW5Pnt6pHh0ahvLMwgXw937jS0kSgvEtenp0gjoiAxx8/42XGGOJ3VuKNZIXp3Rvq1YPvvnNbkyLC6L4t2Lo/g183p7itXVWxaCJQ3uW992DlSnjpJah25iWhSQePcfBoduXeSHa6gAAYPNguqc1x30qfy6MaERZShY8XJ7qtTVWxaCJQ3uPQIfj736FvX7ub9ix8YiNZYYYMgcOH4ddf3dZkoL8f1/dsyq+bU9iRetRt7aqKw9FEICIDRWSTiGwVkTPex4vINSJiRCTGyXiUl3vhBTh40NYTKmJfQHxSGtWC/GnToEY5BVdBDBgAVau6dfUQwPXnNMVfhE+1RHWl5FgiEBF/YDIwCOgAXCciHQq5LgQYCyx1KhZVCZzYL3DLLRAdXeTl8UmHiAqvSYC/j930VqsGl15q5wnceOxkg9BgLu3YkGlxyRzP1qWklY2TPyU9ga3GmARjTDYwFbiykOv+AbwIZDoYi/J2Tz4J/v7wj38UeWlmTh7r96QTHeFD8wMFDRli91msWOHWZm/s1YzDx3P4fpUuJa1snEwETYCCh6kmu547SUS6ARHGmFlna0hERotInIjEpaToygWfs2wZTJ0KDz4ITZoUefm63enk5Bnf2EhWmCuuAD8/tw8PndO8Dm0a1GDKkkQ95L6SKVYiEJEZInK5iLgtcbjaegUovEhMAcaYd4wxMcaYmLCwMHeFoLyBMfDwwxAWZjeRFUN80iEA31o6WlDdunZC3c2JQES4sVcka3elE++ajFeVQ3F/sb8JXA9sEZF/iUjbYrxnFxBR4Otw13MnhACdgAUikgicC8zUCWN1iu+/h99+g/HjITS0WG9ZuTONJrWqUj802NnYKrIrr4S1a2Gre08au6prE2pUCeCTxTppXJkUKxEYY342xtwAdAMSgZ9FZJGIjBKRM23bXAa0FpHmIhIEXAvMLNDmYWNMPWNMpDEmElgCxBpj4srw36Mqk9xceOwxaNMG7rij2G+LT0oj2leHhU6IjbV/urEIHUCNKgFc060Js9bsIe1YtlvbVp5T7KEeEakL3ALcDsQDr2ETw9zCrjfG5AL3AHOADcA0Y8w6EXlORGLLGLfyBe+9Bxs3wosvQmDxykTsP5LJrrTjvjssdEKLFrYQnZsTAcCIHk3Jzs3n2/hdRV+svEJx5wi+ARYC1YDBxphYY8yXxph7gTMu1DbGzDbGtDHGtDTGvOB6bpwxZmYh116odwPqpKNH7XDQ+efbYY5iWpmUBvhIxdGiDB5sh9UOHXJrsx0ahxIVXpOpy3bqpHElUdw7gneNMR2MMf9njNkDICJVAIwxOqav3O/112HfPns3UIJDZeJ3phHoL3RsXLPoiyu72Fhbm+nHH93e9IgeEWzce4TVyYfd3rYqf8VNBM8X8txidwai1ElpaTBhAlx+uS2kVgLxSYdo3yiU4EB/Z2LzJj17Qv36jgwPxXZpTNVAf6Yu21n0xarCO2siEJGGItIdqCoiXUWkm+txIXaYSCn3mzjRJoPnC/v8cWa5efmsTj5MN18qNHc2fn52eOjHH215ajcKCQ7kss6N+H7Vbo5l57q1bVX+irojuBSYiF36+QrwsuvxIPCks6Epn7RvH7z6KowYUaxSEgVt3pfBsew8nR8oaPBgW4Ru4UK3N31tzwgysnKZtXqP29tW5eusicAY87Exph9wizGmX4FHrDFmRjnFqHzJ//0fHD8Ozz5b4rfG7zyxkUzvCE4aMACCg2HmX9ZnlFlMs9q0CKvOlzo85PWKGhoa6fprpIg8ePqjHOJTviQpCf7zH1tYrm1x9iyeKj4pjbrVg4ioU9X9sXmr6tVtMvj+e7cWoQO70/jaHhHE7TjE1v3uOx5Tlb+ihoaqu/6sgd0JfPpDKfc5UVBu3LhSvT0+6RBdm9ZCSrDKyCfExtrqrevWub3pq7uFE+AnTItLdnvbqvwEnO1FY8zbrj9Lfp+uVEls3gwffgh33w3NmpX47YeP5bAt5ShXdwt3IDgvd8UV9s+ZM+0mMzeqV6MK/dvVZ8aKXTxyaVsCfa3sdyVR3A1lE0QkVEQCReQXEUkpMGykVNk98wxUqWLLTZfCyuQ0wIcLzZ1No0bQo4cjy0gBhsVEcCAjiwWbtDKwtypu+r7EGJMOXIGtNdQKeMSpoJSPWbXKlpkeOxYaNChVE/FJhxCBKE0EhYuNhaVLYe9etzd9Ydsw6tWowldxOmnsrYqbCE4MIV0OfGWM0e2Eyn2efhpq1oRHSv/ZIj4pjbYNQqhR5ayjnb5r8GA7WTzrrEd/lEqgvx9Xd2vCvI37OZCR5fb2lfOKmwh+EJGNQHfgFxEJQ08UU+6weLEdsnj0UahdumWf+fmGlTvTdP/A2URFQdOmjiwjBRjWPZzcfKOF6LxUcctQPw70BmKMMTnAUQo/dlKpkvn7320ZhPvuK3UT21OPcvh4ju4fOBsROzw0d67dp+FmrRuEEB1Ri2lxWojOG5Vkir8dMEJEbgKGApc4E5LyGb/8AvPn2wniGmcsYlukeK04WjyxsTYJ/PKLI80Piwln874MLUTnhYq7augTbKmJ84EerodWHVWlZ4xNABER8Le/lamp+KRDhFQJoGVY6ZOJT7jgAggJcWx4aHCXxlQJ8OOr5Tpp7G2KO7MWA3Qwes+n3GXmTPjzT3v4THDZjpQ8cSKZn59uJDuroCAYOBB++AHy821ROjcKDQ5kUKeGfLdyN09d3kErwHqR4v5LWAs0dDIQ5UPy8+Gpp6B1a7j55jI1dSw7l41703X/QHHFxsKePbB8uSPND4+J4EhmLnPWuX+ZqnJOcRNBPWC9iMwRkZknHk4GpiqxqVPtwerPPQcBZVvuuTr5MPkGumrp6eK57DLw93dseOjcFnUJr12Vr5dryQlvUtyfwvFOBqF8SE6OrSUUFQXDh5e5uRMTxdF6R1A8derAeefZRHCitpMb+fkJQ7uH89ovW9iVdpwmtbQAoDco7vLRX7E7igNdf18GrHAwLlVZffghbNsGL7zgljHq+KRDNK9XndrVg9wQnI+IjYXVq2HHDkeav6ZbOMbAdL0r8BrFXTV0B/A18LbrqSbAtw7FpCqrE+cM9Oplj6EsI2MM8TvTdH6gpGJj7Z8O1R6KqFON3i3r8tXyneTn6/oSb1Dcj2R3A+cB6QDGmC1AfaeCUpXU5Mmwe7c9fMYNpaJ3pR0n5UiW7h8oqdat7XkPDs0TgJ003nnwOEu3H3SsD+U+xU0EWcaYk4eeikgAUGSqF5GBIrJJRLaKyOOFvH6niKwRkZUi8ruIdCh+6MqrHD5sE8Cll9r17G6w4uT8gE4Ul1hsLCxYAOnpjjR/aceGhFQJ0D0FXqK4ieBXEXkSe4j9xcBXwFnvK0XEH5gMDAI6ANcV8ov+c2NMZ2NMNDABey6yqoxefhkOHoR//tNtTS5PPEi1IH/aN9IzkkosNtZO3M+Z40jzVYP8GRzdmNlr9nAkM8eRPpT7FDcRPA6kAGuAvwGzgaeKeE9PYKsxJsF1NzGV0+oTuUpbn1CdYtxlKC+0bx+88goMGwbdurmt2bgd9kSyAD0MpeR69YK6dR0dHhrWPZzMnHw93N4LFHfVUD52cniMMWaoMebdYuwybgIUvC9Mdj13ChG5W0S2Ye8ISl95TFVc//wnZGa6dbliRlYuG/ak071ZHbe16VP8/e2E/axZkJvrSBfREbVoVb8G0/ScggqvqMPrRUTGi8gBYBOwyXU6WekOlS2EMWayMaYl8BhnuMsQkdEiEicicSkpegqSV9mxA956C0aNKtWB9GcSn3SIfAMxzXR+oNRiY+HQIVi0yJHmRYThMeGsSEpj6/4MR/pQ7lHUHcED2NVCPYwxdYwxdYBzgPNE5IEi3rsLiCjwdbjruTOZCgwp7AVjzDvGmBhjTExYWFgR3aoKZfx4u0LomWfc2mxc4iH8RCuOlskll9j6Qw4ODw3p2gR/P9FJ4wquqERwI3CdMWb7iSeMMQnASOCmIt67DGgtIs1FJAi4FjjlX5yItC7w5eXAluIGrrzA+vUwZYo9kD7cvYfKx+04SLuGoYQEB7q1XZ8SEgL9+zuaCOqHBNOvrT3cPjcv37F+VNkUlQgCjTEHTn/SGJMCnPUn0BiTC9wDzAE2ANOMMetE5DkRce1o4R4RWSciK4EHgbJVIFMVy9NPQ/Xq8MQTbm02Ny+f+KQ0ekTqsFCZDR4MW7bApk2OdTEsJpyUI1n8tkWHdSuqohJBdilfA8AYM9sY08YY09IY84LruXHGmJmuv481xnQ0xkQbY/oZY9YVP3RVof35J8yYAQ8/DPXqubXpjXuPcCw7j+6ROlFcZoMH2z8dvCvo364+dasHMW2ZlpyoqIpKBF1EJL2QxxGgc3kEqLyQMfD44zYBPFDUVFLJLUu0u1V1otgNIiKga1f47jvHugj09+Oqrk34ZeM+UvVw+wrprInAGONvjAkt5BFijNHBWVW42bPtEZTPPGPHod0sbschmtSqSmOtbOkeV15pVw7tde4MgWExEeTkGb5duduxPlTp6U4c5V65ufDII7aeTRmPoCyMMYa4xIN017sB97nmGnsX9803jnXRtmEIXcJr8pUebl8haSJQ7vX++7BhA7z4IgS6/6Yx+dBx9qVnEaMTxe7TsaPd4zF9uqPdDI2JYOPeI6zb7Ux9I1V6mgiU+xw5YoeDzj8fhgxxpIvlOw4BEKM7it1HxN4VLFgAB/6ySNBtYqMaExTgpzuNKyBNBMp9XnrJ1hWaONEtZaYLsyzxICFVAmjbUAvNudXQoZCX5+ikcc1qgQzsaA+3z8zJc6wfVXKaCJR77NplE8C118I55zjWzfIdh+jarDb+fs4kGp8VHQ3Nm8PXXzvazbCYcA4fz2Hu+n2O9qNKRhOBco+nn7afKN1YZvp0h45ms3HvEXroRLH7idi7gl9+sfWHHNK7ZT2a1KrKV3qMZYWiiUCV3apV8NFHcO+99lOlQ06cdtWrZV3H+vBp11xjzyhw6AhLAH8/4ZpuTVi4JYXdaccd60eVjCYCVTbGwH33QZ068Pe/O9rVkoRUqgb6ExVey9F+fFbPnnaDmdOrh7pHYAzMWKF3BRWFJgJVNtOmwW+/2SGh2s4O2SxJSCUmsjZBAfrP1hEnVg/99JM9WtQhTetW49wWdfhqebLuKagg9CdKld7Ro7aWUNeucNttjnZ10DU/cG4LHRZy1LXXQna2o5vLAIZ1j2BH6jH+1MPtKwRNBKr0/vUvSE6GN96wJ1456M/tqQCc20L3DziqZ09o0QI+/9zRbgZ1bkiNKgE6aVxBaCJQpZOQYPcNXH89nHee490t3qbzA+VCBK67zq4e2ufcEs9qQQFcEdWIWav3kJHlzFGZqvg0EajSefhhCAiACRPKpbslCQeJiaxNoB5U77zrr4f8fDv/46BhMeEcz8ljth5u73H6U6VKbu5cO4b8979DkyaOd5eakcWmfTo/UG46dICoKPjiC0e76da0Ni3CqusxlhWAJgJVMtnZMHYstGzpyFkDhflT9w+Uv+uvh8WLYfv2oq8tJRFhWPcIliUeIiFFD7f3JE0EqmQmTrTVRV97DYKDy6XLxQmpVAvyp3OTmuXSn8KuHgKYOtXRbq7pZg+3/1onjT1KE4EqvoQE+Mc/7Frzyy8vt27t/oE6Oj9Qnpo1s4sAHF49VD80mAvahDF9RbIebu9B+pOliscYuPtuO0H86qvl1u2BjCw278vQZaOecMMNsHYtxMc72s2IHhHsS8/i5w37He1HnZkmAlU806fbHafPPw/h4eXW7dIE1/yAThSXv2uvhSpV4IMPHO3monb1aVwzmE+WJDrajzozTQSqaOnpdoK4a1d7V1CO/th2gBpVAuik8wPlr3ZtuPpq+OwzyMx0rJsAfz9uOLcZf2xNZet+nTT2BE0EqmhPPw179sBbb9mhoXJijOG3zSn0allX5wc85dZbbVnqmTMd7WZEjwiC/P34dMkOR/tRhXP0p0tEBorIJhHZKiKPF/L6gyKyXkRWi8gvItLMyXhUKSxfDv/+N9x1ly0/UI52pB4j+dBx+rauV679qgL694emTR0fHqpXowqXdW7I9OXJutPYAxxLBCLiD0wGBgEdgOtEpMNpl8UDMcaYKOBroHy2qariycmB22+H+vXhhRfKvfuFW1IA6NM6rNz7Vi5+fnDLLfDf/8JOZzd+3dgrkiNZuXwTv8vRftRfOXlH0BPYaoxJMMZkA1OBKwteYIyZb4w55vpyCVB+s5CqaBMmwMqV8J//QK1a5d79b1sOEFGnKs3qViv3vlUBt9xiV419/LGj3XRrWouOjUP5ZHGilqcuZ04mgiZAwY8Qya7nzuQ24MfCXhCR0SISJyJxKSkpbgxRndH69fDcczB8OAwZUu7d5+Tls3hbKn1ahyGi5xN7VPPmdojoww9tDSKHiAg39WrG5n0ZJ0+jU+WjQszAichIIAZ4qbDXjTHvGGNijDExYWE6TOC4vDx7vkBIiC0x7QErd6aRkZWr8wMVxW232Q2Fc+c62k1slybUrBrIJ4t10rg8OZkIdgERBb4Odz13ChEZAPwdiDXGZDkYjyquN96AJUtsGYn69T0SwsLNKfgJ9GqpiaBCGDoUGjSA1193tJuqQf4Mjwlnzrq97Et3bsmqOpWTiWAZ0FpEmotIEHAtcMoaNBHpCryNTQK6rbAiSEiwVUUvv9wWHvOQ37YcoEtELWpWDfRYDKqAoCD429/gxx9h61ZHuxp5bjPyjOHzpUmO9qP+x7FEYIzJBe4B5gAbgGnGmHUi8pyIxLouewmoAXwlIitFxNnFyursjIE77rCnjb31lj2kxAMOZGSxKjmNfm09czeizuDOO+2/jcmTHe2mWd3qXNgmjM+WJpGVm+doX8pydI7AGDPbGNPGGNPSGPOC67lxxpiZrr8PMMY0MMZEux6xZ29ROer992HePHvyWDmWkTjdgk0pGAP922kiqFAaNYJhw+yeggxndwDfen5zDmRkMXPlbkf7UVaFmCxWFcCuXfDQQ3DhhfauwIPmbdxHg9AqdGwc6tE4VCHuvdeWHPnkE0e7Ob9VPdo2COH937frUtJyoIlA2SGh0aPtBrL33rObiDwkOzef3zYfoH+7BrpstCI691zo3t0uKHDwF7SIcFuf5mzce4Q/tqY61o+yNBEoe6s/eza8+KI9ecyDliUeJCMrV4eFKioRuO8+ezjR7NmOdnVldGPq1ajC+78nONqP0kSgEhPh/vuhX79yryxamHkb9xMU4Md5rbTsdIV13XX24Jp//MPRu4IqAf7c1KsZ8zelsHX/Ecf6UZoIfFt+PowaZT/lffihR4eETpi3cT+9W9alWlD5VTlVJRQYCI8/DkuX2sUFDrrhnKYEBfjx/u+Jjvbj6zz/k6885403YMECe+JYM88Xft2WksH2A0e5SIeFKr5bboHGje1BRQ6qW6MK13RrwowVyRw8mu1oX75ME4Gv2rjRfqq7/HJ7V1AB/LR2LwADOjTwcCSqSMHB8Mgj9oPE77872tVt5zcnKzefjxclOtqPL9NE4Ityc+Hmm6FaNXj3XY9tHDvdT2v3Eh1Ri0Y1q3o6FFUco0dDWJjjJcpb1Q/h4g4N+GhRIkf1rAJHaCLwRS++CH/+CW++aTcJVQA7Dx5jza7DXNa5oadDUcVVrZrde/LTT7BokaNd3XVhSw4fz+GLP7XshBM0EfialSvh2WdhxAj7qCBODAsN6lQxEpMqpnvusR8mHnrI0RVE3ZrW5twWdXh3YYKWnXCAJgJfkpUFN90Edes6Xi+mpH5cu4eOjUOJqKOH0HiV6tXt0NCSJTBtmqNdjbmwFfvSs/hmhZ5g5m6aCHzJs8/CmjV2XqBuxVmnv/dwJiuS0hjUSYeFvNJNN0F0NDz2GGQ6Vzq6T+t6dGoSytu/JZCXr2Un3EkTga9YtMjODdx6K1xxhaejOcWcdXZYaKAOC3knf394+WXYscOeYeEQEWHMha3YfuDoyaFE5R6aCHxBejqMHAlNm8KkSZ6O5i++X7Wbtg1CaFW/hqdDUaXVvz8MHmyHifY690v60o4NaVGvOpPnb9VidG6kicAX3Huv/bT26acQWrEqeialHiNuxyGGdD3bcdbKK0ycCNnZdgLZIf5+wl0XtmT9nnTmrt/nWD++RhNBZTdtGkyZYk8dO+88T0fzF9+ttBN/V0Y39nAkqszatIHx42H6dPjqK8e6uaprEyLrVmPSz1vI17kCt9BEUJnt3GmPFzznHHj6aU9H8xfGGL5ZuYtzmtehcS3dRFYpPPwwxMTAmDGQkuJIFwH+fowd0JoNe9JPzi+pstFEUFnl5dnVHDk5dkgosOKd/btm12ESUo5ylQ4LVR4BAbaA4eHDdkjSIbFdmtAirDqv6l2BW2giqKxeftnWgXnjDWjVytPRFOqb+F0E+fsxqLOuFqpUOnWCcePgyy/hs88c6cLfTxh7UWs27TvC7LV7HOnDl2giqIxWrICnnoJrrrFVIiugnLx8vl+1m/7t6lOzasW7W1Fl9Nhj0KePPfZ09WpHurgiqjGt69fg1Z+36L6CMtJEUNkcOwY33AD168M771SYgnKnm7t+HwcyshneI9zToSgnBAbahQq1a8NVV8GhQ27vwt9PuH9AG7buz+D7VXrIfVloIqhsxo61JaY//hjq1PF0NGf0+dIkmtSqygVt9OyBSqthQ/j6a7toYeRIexCSmw3q1JAOjUJ5ac4mMnO0BlFpOZoIRGSgiGwSka0i8nghr/cVkRUikisiQ52MxSd8/rk9fP6JJ+CiizwdzRklHjjK71sPMKJHBP5+FfOORblJr152t/Hs2fZIVDdvAvPzE/5+eXt2pR1nyuJEt7btSxxLBCLiD0wGBgEdgOtEpMNplyUBtwCfOxWHz9iyxS4VPe88eO45T0dzVl8sS8LfTxjRI8LToajycOed8MADduHCuHFub/68VvW4sG0Y/563lbRjeopZaTh5R9AT2GqMSTDGZANTgSsLXmCMSTTGrAbcf8/oSzIzYfhwCAqCL76wS/gqqOzcfL6OS2ZA+/o0CA32dDiqPIjYVWy3326PtnzpJbd38cSg9mRk5fLGvK1ub9sXOJkImgA7C3yd7HquxERktIjEiUhcikObVLzaww/bcwY+/hgiKvan7B/X7iH1aDbXn+P5M5JVORKBt96yZ2A8+qhNBm4cJmrbMIRh3SOYsjiRHalH3daur/CKyWJjzDvGmBhjTExYWJinw6lYpk+3Zws89FCFqyp6OmMM7/yWQMuw6vRpVc/T4ajy5u8Pn3xi714ffdTOGeS5b4L3wUvaEODnx4Q5m9zWpq9wMhHsAgp+PA13PafcZfNmW1a6Z0/45z89HU2RFm9LZd3udO7o0wI/nST2TYGBdvjygQfg9ddtUjh+3C1NNwgN5o6+LZi1eg9LE1Ld0qavcDIRLANai0hzEQkCrgVmOtifbzlyBIYMsfMC06bZPyu4dxYmUK9GFa006uv8/OCVV+zjm2/syqItW9zS9F0XtKRJraqM+24dOXk69VhcjiUCY0wucA8wB9gATDPGrBOR50QkFkBEeohIMjAMeFtE1jkVT6VijN0xvHmzTQLNKv54+6a9R1iwKYVbejcjONDf0+GoiuCBB+D77+0+g27dYOrUMjdZNcifcYM7sGnfEaYs3uGGIH2Do3MExpjZxpg2xpiWxpgXXM+NM8bMdP19mTEm3BhT3RhT1xjT0cl4Ko1//QtmzLATbv36eTqaYnn7t21UDfTnBp0kVgVdfrld6NC5M1x3HYwaVeZdyJd0aMAFbcKYNHcz+9OdOzqzMvGKyWJVwE8/2bMFrr/eTrZ5ga37M/g2fhc3nNOU2tUr/hCWKmcREfDrr/Dkk3YyuUMH+PbbUjcnIoyP7Uh2Xj7PzNRBhuLQROBNtm2zn5qiouwB9BW0jtDpJv28maqB/tx1YUtPh6IqqsBAe8zln39Cgwa2PtHVV8P27aVqrnm96oy9qDU/rt3Lj2u0OmlRNBF4i4MH7W20n5+dYKtWzdMRFcu63YeZtXoPt57fnLo1qng6HFXRdesGy5bZVXBz5kD79raS7tGS7w0Y3bcFHRuH8vR363THcRE0EXiDrKz/fTr69lto3tzTERXby//dTGhwALf3aeHpUJS3CAy09bI2bbKl1F94Adq2tbW0SlC4LtDfjwlDo0g7ls1z3693MGDvp4mgojPGbs3/9Vd78lOfPp6OqNj+2HqAeRv387cLWuqZA6rkwsPtwTa//26Hi264wR67Om9esZvo2LgmY/q1Ykb8Ln5YraWqz0QTQUX31FP2qMnnn7cTxF4iOzefcd+tpWmdatx2vvfcwagK6Lzz7NzBxx/Dvn22su6gQbBqVbHefm//VkRH1OLJGWvYleaezWuVjSaCiuyll+xY6R132BUVXuTDP7azLeUo42M76L4BVXb+/vYM7s2b7c/F0qXQtat9bsfZ9wsE+vvx2rXR5OUbHvhypZ5mVghNBBXV22/beiwjRsB//uM1K4QA9hw+zmu/bGFA+wb0b9fA0+GoyiQ42BZZ3LYNHnnEbqhs08bW2ko9c1mJZnWr8+yVnfhz+0Em/ldrEZ1OE0FF9OmncNdddpXQJ5/YT0NewhjD49PXkJdveGbw6cdPKOUmtWvDiy/a0hQ33ACvvgotW9rNlmeoXTS0ezjX9YzgPwu26ZLS02giqGjef9/e7l5wAXz1lV1B4UU+WbKDXzen8NTl7Ymo4x1LXJUXi4iADz6w8wV9+tjVRq1b25+jQiqbjo/tSJeIWjz81Sq27DvigYArJk0EFcnrr9sVQpdcArNmQdWqno6oRLbuP8ILszZwYdswRp6rpSRUOerUydYtWrDArja6/Xa78fL7708596BKgD9vjexG1aAAbvlwmZagcNFEUBEYY1cFjR1rK4p+953XbBg74WhWLvd8Hk/1KgFMGBqFeNGchqpELrgAFi+Gr7+GnByIjf3fcy6Nalblg1tiOHQsm1EfLSMjK9eDAVcMmgg8LTvbFtp6+mkYOdJOflXxrh24+a7VGJv3HWHSiGjqh+gRlMqDROxGtHXr7EKLzZuhd29btmLtWgCiwmsx+YZubNx7hDs/WU5mjvsOyPFGmgg86cABuPhiuz762WdhyhSvmxMAeHnuJv67fh9PXd6BC9roCXKqgggMhDvvhK1b4bnn7Ea0qCg7B5eQQL+29ZlwTRR/bDvAHVPiOJ7tu8lAE4GnLFkCMTF2PfQXX8C4cV61RPSEj/7YzuT527iuZ1NGnRfp6XCU+qsaNewdd0KCXXr61VfQrh3cfTfXNPbnpaFd+H3rAW77eBlHfXSYSBNBecvPt8vezj/f/uL/7Te49lpPR1UqH/2xnfHfr+fSjg147sqOOi+gKra6dWHCBLsH4bbb4J13oGVLhn7xKpP7NWRJQirD3lrMnsO+t/tYE0F52rrVDgU9/rgtIhcfb88b9jLGGN76ddvJJPDGdd0I9Nd/SspLNG5s5w42brRzCZMmcVnseSzc8TW5CQkMmfwHa5IPezrKciXGeNd265iYGBMXF+fpMEomO9t+Enn+eTsRPHGiXd7mhZ+gM3PyePKbNcxYsYsrohrxyvBoggI0CSgvtm2bvUv/6COMMczuchFvRw9myC2XMeq8yEpzpysiy40xMYW+ponAQfn5dhnb00/blQvDhtkdkI0bezqyUtmWksGDX65kVfJhHhjQhvsualVpfkiUYudOmDgR8+67yPHj/Bnegbgrrif22XsIr1/T09GV2dkSgX6Uc0J+PsycCd2721pBgYF2g9i0aV6ZBHLz8nlvYQKXvbaQxNRjvDWyG2MHtNYkoCqXiAh47TVk1y7MxIm0z89gzFtPEdSyBXE33U32mrWejtAxmgjcKS0NJk2yRbCuvBLS022toFWr4LLLPB1diRlj+O+6vQx8bSHPz9pAn9b1mPtAXwZ2auTp0JRyTu3ayEMPEbJzOwe+nMG+Fu3o+ulbBEV1JrVtJ3InTIDkZE9H6VY6NFRWx47ZT/tTp8Ls2ZCZaeun33uvnRD2wn0BmTl5fL9qNx8vTmTtrnRa1KvOI5e2ZWCnhnoXoHzS0kXrWPvqe3T7/Ue67rHVS7OjuhB02SC49FK7YS0oyMNRnp3OEbhTTg6sXm03p/z8MyxcaKsdNmgAw4fDLbfYc1e9TGZOHksSUvlxzV7mrN9L2rEcWtevwW3nN2do93ACdFWQ8nHGGBZuOcDsbxZS58fvuCBhBd13bSAgP4/86jWQvn2Qc86BHj3sI6xiba70WCIQkYHAa4A/8J4x5l+nvV4FmAJ0B1KBEcaYxLO1WW6JIDfXHnixZYt9bNoEy5fDypX2Uz9Ahw4wYICtD9S3r9eUi87LNySmHmXjniNs2JNO3I6DrEhKIzs3nxpVAhjQvj7DYyLo1bKu3gEoVYjkQ8eYsWIXv8Zto86ff9B3+wp67VpHi5Qk/Fy/U3MjmuLfJQpp08YOF7duDa1aQaNGHhkp8EgiEBF/YDNwMZAMLAOuM8asL3DNGCDKGHOniFwLXGWMGXG2dkudCFJS7C/2I0f+98jIsH8ePgz799tj8E48kpPtp/8TatSA6Oj/ZfsLLqiQE787Uo+yK+046cdzST+ew2HXY/+RTPYczmRX2nF2HTpOVq49BNxPoF3DUHq1rMt5repyXqt6VAnwjoSmVEWwI/UoSxJSWbr9IGs2JlNn41qi9myhy94ttD6UTLODuwnOyTp5vREhq3Zdsus3JK9BQySsHrUahUGtWlCzpn3UqgUhIfYgnqpV7SM4GBo2tM+XgqcSQS9gvDHmUtfXTwAYY/6vwDVzXNcsFpEAYC8QZs4SVKkTwYsv2o1chQdrb+MaNPjfIzzcZvATj4YNvWLd/92fr2DW6lMP3fATqFejCo1rVaVxrWCa1KpKmwYhtG8USqv6NfQoSaXcKOVIFlv3Z7A1JYOt+46w59Ax8nbupFpiAqG7k6h35CANMg5SPyOVBhkHqZuVQWOTaReXFPX7+M037aFVpeCpRDAUGGiMud319Y3AOcaYewpcs9Z1TbLr622uaw6c1tZoYLTry7aAU2fN1QMOFHlV5abfA/0egH4PoPJ9D5oZYwqduAgo70hKwxjzDvCO0/2ISNyZMqav0O+Bfg9AvwfgW98DJ5eC7AIiCnwd7nqu0GtcQ0M1sZPGSimlyomTiWAZ0FpEmotIEHAtMPO0a2YCN7v+PhSYd7b5AaWUUu7n2NCQMSZXRO4B5mCXj35gjFknIs8BccaYmcD7wCcishU4iE0WnuT48JMX0O+Bfg9AvwfgQ98Dr9tQppRSyr10u6hSSvk4TQRKKeXjNBEAIvKBiOx37WvwOSISISLzRWS9iKwTkbGejskTRCRYRP4UkVWu78Ozno7JU0TEX0TiReQHT8fiCSKSKCJrRGSliFSgKpfO0DkCQET6AhnAFGNMJ0/HU95EpBHQyBizQkRCgOXAkILlQHyB2MJK1Y0xGSISCPwOjDXGLPFwaOVORB4EYoBQY8wVno6nvIlIIhBz+ubWykrvCABjzG/YVUs+yRizxxizwvX3I8AGoIlnoyp/xspwfRnoevjcJyURCQcuB97zdCyqfGgiUKcQkUigK7DUw6F4hGtIZCWwH5hrjPHF78OrwKNAvofj8CQD/FdElrtK3FRqmgjUSSJSA5gO3G+MSfd0PJ5gjMkzxkRjd8L3FBGfGioUkSuA/caY5Z6OxcPON8Z0AwYBd7uGjystTQQKANeY+HTgM2PMDE/H42nGmDRgPjDQw6GUt/OAWNcY+VSgv4h86tmQyp8xZpfrz/3AN0BPz0bkLE0E6sQk6fvABmPMK56Ox1NEJExEarn+XhV7lsZGjwZVzowxTxhjwo0xkdid/vOMMSM9HFa5EpHqrkUTiEh14BKgUq8o1EQAiMgXwGKgrYgki8htno6pnJ0H3Ij99LfS9bjM00F5QCNgvoisxtbKmmuM8cnlkz6uAfC7iKwC/gRmGWN+8nBMjtLlo0op5eP0jkAppXycJgKllPJxmgiUUsrHaSJQSikfp4lAKaV8nCYCVSmJyCQRub/A13NE5L0CX7/sKqx2pvc/JyIDiuhjvIg8XMjztURkzBneEykix11lLE58XaI16q5KsRki4hMHqyvnaSJQldUfQG8AEfED6gEdC7zeG1h0pjcbY8YZY34uZd+1gEITgcs2VxmLUjHG9AMqfWlkVX40EajKahHQy/X3jtidoUdEpLaIVAHaAytEpLuI/OoqLjbHVZIbEflIRIa6/n6ZiGx0XfP6aTX6O4jIAhFJEJH7XM/9C2jp2pj3UnEDFpEWrjMAeohINRGZ5joj4hsRWap3AMopjh1er5QnGWN2i0iuiDTFfvpfjC2t3Qs4DKzBVph8A7jSGJMiIiOAF4BbT7QjIsHA20BfY8x21y70gtoB/YAQYJOI/Ad4HOhUkk/9ItIWW9vnFmPMKteQ0yFjTAdX4buVJf4mKFVMmghUZbYImwR6A69gE0FvbCL4A2gLdALm2nJL+AN7TmujHZBgjNnu+voLoGBZ4lnGmCwgS0T2Y8sTlFQY8B1wdYHDgM4HXgMwxqx1lb1QyhGaCFRldmKeoDN2aGgn8BCQDnwICLDOGNPrjC0ULavA3/Mo3c/UYSAJ+8vfp06FUxWDzhGoymwRcAVw0HXOwEHsRG4v12ubgDAR6QW2FLeIdDytjU1AC9eBPQAjitHvEexQUXFlA1cBN4nI9a7n/gCGu+LqgE1mSjlC7whUZbYGu1ro89Oeq3HiLFrXhPDrIlIT+/PwKrDuxMXGmOOupaA/ichRbFXSszLGpIrIH65loT8aYx4pxnuOug6FmSsiGcCbwMcish5bCnsd9s5BKbfT6qNKFUFEargOtBdgMrDFGDOplG1FAj8YY8568pmI+AOBxphMEWkJ/Ay0NcZku15fADxsjNFlpKrM9I5AqaLdISI3A0FAPHYVUWnlATVFZGURq4qqYc9GCMTOZYwpkATmAy2AnDLEodRJekeglFI+TieLlVLKx2kiUEopH6eJQCmlfJwmAqWU8nGaCJRSysf9P3HG4fz2KcBtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(weight_NO_smoke,label=\"No fumadora\")\n",
    "sns.kdeplot(weight_YES_smoke,color=\"red\",label=\"Fumadora\")\n",
    "plt.xlabel(\"Weight [kg]\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La diferencia de medias NO_smoker-YES_smoker es:0.37\n",
      "La diferencia de medias YES_smoker-NO_smoker es:-0.37\n"
     ]
    }
   ],
   "source": [
    "diff_NO_YES=np.mean(weight_NO_smoke.values)-np.mean(weight_YES_smoke.values)\n",
    "diff_YES_NO=np.mean(weight_YES_smoke.values)-np.mean(weight_NO_smoke.values)\n",
    "print(f\"La diferencia de medias NO_smoker-YES_smoker es:{np.round(diff_NO_YES,2)}\")\n",
    "print(f\"La diferencia de medias YES_smoker-NO_smoker es:{np.round(diff_YES_NO,2)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "¿Cómo de probable es que estos cambios hayan ocurrido al azar?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "X1=weight_NO_smoke\n",
    "X2=weight_YES_smoke\n",
    "\n",
    "def perm_func(X1: pd.Series, X2:pd.Series) -> (pd.Series,pd.Series): \n",
    "    X = X1.append(X2).reset_index(drop=True)\n",
    "\n",
    "    X1_reorder=X.sample(frac=0.5)\n",
    "    X2_reorder=X.drop(X1_reorder.index)\n",
    "    return (X1_reorder.reset_index(drop=True),X2_reorder.reset_index(drop=True))\n",
    "\n",
    "X1_reorder, X2_reorder= perm_func(weight_NO_smoke,weight_YES_smoke)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_values = []\n",
    "num_mean_X1_larger_X2 = 0\n",
    "num_mean_X2_larger_X1 = 0\n",
    "\n",
    "total_trials = 10000\n",
    "for i in range(total_trials):\n",
    "    X1_reorder, X2_reorder= perm_func(weight_NO_smoke,weight_YES_smoke)\n",
    "    \n",
    "    mean_diff = np.mean(X1_reorder.values) - np.mean(X2_reorder.values)\n",
    "    mean_values.append(mean_diff)\n",
    "    \n",
    "    if mean_diff>diff_NO_YES:\n",
    "        num_mean_X1_larger_X2 += 1\n",
