Second type test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.linear_model import Lasso, LassoCV\n",
    "import numpy as np\n",
    "from sklearn.preprocessing import MinMaxScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_excel('data/Freq_statistics.xlsx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Freq_statistics.xlsx\n",
      "Lapse_statistics.xlsx\n",
      "Sev_statistics.xlsx\n"
     ]
    }
   ],
   "source": [
    "%%bash\n",
    "ls data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Horse_power</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Area</th>\n",
       "      <th>Exposed</th>\n",
       "      <th>Claims</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>78</td>\n",
       "      <td>0.74</td>\n",
       "      <td>2</td>\n",
       "      <td>0.827397</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>79</td>\n",
       "      <td>0.82</td>\n",
       "      <td>2</td>\n",
       "      <td>0.594521</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>0.74</td>\n",
       "      <td>2</td>\n",
       "      <td>0.816438</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>0.83</td>\n",
       "      <td>2</td>\n",
       "      <td>0.621918</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>86</td>\n",
       "      <td>0.84</td>\n",
       "      <td>2</td>\n",
       "      <td>0.904110</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Age  Experience  Horse_power  Weight  Area   Exposed  Claims\n",
       "0   18           0           78    0.74     2  0.827397       1\n",
       "1   18           0           79    0.82     2  0.594521       1\n",
       "2   18           0           80    0.74     2  0.816438       1\n",
       "3   18           0           80    0.83     2  0.621918       1\n",
       "4   18           0           86    0.84     2  0.904110       1"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Claims</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3636.0</td>\n",
       "      <td>0.700818</td>\n",
       "      <td>0.230364</td>\n",
       "      <td>0.197260</td>\n",
       "      <td>0.506849</td>\n",
       "      <td>0.745205</td>\n",
       "      <td>0.909589</td>\n",
       "      <td>1.857534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1255.0</td>\n",
       "      <td>0.695683</td>\n",
       "      <td>0.227729</td>\n",
       "      <td>0.219178</td>\n",
       "      <td>0.495890</td>\n",
       "      <td>0.742466</td>\n",
       "      <td>0.904110</td>\n",
       "      <td>0.997260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>91.0</td>\n",
       "      <td>0.728526</td>\n",
       "      <td>0.298381</td>\n",
       "      <td>0.252055</td>\n",
       "      <td>0.489041</td>\n",
       "      <td>0.802740</td>\n",
       "      <td>0.909589</td>\n",
       "      <td>1.775342</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count      mean       std       min       25%       50%       75%  \\\n",
       "Claims                                                                       \n",
       "0       3636.0  0.700818  0.230364  0.197260  0.506849  0.745205  0.909589   \n",
       "1       1255.0  0.695683  0.227729  0.219178  0.495890  0.742466  0.904110   \n",
       "2         91.0  0.728526  0.298381  0.252055  0.489041  0.802740  0.909589   \n",
       "\n",
       "             max  \n",
       "Claims            \n",
       "0       1.857534  \n",
       "1       0.997260  \n",
       "2       1.775342  "
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.groupby(['Claims']).Exposed.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.0004774525232424959, 0.9731229876316662)"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import pearsonr\n",
    "pearsonr(data.Exposed, data.Claims)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Horse_power</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Area</th>\n",
       "      <th>Exposed</th>\n",
       "      <th>Claims</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>4982.000000</td>\n",
       "      <td>4982.000000</td>\n",
       "      <td>4982.000000</td>\n",
       "      <td>4982.000000</td>\n",
       "      <td>4982.000000</td>\n",
       "      <td>4982.000000</td>\n",
       "      <td>4982.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>43.712365</td>\n",
       "      <td>7.233641</td>\n",
       "      <td>136.434163</td>\n",
       "      <td>1.190974</td>\n",
       "      <td>1.518065</td>\n",
       "      <td>0.700031</td>\n",
       "      <td>0.288438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>14.904075</td>\n",
       "      <td>8.365713</td>\n",
       "      <td>36.077912</td>\n",
       "      <td>0.294707</td>\n",
       "      <td>0.523657</td>\n",
       "      <td>0.231111</td>\n",
       "      <td>0.491754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>18.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>75.000000</td>\n",
       "      <td>0.610000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.197260</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>31.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>106.000000</td>\n",
       "      <td>0.940000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.504110</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>44.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>135.000000</td>\n",
       "      <td>1.180000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.745205</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>56.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>168.000000</td>\n",
       "      <td>1.440000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.906849</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>70.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>199.000000</td>\n",
       "      <td>1.790000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.857534</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Age   Experience  Horse_power       Weight         Area  \\\n",
       "count  4982.000000  4982.000000  4982.000000  4982.000000  4982.000000   \n",
       "mean     43.712365     7.233641   136.434163     1.190974     1.518065   \n",
       "std      14.904075     8.365713    36.077912     0.294707     0.523657   \n",
       "min      18.000000     0.000000    75.000000     0.610000     1.000000   \n",
       "25%      31.000000     3.000000   106.000000     0.940000     1.000000   \n",
       "50%      44.000000     5.000000   135.000000     1.180000     2.000000   \n",
       "75%      56.000000     8.000000   168.000000     1.440000     2.000000   \n",
       "max      70.000000    50.000000   199.000000     1.790000     3.000000   \n",
       "\n",
       "           Exposed       Claims  \n",
       "count  4982.000000  4982.000000  \n",
       "mean      0.700031     0.288438  \n",
       "std       0.231111     0.491754  \n",
       "min       0.197260     0.000000  \n",
       "25%       0.504110     0.000000  \n",
       "50%       0.745205     0.000000  \n",
       "75%       0.906849     1.000000  \n",
       "max       1.857534     2.000000  "
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data.Claims/data.Exposed\n",
    "X = data.drop(['Claims'], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Horse_power</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Area</th>\n",
       "      <th>Exposed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>78</td>\n",
       "      <td>0.74</td>\n",
       "      <td>2</td>\n",
       "      <td>0.827397</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>79</td>\n",
       "      <td>0.82</td>\n",
       "      <td>2</td>\n",
       "      <td>0.594521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>0.74</td>\n",
       "      <td>2</td>\n",
       "      <td>0.816438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>0.83</td>\n",
       "      <td>2</td>\n",
       "      <td>0.621918</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>86</td>\n",
       "      <td>0.84</td>\n",
       "      <td>2</td>\n",
       "      <td>0.904110</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Age  Experience  Horse_power  Weight  Area   Exposed\n",
       "0   18           0           78    0.74     2  0.827397\n",
       "1   18           0           79    0.82     2  0.594521\n",
       "2   18           0           80    0.74     2  0.816438\n",
       "3   18           0           80    0.83     2  0.621918\n",
       "4   18           0           86    0.84     2  0.904110"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [],
   "source": [
    "X.drop(['Horse_power', 'Weight', 'Exposed'], axis = 1, inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Area</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
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       "  </tbody>\n",
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      ],
      "text/plain": [
       "   Age  Experience  Area\n",
       "0   18           0     2\n",
       "1   18           0     2\n",
       "2   18           0     2\n",
       "3   18           0     2\n",
       "4   18           0     2"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [],
   "source": [
    "X['Age*Exp'] = X.Age*X.Experience\n",
    "X['Age*Area'] = X.Age*X.Area\n",
    "X['Exp*Area'] = X.Experience*X.Area\n",
    "X['Age*Exp*Area'] = X.Age*X.Experience*X.Area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Area</th>\n",
       "      <th>Age*Exp</th>\n",
       "      <th>Age*Area</th>\n",
       "      <th>Exp*Area</th>\n",
       "      <th>Age*Exp*Area</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>36</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>36</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>36</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>36</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>36</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Age  Experience  Area  Age*Exp  Age*Area  Exp*Area  Age*Exp*Area\n",
       "0   18           0     