    "    \n",
    "    if mean_diff<diff_YES_NO:\n",
    "        num_mean_X2_larger_X1 += 1\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "La probabilidad por puro azar la media de X1 menos X2 sea mayor que la diferencia original: \n",
      "    2.43%\n",
      "La probabilidad por puro azar la media de X1 menos X2 sea menor que la diferencia original: \n",
      "    2.3%\n",
      "La probabilidad de que por puro azar los valores de NO_smoker y YES_smoker se hayan reordenado\n",
      "para dar diferencias tan grandes es:4.73%\n"
     ]
    }
   ],
   "source": [
    "print(f\"\"\"La probabilidad por puro azar la media de X1 menos X2 sea mayor que la diferencia original: \n",
    "    {np.round(num_mean_X1_larger_X2/total_trials*100,2)}%\"\"\")\n",
    "\n",
    "print(f\"\"\"La probabilidad por puro azar la media de X1 menos X2 sea menor que la diferencia original: \n",
    "    {np.round(num_mean_X2_larger_X1/total_trials*100,2)}%\"\"\")\n",
    "\n",
    "print(f\"\"\"La probabilidad de que por puro azar los valores de NO_smoker y YES_smoker se hayan reordenado\n",
    "para dar diferencias tan grandes es:{np.round((num_mean_X2_larger_X1+num_mean_X1_larger_X2)/total_trials*100,2)}%\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0fea6f5a58>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "#sns.displot(mean_values)\n",
    "sns.kdeplot(mean_values)\n",
    "plt.axvline(diff_NO_YES, 0,2,color=\"#FF0000\")\n",
    "plt.axvline(diff_YES_NO, 0,2,color=\"#FF0000\")\n",
    "x=np.linspace(-1, 1, 100)\n",
    "plt.plot( x, norm.pdf(x, 0, np.std(mean_values,ddof=1)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.034784541157748046"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(mean_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que la probabilidad de que esos datos se hayan conseguido por puro hazar es muy baja, inferior al 5%-"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### T-student"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El t-test es usado cuando tienes dos grupos de datos y quieres saber si la media de ambos grupos es igual o no. Tenemos dos hipótesis:\n",
    "\\\\[H_0 : \\mu(X) = \\mu(Y) \\\\]\n",
    "\\\\[H_1 : \\mu(X) \\ne \\mu(Y) \\\\]\n",
    "\n",
    "Empezamos con las siguientes suposiciones:\n",
    "1. Las muestras han sido seleccionas por muestreo aleatorio simple dentro de la población.\n",
    "2. Las poblaciones siguen una distribución normal. (sino usar test Wilcoxon-Mann-Whitney)\n",
    "3. Ambas poblaciones tienen la misma varianza. (sino usar test Welch)\n",
    "4. Las poblaciones no están correladas. (sino usar t-test emparejado)\n",
    "\n",
    "Primero calculamos la media y varianza de ambos grupos. El test para verificar si la hipótesis nula $H_0$ es cierta puede ser calculado como sigue:\n",
    "\n",
    "\\\\[ t=\\frac{E[X]-E[Y]}{s_p·\\sqrt{\\frac{1}{n_x}+\\frac{1}{n_y}}} \\\\]\n",
    "\n",
    "Donde $s_p$ es la desviación estandar compuesta, calculada como:\n",
    "\n",
    "\\\\[ s^2_p=\\frac{(n_x-1)Var[X]+(n_y-1)Var[Y]}{n_x+n_y-2} \\\\]\n",
    "\n",
    "Donde $n_x$ y $n_y$ son los números de muestras en cada uno de los grupos muestreados. El número de grados de libertad es \n",
    "$d.f.=n_x+n_y-2$. Podemos asumir que las dos varianzas son iguales si ambas pasan el test de varianza de Fisher(F-test).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.046502721823500064"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "t, p = stats.ttest_ind(weight_NO_smoke,weight_YES_smoke)\n",
    "p\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ejemplo practico\n",
    "\n",
    "¿Cuantos caramelos hay en estos grupos?\n",
    "\n",
    "![](https://github.com/calabozo/orange-stats/raw/master/caramelos.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regresiones lineales\n",
    "\n",
    "Modelo matemático usado para aproximar la relación de dependencia entre una variable dependiente $Y$, diferentes variables independientes definidas en la matriz $X$ y un término aleatorio $\\varepsilon$. Este modelo puede ser expresado como:\n",
    "\n",
    "\\\\[\n",
    "\\hat{Y}=\\beta_1 X_1+\\beta_2 X_2+\\cdots +\\beta_p X_p = \\sum \\beta_k X_k\n",
    "\\\\]\n",
    "\n",
    "\n",
    "Tratamos de encontrar la predicción $\\hat{Y}$ tal que minimize el error cuadrático medio:\n",
    "\\\\[\n",
    "MSE = {1 \\over n} \\sum_{i=0}^n{(Y-\\hat{Y})^2}\n",
    "\\\\]\n",
    "\n",
    "\n",
    "\n",
    "![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Linear_regression.svg/400px-Linear_regression.svg.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "train,test = train_test_split(birth_weight,test_size=0.33, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.formula.api import ols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>id</th>\n",
       "      <th>headcirumference</th>\n",
       "      <th>length</th>\n",
       "      <th>Birthweight</th>\n",
       "      <th>Gestation</th>\n",
       "      <th>smoker</th>\n",
       "      <th>motherage</th>\n",
       "      <th>mnocig</th>\n",
       "      <th>mheight</th>\n",
       "      <th>mppwt</th>\n",
       "      <th>fage</th>\n",
       "      <th>fedyrs</th>\n",
       "      <th>fnocig</th>\n",
       "      <th>fheight</th>\n",
       "      <th>lowbwt</th>\n",
       "      <th>mage35</th>\n",
       "      <th>LowBirthWeight</th>\n",
       "      <th>Birthweight_kg</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1600</td>\n",
       "      <td>13</td>\n",
       "      <td>21</td>\n",
       "      <td>6.3</td>\n",
       "      <td>39</td>\n",
       "      <td>0</td>\n",
       "      <td>19</td>\n",
       "      <td>0</td>\n",
       "      <td>64</td>\n",
       "      <td>125</td>\n",
       "      <td>23</td>\n",
       "      <td>14</td>\n",
       "      <td>2</td>\n",
       "      <td>76</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>Normal</td>\n",
       "      <td>2.857630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>27</td>\n",
       "      <td>14</td>\n",
       "      <td>20</td>\n",
       "      <td>7.8</td>\n",
       "      <td>41</td>\n",
       "      <td>1</td>\n",
       "      <td>37</td>\n",
       "      <td>25</td>\n",
       "      <td>63</td>\n",
       "      <td>145</td>\n",
       "      <td>46</td>\n",
       "      <td>16</td>\n",
       "      <td>0</td>\n",
       "      <td>68</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Normal</td>\n",
       "      <td>3.538018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>57</td>\n",
       "      <td>14</td>\n",
       "      <td>20</td>\n",
       "      <td>7.3</td>\n",
       "      <td>39</td>\n",
       "      <td>1</td>\n",
       "      <td>23</td>\n",
       "      <td>17</td>\n",
       "      <td>62</td>\n",
       "      <td>104</td>\n",
       "      <td>32</td>\n",
       "      <td>12</td>\n",
       "      <td>25</td>\n",
       "      <td>66</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>Normal</td>\n",
       "      <td>3.311222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>1764</td>\n",
       "      <td>15</td>\n",
       "      <td>22</td>\n",
       "      <td>10.0</td>\n",
       "      <td>41</td>\n",
       "      <td>1</td>\n",
       "      <td>32</td>\n",
       "      <td>12</td>\n",
       "      <td>68</td>\n",
       "      <td>154</td>\n",
       "      <td>38</td>\n",
       "      <td>14</td>\n",
       "      <td>25</td>\n",
       "      <td>71</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>Normal</td>\n",
       "      <td>4.535920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>1388</td>\n",
       "      <td>13</td>\n",
       "      <td>20</td>\n",
       "      <td>6.9</td>\n",
       "      <td>41</td>\n",
       "      <td>1</td>\n",
       "      <td>22</td>\n",
       "      <td>7</td>\n",
       "      <td>63</td>\n",
       "      <td>117</td>\n",
       "      <td>24</td>\n",
       "      <td>16</td>\n",
       "      <td>12</td>\n",
       "      <td>69</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>Normal</td>\n",
       "      <td>3.129785</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      id  headcirumference  length  Birthweight  Gestation  smoker  motherage  \\\n",
       "15  1600                13      21          6.3         39       0         19   \n",
       "33    27                14      20          7.8         41       1         37   \n",
       "16    57                14      20          7.3         39       1         23   \n",
       "36  1764                15      22         10.0         41       1         32   \n",
       "35  1388                13      20          6.9         41       1         22   \n",
       "\n",
       "    mnocig  mheight  mppwt  fage  fedyrs  fnocig  fheight  lowbwt  mage35  \\\n",
       "15       0       64    125    23      14       2       76       0       0   \n",
       "33      25       63    145    46      16       0       68       0       1   \n",
       "16      17       62    104    32      12      25       66       0       0   \n",
       "36      12       68    154    38      14      25       71       0       0   \n",
       "35       7       63    117    24      16      12       69       0       0   \n",
       "\n",
       "   LowBirthWeight  Birthweight_kg  \n",
       "15         Normal        2.857630  \n",
       "33         Normal        3.538018  \n",
       "16         Normal        3.311222  \n",
       "36         Normal        4.535920  \n",
       "35         Normal        3.129785  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         Birthweight_kg   R-squared:                       0.322\n",
      "Model:                            OLS   Adj. R-squared:                  0.228\n",
      "Method:                 Least Squares   F-statistic:                     3.426\n",
      "Date:                Thu, 10 Dec 2020   Prob (F-statistic):             0.0124\n",
      "Time:                        10:59:10   Log-Likelihood:                -29.681\n",
      "No. Observations:                  42   AIC:                             71.36\n",
      "Df Residuals:                      36   BIC:                             81.79\n",
      "Df Model:                           5                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -4.1471      2.838     -1.461      0.153      -9.903       1.609\n",
      "mheight        0.1129      0.035      3.262      0.002       0.043       0.183\n",
      "motherage     -0.0482      0.026     -1.873      0.069      -0.100       0.004\n",
      "fheight       -0.0014      0.032     -0.044      0.965      -0.066       0.063\n",
      "fage           0.0556      0.021      2.630      0.012       0.013       0.098\n",
      "mnocig        -0.0114      0.007     -1.596      0.119      -0.026       0.003\n",
      "==============================================================================\n",
      "Omnibus:                        1.441   Durbin-Watson:                   1.202\n",
      "Prob(Omnibus):                  0.487   Jarque-Bera (JB):                0.672\n",
      "Skew:                           0.257   Prob(JB):                        0.715\n",
      "Kurtosis:                       3.346   Cond. No.                     3.60e+03\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, 3.6e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = ols(formula='Birthweight_kg ~ mheight + motherage + fheight + fage + mnocig', data=birth_weight)\n",
    "res = model.fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:         Birthweight_kg   R-squared:                       0.183\n",
      "Model:                            OLS   Adj. R-squared:                  0.141\n",
      "Method:                 Least Squares   F-statistic:                     4.362\n",
      "Date:                Thu, 10 Dec 2020   Prob (F-statistic):             0.0195\n",
      "Time:                        10:59:10   Log-Likelihood:                -33.616\n",
      "No. Observations:                  42   AIC:                             73.23\n",
      "Df Residuals:                      39   BIC:                             78.45\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -2.7943      2.232     -1.252      0.218      -7.308       1.720\n",
      "mheight        0.0961      0.035      2.763      0.009       0.026       0.166\n",
      "mnocig        -0.0107      0.007     -1.504      0.141      -0.025       0.004\n",
      "==============================================================================\n",
      "Omnibus:                        1.445   Durbin-Watson:                   1.204\n",
      "Prob(Omnibus):                  0.485   Jarque-Bera (JB):                0.714\n",
      "Skew:                          -0.284   Prob(JB):                        0.700\n",
      "Kurtosis:                       3.291   Cond. No.                     1.69e+03\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, 1.69e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model = ols(formula='Birthweight_kg ~ mheight+ mnocig', data=birth_weight)\n",
    "res = model.fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clasificación: Regresión logística"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En lugar de realizar una predicción de un valor queremos hacer un clasificador.\n",
    "Podemos tratar de asignar una probabilidad. Pero hay un problema porque la regresión lineal va entre 0 y 1.\n",
    "\n",
    "Para ello transformarmos la regresión lineal mediante la función logit:\n",
    "\n",
    "![](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Logit.svg/350px-Logit.svg.png)\n",
    "\n",
    "#### función de enlace (link function)\n",
    "\n",
    "Para pasar del dominio de números reales $(-\\infty,\\infty)$ al de probabilidades $[0,1]$ a vamos a utilizar la **función logística**:\n",
    "\\\\[\n",
    "p = h(x)=  \\frac{1}{1+e^{-x}}\n",
    "\\\\]\n",
    "Su inversa se conoce como la función **logit**:\n",
    "\\\\[\n",
    "h^{-1}(p) = log \\left( \\frac{p}{1-p} \\right)\n",
    "\\\\]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es decir, cuando estemos trabajando con una **distribución binomial** un modelo lineal del tipo:\n",
    "\\\\[\n",
    "y = \\beta \\vec{x}+\\beta_0\n",
    "\\\\]\n",
    "lo podemos trasnformar en:\n",
    "\\\\[\n",
    "y = p(x) = \\frac{1}{1+e^{-\\beta \\vec{x}-\\beta_0}} \n",
    "\\\\]\n",
    "Ahora $p(x)$ es una función que muestra valores en el rango $[0,1]$, puede ser considerada como una probabilidad.\n",
    "\n",
    "Y definiendo un umbral podríamos tener el siguiente clasificador:\n",
    "* Seleccionamos clase 1 si p(x)>=0.5\n",
    "* Seleccionamos clase 0 si p(x)< 0.5\n",
    "\n",
    "\n",
    "\n",
    "Es decir, tenemos una probabilidad, su valor está en el rango $[0,1]$:\n",
    "\\\\[\n",
    "    p = \\frac{1}{1-e^{-\\hat{Y}}}= \\frac{1}{1-e^{-(\\beta_1 X_1+\\beta_2 X_2+\\cdots +\\beta_p X_p)}}   \n",
    "\\\\]\n",
    "\n",
    "Definimos la razón de monomios (Odds ratio) como el cociente entre dos probabilidades, su valor está en el rango $[0,\\infty]$:\n",
    "\n",
    "\\\\[\n",
    " Odds = \\frac{p}{1-p}=\\frac{\\frac{1}{1-e^{-(\\beta_1 X_1+\\beta_2 X_2+\\cdots +\\beta_p X_p)}}}{\\frac{e^{-(\\beta_1 X_1+\\beta_2 X_2+\\cdots +\\beta_p X_p)}}{1-e^{-(\\beta_1 X_1+\\beta_2 X_2+\\cdots +\\beta_p X_p)}}}=e^{(\\beta_1 X_1+\\beta_2 X_2+\\cdots +\\beta_p X_p)}\n",
    "\\\\]\n",
    "\n",
    "Si aplicamos el logaritmo a la razón de monomios tenemos un valor que está en el rango $[-\\infty,\\infty]$:\n",
    "\\\\[\n",
    " log(Odds)= log \\left(\\frac{p}{1-p} \\right) = \\beta_1 X_1+\\beta_2 X_2+\\cdots +\\beta_p X_p\n",
    "\\\\]\n",
    "\n",
    "La función de coste que vamos a tratar de minimizar será:\n",
    "\\\\[\n",
    "\\begin{split}\n",
    "Cost(p(x),y) &= {1 \\over n} \\sum_{i=0}^n{(y-\\hat{y})^2}\\\\\n",
    "Cost(p(x),y) &= {1 \\over n} \\sum_{i=0}^n{(y-p(x))^2}\n",
    "\\end{split}\n",
    "\\\\]\n",
    "Que transformaremos en:\n",
    "\\\\[\n",
    "Cost(p(x),y) = -y ·log(p(x))-(1-y)·log(1-p(x))\n",
    "\\\\]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ejemplo:Churn rate\n",
    "\n",
    "Vamos a utilizar un dataset publicado por IBM en [kaggle](https://www.kaggle.com/blastchar/telco-customer-churn).\n",
    "\n",
    "\n",
    "En este ejemplo vamos a cargar el dataset proporcionado y ver si somos capaces de ver qué usuarios son los que corren más riesgo de irse.\n",
    "\n",
    "El conjunto de datos incluye información sobre:\n",
    "\n",
    "* Clientes que se fueron en el último mes: la columna se llama Churn\n",
    "* Servicios para los que se ha registrado cada cliente: teléfono, líneas múltiples, Internet, seguridad en línea, copia de seguridad en línea, protección de dispositivos, soporte técnico y transmisión de TV y películas\n",
    "* Información de la cuenta del cliente: cuánto tiempo han sido cliente (columna tenure), contrato, método de pago, facturación electrónica, cargos mensuales y cargos totales\n",
    "* Información demográfica sobre los clientes: sexo, rango de edad y si tienen socios y dependientes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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>customerID</th>\n",
       "      <th>gender</th>\n",
       "      <th>SeniorCitizen</th>\n",
       "      <th>Partner</th>\n",
       "      <th>Dependents</th>\n",
       "      <th>tenure</th>\n",
       "      <th>PhoneService</th>\n",
       "      <th>MultipleLines</th>\n",
       "      <th>InternetService</th>\n",
       "      <th>OnlineSecurity</th>\n",
       "      <th>...</th>\n",
       "      <th>DeviceProtection</th>\n",
       "      <th>TechSupport</th>\n",
       "      <th>StreamingTV</th>\n",
       "      <th>StreamingMovies</th>\n",
       "      <th>Contract</th>\n",
       "      <th>PaperlessBilling</th>\n",
       "      <th>PaymentMethod</th>\n",
       "      <th>MonthlyCharges</th>\n",
       "      <th>TotalCharges</th>\n",
       "      <th>Churn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7590-VHVEG</td>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>1</td>\n",
       "      <td>No</td>\n",
       "      <td>No phone service</td>\n",
       "      <td>DSL</td>\n",
       "      <td>No</td>\n",
       "      <td>...</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Month-to-month</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Electronic check</td>\n",
       "      <td>29.85</td>\n",
       "      <td>29.85</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5575-GNVDE</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>34</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>DSL</td>\n",
       "      <td>Yes</td>\n",
       "      <td>...</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>One year</td>\n",
       "      <td>No</td>\n",
       "      <td>Mailed check</td>\n",
       "      <td>56.95</td>\n",
       "      <td>1889.5</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3668-QPYBK</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>2</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>DSL</td>\n",
       "      <td>Yes</td>\n",
       "      <td>...</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Month-to-month</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Mailed check</td>\n",
       "      <td>53.85</td>\n",
       "      <td>108.15</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7795-CFOCW</td>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>45</td>\n",
       "      <td>No</td>\n",
       "      <td>No phone service</td>\n",
       "      <td>DSL</td>\n",
       "      <td>Yes</td>\n",
       "      <td>...</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>One year</td>\n",
       "      <td>No</td>\n",
       "      <td>Bank transfer (automatic)</td>\n",
       "      <td>42.30</td>\n",
       "      <td>1840.75</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9237-HQITU</td>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>2</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>Fiber optic</td>\n",
       "      <td>No</td>\n",
       "      <td>...</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Month-to-month</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Electronic check</td>\n",
       "      <td>70.70</td>\n",
       "      <td>151.65</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   customerID  gender  SeniorCitizen Partner Dependents  tenure PhoneService  \\\n",
       "0  7590-VHVEG  Female              0     Yes         No       1           No   \n",
       "1  5575-GNVDE    Male              0      No         No      34          Yes   \n",
       "2  3668-QPYBK    Male              0      No         No       2          Yes   \n",
       "3  7795-CFOCW    Male              0      No         No      45           No   \n",
       "4  9237-HQITU  Female              0      No         No       2          Yes   \n",
       "\n",
       "      MultipleLines InternetService OnlineSecurity  ... DeviceProtection  \\\n",
       "0  No phone service             DSL             No  ...               No   \n",
       "1                No             DSL            Yes  ...              Yes   \n",
       "2                No             DSL            Yes  ...               No   \n",
       "3  No phone service             DSL            Yes  ...              Yes   \n",
       "4                No     Fiber optic             No  ...               No   \n",
       "\n",
       "  TechSupport StreamingTV StreamingMovies        Contract PaperlessBilling  \\\n",
       "0          No          No              No  Month-to-month              Yes   \n",
       "1          No          No              No        One year               No   \n",
       "2          No          No              No  Month-to-month              Yes   \n",
       "3         Yes          No              No        One year               No   \n",
       "4          No          No              No  Month-to-month              Yes   \n",
       "\n",
       "               PaymentMethod MonthlyCharges  TotalCharges Churn  \n",
       "0           Electronic check          29.85         29.85    No  \n",
       "1               Mailed check          56.95        1889.5    No  \n",
       "2               Mailed check          53.85        108.15   Yes  \n",
       "3  Bank transfer (automatic)          42.30       1840.75    No  \n",
       "4           Electronic check          70.70        151.65   Yes  \n",
       "\n",
       "[5 rows x 21 columns]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#df_churn=pd.read_csv(\"WA_Fn-UseC_-Telco-Customer-Churn.csv\")\n",
    "df_churn=pd.read_csv(\"https://github.com/calabozo/orange-stats/raw/master/WA_Fn-UseC_-Telco-Customer-Churn.csv\")\n",
    "df_churn.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "customerID           object\n",
       "gender               object\n",
       "SeniorCitizen         int64\n",
       "Partner              object\n",
       "Dependents           object\n",
       "tenure                int64\n",
       "PhoneService         object\n",
       "MultipleLines        object\n",
       "InternetService      object\n",
       "OnlineSecurity       object\n",
       "OnlineBackup         object\n",
       "DeviceProtection     object\n",
       "TechSupport          object\n",
       "StreamingTV          object\n",
       "StreamingMovies      object\n",
       "Contract             object\n",
       "PaperlessBilling     object\n",
       "PaymentMethod        object\n",
       "MonthlyCharges      float64\n",
       "TotalCharges         object\n",
       "Churn                object\n",
       "dtype: object"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_churn.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_churn=df_churn.drop(\n",
    "    columns=[\"customerID\",\"OnlineSecurity\",\"OnlineBackup\",\n",
    "             \"DeviceProtection\",\"TechSupport\",\"StreamingTV\",\"StreamingMovies\",\"TotalCharges\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "gender               object\n",
       "SeniorCitizen         int64\n",
       "Partner              object\n",
       "Dependents           object\n",
       "tenure                int64\n",
       "PhoneService         object\n",
       "MultipleLines        object\n",
       "InternetService      object\n",
       "Contract             object\n",
       "PaperlessBilling     object\n",
       "PaymentMethod        object\n",
       "MonthlyCharges      float64\n",
       "Churn                object\n",
       "dtype: object"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_churn.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.formula.api import logit\n",
    "# https://www.statsmodels.org/stable/generated/statsmodels.formula.api.logit.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[No, Yes]\n",
       "Categories (2, object): [No, Yes]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_churn[\"Churn\"].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_churn[\"Churn\"]=df_churn[\"Churn\"].astype('category')\n",
    "df_churn[\"Churn_id\"]=df_churn[\"Churn\"].cat.codes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "df_churn_train,df_churn_test = train_test_split(df_churn,test_size=0.33, random_state=42)\n",
    "df_churn_test=df_churn_test.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.441677\n",
      "         Iterations 7\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>Churn_id</td>     <th>  No. Observations:  </th>   <td>  4718</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>   <td>  4710</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>   <td>     7</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Thu, 10 Dec 2020</td> <th>  Pseudo R-squ.:     </th>   <td>0.2335</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>14:52:58</td>     <th>  Log-Likelihood:    </th>  <td> -2083.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th>  <td> -2718.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>6.808e-270</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>   -0.3861</td> <td>    0.209</td> <td>   -1.852</td> <td> 0.064</td> <td>   -0.795</td> <td>    0.023</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(InternetService)[T.Fiber optic]</th>           <td>    1.2640</td> <td>    0.148</td> <td>    8.536</td> <td> 0.000</td> <td>    0.974</td> <td>    1.554</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(InternetService)[T.No]</th>                    <td>   -1.1586</td> <td>    0.178</td> <td>   -6.492</td> <td> 0.000</td> <td>   -1.508</td> <td>   -0.809</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(PaymentMethod)[T.Credit card (automatic)]</th> <td>   -0.0454</td> <td>    0.132</td> <td>   -0.343</td> <td> 0.732</td> <td>   -0.305</td> <td>    0.214</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(PaymentMethod)[T.Electronic check]</th>        <td>    0.5076</td> <td>    0.110</td> <td>    4.626</td> <td> 0.000</td> <td>    0.293</td> <td>    0.723</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(PaymentMethod)[T.Mailed check]</th>            <td>   -0.0996</td> <td>    0.133</td> <td>   -0.750</td> <td> 0.453</td> <td>   -0.360</td> <td>    0.161</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>tenure</th>                                      <td>   -0.0414</td> <td>    0.002</td> <td>  -18.646</td> <td> 0.000</td> <td>   -0.046</td> <td>   -0.037</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MonthlyCharges</th>                              <td>   -0.0024</td> <td>    0.004</td> <td>   -0.690</td> <td> 0.490</td> <td>   -0.009</td> <td>    0.004</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:               Churn_id   No. Observations:                 4718\n",
       "Model:                          Logit   Df Residuals:                     4710\n",
       "Method:                           MLE   Df Model:                            7\n",
       "Date:                Thu, 10 Dec 2020   Pseudo R-squ.:                  0.2335\n",
       "Time:                        14:52:58   Log-Likelihood:                -2083.8\n",
       "converged:                       True   LL-Null:                       -2718.5\n",
       "Covariance Type:            nonrobust   LLR p-value:                6.808e-270\n",
       "===============================================================================================================\n",
       "                                                  coef    std err          z      P>|z|      [0.025      0.975]\n",
       "---------------------------------------------------------------------------------------------------------------\n",
       "Intercept                                      -0.3861      0.209     -1.852      0.064      -0.795       0.023\n",
       "C(InternetService)[T.Fiber optic]               1.2640      0.148      8.536      0.000       0.974       1.554\n",
       "C(InternetService)[T.No]                       -1.1586      0.178     -6.492      0.000      -1.508      -0.809\n",
       "C(PaymentMethod)[T.Credit card (automatic)]    -0.0454      0.132     -0.343      0.732      -0.305       0.214\n",
       "C(PaymentMethod)[T.Electronic check]            0.5076      0.110      4.626      0.000       0.293       0.723\n",
       "C(PaymentMethod)[T.Mailed check]               -0.0996      0.133     -0.750      0.453      -0.360       0.161\n",
       "tenure                                         -0.0414      0.002    -18.646      0.000      -0.046      -0.037\n",
       "MonthlyCharges                                 -0.0024      0.004     -0.690      0.490      -0.009       0.004\n",
       "===============================================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "churn_model=logit(formula=\"Churn_id ~ tenure+C(InternetService)+MonthlyCharges+C(PaymentMethod)\",\n",
    "                  data=df_churn_train).fit()\n",
    "churn_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Salida de un modelo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La salida de esta predicción es el logaritmo de la razón de monomios:\n",
    "\\\\[\n",
    " log(Odds)= log \\left(\\frac{p}{1-p} \\right) = \\beta_1 X_1+\\beta_2 X_2+\\cdots +\\beta_p X_p\n",
    "\\\\]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "user_test = df_churn_test.iloc[5:6,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_odds=churn_model.predict(user_test, linear=True).values[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Es 0.12 veces más probable que user_test haga Churn que permanezca en la compañia\n"
     ]
    }
   ],
   "source": [
    "print(f\"Es {np.round(np.exp(log_odds),2)} veces más probable que user_test haga Churn que permanezca en la compañia\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob_est = churn_model.predict(user_test, linear=False).values[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aunque no se corresponde con la probabilidad teórica, \n",
      "una aproximación a la probabilidad de churn para el usuario test rondaría 0.1\n"
     ]
    }
   ],
   "source": [
    "print(f\"\"\"Aunque no se corresponde con la probabilidad teórica, \n",
    "una aproximación a la probabilidad de churn para el usuario test rondaría {np.round(prob_est,2)}\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def sigmoid(x):\n",
    "    return 1/(1+np.exp(-x))\n",
    "\n",
    "prob_est == sigmoid(log_odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Medidas de calidad de un modelo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aqui lo que tenemos es un clasificador con dos hipótesis $H_0$ y $H_1$. \n",
    "Si nuestro test estadístico dice que la hipótesis $H_1$ es cierta pero en realidad la que es cierta es la hipótesis $H_0$ estaremos cometiendo un error.\n",
    "El tipo de error depende de si nos hemos equivocado prediciendo $H_0$ o $H_1$.\n",
    "\n",
    "|.|Elegimos $H_0$|Elegimos $H_1$|\n",
    "|-|-|-|\n",
    "|$H_0$ cierta| No hay error | falso positivo|\n",
    "|$H_1$ cierta| falso negativo| No hay error |\n",
    "\n",
    "La matriz de confusión lo que hace es contar el número de ocurrencias que ha habido en cada celda."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "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>Churn</th>\n",
       "      <th>No</th>\n",
       "      <th>Yes</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>row_0</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>1552</td>\n",
       "      <td>324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>145</td>\n",
       "      <td>304</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Churn    No  Yes\n",
       "row_0           \n",
       "False  1552  324\n",
       "True    145  304"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cnf_mat=pd.crosstab(columns=df_churn_test[\"Churn\"],index=churn_model.predict(df_churn_test)>0.5 )\n",
    "cnf_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_churn_test[\"pred\"]=churn_model.predict(df_churn_test)>0.5\n",
    "df_churn_test[\"pred\"] = df_churn_test[\"pred\"].replace({True: 'Yes', False: 'No'})\n",
    "df_churn_test=df_churn_test.dropna(subset=[\"Churn\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1552,  145],\n",
       "       [ 324,  304]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "M=confusion_matrix(df_churn_test[\"Churn\"], df_churn_test[\"pred\"], labels=[\"No\",\"Yes\"] )\n",
    "M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Precisión** : $\\frac{M_{11}}{M_{01}+M_{11}}$. Cuantos aciertos tengo del total de predicciones.\n",
    "\n",
    "**Exhaustividad** (recall, true positive): $\\frac{M_{11}}{M_{10}+M_{11}}$. Que ratio de los casos positivos soy capaz de encontrar.\n",
    "\n",
    "**Prob Falso positivo** (false positive rate): $\\frac{M_{01}}{M_{00}+M_{01}}$. Que ratio de los casos positivos soy capaz de encontrar.\n",
    "\n",
    "**Exactitud** (Accuracy): $\\frac{M_{11}+M_{22}}{M_{11}+M_{12}+M_{21}+M_{22}}$: Cuantas predicciones correctas he hecho.\n",
    "\n",
    "**Valor-F**: $F_\\beta=(1+\\beta^2)\\frac{Precisión·Exhaustividad}{\\beta^2·Precisión+Exhaustividad}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision: 0.6770601336302895\n"
     ]
    }
   ],
   "source": [
    "# Precision or positive predictive value\n",
    "PPV = M[1,1]/np.sum(M[:,1])\n",
    "print(f\"Precision: {PPV}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Recall o True Positive Rate: 0.4840764331210191\n"
     ]
    }
   ],
   "source": [
    "# Sensitivity, hit rate, recall, or true positive rate\n",
    "TPR=M[1,1]/np.sum(M[1,:])\n",
    "print(f\"Recall o True Positive Rate: {TPR}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False Positive Rate: 0.0854449027695934\n"
     ]
    }
   ],
   "source": [
    "# False positive rate\n",
    "FPR = M[0,1]/np.sum(M[0,:])\n",
    "print(f\"False Positive Rate: {FPR}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.7982795698924732\n"
     ]
    }
   ],
   "source": [
    "# Overall accuracy\n",
    "ACC = (M[0,0]+M[1,1])/np.sum(M.ravel())\n",
    "print(f\"Accuracy: {ACC}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ValorF: 0.5645311049210772\n"
     ]
    }
   ],
   "source": [
    "# Overall accuracy\n",
    "Bt=1\n",
    "ValorF = (1+Bt**2)*PPV*TPR/((Bt**2)*PPV+TPR)\n",
    "print(f\"ValorF: {ValorF}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve\n",
    "fpr, tpr, thresholds = roc_curve(df_churn_test[\"Churn\"]==\"Yes\", churn_model.predict(df_churn_test, linear=False))\n",
    "plt.plot(fpr, tpr)\n",
    "plt.title(\"ROC Curve\")\n",
    "plt.xlabel(\"False Positive Rate\")\n",
    "plt.ylabel(\"True Positive Rate\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8424026663764079"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.metrics import roc_auc_score\n",
    "\n",
    "roc_auc_score(df_churn_test[\"Churn\"], churn_model.predict(df_churn_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Como se calcula la ROC**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_small_test=df_churn_test.copy()\n",
    "df_small_test[\"pred\"]=churn_model.predict(df_churn_test, linear=False)\n",
    "df_small_test=df_small_test[[\"Churn\",\"pred\"]].sort_values(by=\"pred\").reset_index(drop=True)\n",
    "df_small_test[\"Pred_Churn\"]=(df_small_test[\"pred\"]>=0.5020861589375786).replace({True: 'Yes', False: 'No'})\n",
    "#df_small_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "cnf_mat=confusion_matrix(df_small_test[\"Churn\"], df_small_test[\"Pred_Churn\"], labels=[\"No\",\"Yes\"] )\n",
    "cnf_mat\n",
    "TPR = cnf_mat[1,1]/np.sum(cnf_mat[1,:])\n",
    "FPR = cnf_mat[0,1]/np.sum(cnf_mat[:,1])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1554,  143],\n",
       "       [ 325,  303]])"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cnf_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.482484076433121\n",
      "0.08426635238656452\n"
     ]
    }
   ],
   "source": [
    "idx=200\n",
    "thresholds[idx]\n",
    "print(tpr[idx])\n",
    "print(fpr[idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08426635238656452"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "143/(1554+143)\n",
    "cnf_mat[0,1]/np.sum(cnf_mat[0,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_TPR=[]\n",
    "all_FPR=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.0)"
      ]
     },
     "execution_count": 232,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for th in np.linspace(0,1,20):\n",
    "    df_small_test[\"Pred_Churn\"]=(df_small_test[\"pred\"]>th).replace({True: 'Yes', False: 'No'})\n",
    "    cnf_mat=confusion_matrix(df_small_test[\"Churn\"], df_small_test[\"Pred_Churn\"], labels=[\"No\",\"Yes\"] )\n",
    "    TPR = cnf_mat[1,1]/np.sum(cnf_mat[1,:]) \n",
    "    \n",
    "    FPR = cnf_mat[0,1]/np.sum(cnf_mat[0,:])\n",
    "    \n",
    "    all_FPR.append(FPR)\n",
    "    all_TPR.append(TPR)\n",
    "(TPR,FPR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [],
   "source": [
    "#df_small_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0fe79a2eb8>]"
      ]
     },
     "execution_count": 234,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(all_FPR,all_TPR)\n",
    "plt.plot(fpr, tpr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mejorando la calidad del modelo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "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>PaymentMethod</th>\n",
       "      <th>Bank transfer (automatic)</th>\n",
       "      <th>Credit card (automatic)</th>\n",
       "      <th>Electronic check</th>\n",
       "      <th>Mailed check</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Churn</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>No</th>\n",
       "      <td>866</td>\n",
       "      <td>855</td>\n",
       "      <td>891</td>\n",
       "      <td>865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yes</th>\n",
       "      <td>179</td>\n",
       "      <td>157</td>\n",
       "      <td>704</td>\n",
       "      <td>201</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "PaymentMethod  Bank transfer (automatic)  Credit card (automatic)  \\\n",
       "Churn                                                               \n",
       "No                                   866                      855   \n",
       "Yes                                  179                      157   \n",
       "\n",
       "PaymentMethod  Electronic check  Mailed check  \n",
       "Churn                                          \n",
       "No                          891           865  \n",
       "Yes                         704           201  "
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_payment=pd.crosstab(index=df_churn_train[\"Churn\"],columns=df_churn_train[\"PaymentMethod\"])\n",
    "df_payment\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "from statsmodels.stats.proportion import proportion_confint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.056846867590246805, 0.4657222213498857)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proportion_confint(3, nobs=15, method='binom_test')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PaymentMethod\n",
       "Bank transfer (automatic)    (0.8043989682028564, 0.8508284713881769)\n",
       "Credit card (automatic)       (0.821239099727908, 0.8662205018841802)\n",
       "Electronic check             (0.5338623831408056, 0.5830881151248672)\n",
       "Mailed check                 (0.7866683377891794, 0.8340532256476413)\n",
       "dtype: object"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_payment.apply(lambda x:proportion_confint(x[0],nobs=x[0]+x[1],method='binom_test'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_churn[\"ElectronicCheck\"]=df_churn.PaymentMethod==\"Electronic check\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "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>gender</th>\n",
       "      <th>SeniorCitizen</th>\n",
       "      <th>Partner</th>\n",
       "      <th>Dependents</th>\n",
       "      <th>tenure</th>\n",
       "      <th>PhoneService</th>\n",
       "      <th>MultipleLines</th>\n",
       "      <th>InternetService</th>\n",
       "      <th>Contract</th>\n",
       "      <th>PaperlessBilling</th>\n",
       "      <th>PaymentMethod</th>\n",
       "      <th>MonthlyCharges</th>\n",
       "      <th>Churn</th>\n",
       "      <th>Churn_id</th>\n",
       "      <th>ElectronicCheck</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>1</td>\n",
       "      <td>No</td>\n",
       "      <td>No phone service</td>\n",
       "      <td>DSL</td>\n",
       "      <td>Month-to-month</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Electronic check</td>\n",
       "      <td>29.85</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>34</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>DSL</td>\n",
       "      <td>One year</td>\n",
       "      <td>No</td>\n",
       "      <td>Mailed check</td>\n",
       "      <td>56.95</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>2</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>DSL</td>\n",
       "      <td>Month-to-month</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Mailed check</td>\n",
       "      <td>53.85</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Male</td>\n",
       "      <td>0</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>45</td>\n",
       "      <td>No</td>\n",
       "      <td>No phone service</td>\n",
       "      <td>DSL</td>\n",
       "      <td>One year</td>\n",
       "      <td>No</td>\n",
       "      <td>Bank transfer (automatic)</td>\n",
       "      <td>42.30</td>\n",
       "      <td>No</td>\n",
       "      <td>0</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Female</td>\n",
       "      <td>0</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>2</td>\n",
       "      <td>Yes</td>\n",
       "      <td>No</td>\n",
       "      <td>Fiber optic</td>\n",
       "      <td>Month-to-month</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Electronic check</td>\n",
       "      <td>70.70</td>\n",
       "      <td>Yes</td>\n",
       "      <td>1</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   gender  SeniorCitizen Partner Dependents  tenure PhoneService  \\\n",
       "0  Female              0     Yes         No       1           No   \n",
       "1    Male              0      No         No      34          Yes   \n",
       "2    Male              0      No         No       2          Yes   \n",
       "3    Male              0      No         No      45           No   \n",
       "4  Female              0      No         No       2          Yes   \n",
       "\n",
       "      MultipleLines InternetService        Contract PaperlessBilling  \\\n",
       "0  No phone service             DSL  Month-to-month              Yes   \n",
       "1                No             DSL        One year               No   \n",
       "2                No             DSL  Month-to-month              Yes   \n",
       "3  No phone service             DSL        One year               No   \n",
       "4                No     Fiber optic  Month-to-month              Yes   \n",
       "\n",
       "               PaymentMethod  MonthlyCharges Churn  Churn_id  ElectronicCheck  \n",
       "0           Electronic check           29.85    No         0             True  \n",
       "1               Mailed check           56.95    No         0            False  \n",
       "2               Mailed check           53.85   Yes         1            False  \n",
       "3  Bank transfer (automatic)           42.30    No         0            False  \n",
       "4           Electronic check           70.70   Yes         1             True  "
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_churn.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_churn_train,df_churn_test = train_test_split(df_churn,test_size=0.33, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.428247\n",
      "         Iterations 8\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>       <td>Churn_id</td>     <th>  No. Observations:  </th>   <td>  4718</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>   <td>  4708</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>   <td>     9</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Thu, 10 Dec 2020</td> <th>  Pseudo R-squ.:     </th>   <td>0.2568</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>10:59:14</td>     <th>  Log-Likelihood:    </th>  <td> -2020.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th>  <td> -2718.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>5.225e-295</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>   -0.8816</td> <td>    0.196</td> <td>   -4.487</td> <td> 0.000</td> <td>   -1.267</td> <td>   -0.496</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(InternetService)[T.Fiber optic]</th> <td>    0.8387</td> <td>    0.155</td> <td>    5.397</td> <td> 0.000</td> <td>    0.534</td> <td>    1.143</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(InternetService)[T.No]</th>          <td>   -0.7286</td> <td>    0.182</td> <td>   -3.995</td> <td> 0.000</td> <td>   -1.086</td> <td>   -0.371</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(PaperlessBilling)[T.Yes]</th>        <td>    0.3627</td> <td>    0.088</td> <td>    4.106</td> <td> 0.000</td> <td>    0.190</td> <td>    0.536</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(Contract)[T.One year]</th>           <td>   -0.7315</td> <td>    0.124</td> <td>   -5.900</td> <td> 0.000</td> <td>   -0.974</td> <td>   -0.488</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(Contract)[T.Two year]</th>           <td>   -1.6594</td> <td>    0.213</td> <td>   -7.807</td> <td> 0.000</td> <td>   -2.076</td> <td>   -1.243</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(ElectronicCheck)[T.True]</th>        <td>    0.4195</td> <td>    0.082</td> <td>    5.101</td> <td> 0.000</td> <td>    0.258</td> <td>    0.581</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>C(SeniorCitizen)[T.1]</th>             <td>    0.2766</td> <td>    0.100</td> <td>    2.777</td> <td> 0.005</td> <td>    0.081</td> <td>    0.472</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>tenure</th>                            <td>   -0.0296</td> <td>    0.003</td> <td>  -11.755</td> <td> 0.000</td> <td>   -0.035</td> <td>   -0.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>MonthlyCharges</th>                    <td>    0.0029</td> <td>    0.004</td> <td>    0.793</td> <td> 0.427</td> <td>   -0.004</td> <td>    0.010</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:               Churn_id   No. Observations:                 4718\n",
       "Model:                          Logit   Df Residuals:                     4708\n",
       "Method:                           MLE   Df Model:                            9\n",
       "Date:                Thu, 10 Dec 2020   Pseudo R-squ.:                  0.2568\n",
       "Time:                        10:59:14   Log-Likelihood:                -2020.5\n",
       "converged:                       True   LL-Null:                       -2718.5\n",
       "Covariance Type:            nonrobust   LLR p-value:                5.225e-295\n",
       "=====================================================================================================\n",
       "                                        coef    std err          z      P>|z|      [0.025      0.975]\n",
       "-----------------------------------------------------------------------------------------------------\n",
       "Intercept                            -0.8816      0.196     -4.487      0.000      -1.267      -0.496\n",
       "C(InternetService)[T.Fiber optic]     0.8387      0.155      5.397      0.000       0.534       1.143\n",
       "C(InternetService)[T.No]             -0.7286      0.182     -3.995      0.000      -1.086      -0.371\n",
       "C(PaperlessBilling)[T.Yes]            0.3627      0.088      4.106      0.000       0.190       0.536\n",
       "C(Contract)[T.One year]              -0.7315      0.124     -5.900      0.000      -0.974      -0.488\n",
       "C(Contract)[T.Two year]              -1.6594      0.213     -7.807      0.000      -2.076      -1.243\n",
       "C(ElectronicCheck)[T.True]            0.4195      0.082      5.101      0.000       0.258       0.581\n",
       "C(SeniorCitizen)[T.1]                 0.2766      0.100      2.777      0.005       0.081       0.472\n",
       "tenure                               -0.0296      0.003    -11.755      0.000      -0.035      -0.025\n",
       "MonthlyCharges                        0.0029      0.004      0.793      0.427      -0.004       0.010\n",
       "=====================================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "churn_new_model=logit(formula=\"Churn_id ~ tenure+C(InternetService)+C(PaperlessBilling)+C(Contract)+MonthlyCharges+C(ElectronicCheck)+C(SeniorCitizen)\",\n",
    "                  data=df_churn_train).fit()\n",
    "churn_new_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7efef73f03c8>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "fpr_new, tpr_new, thresholds_new = roc_curve(df_churn_test[\"Churn\"]==\"Yes\", churn_new_model.predict(df_churn_test))\n",
    "plt.plot(fpr, tpr,label='original')\n",
    "plt.plot(fpr_new, tpr_new,label='new')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}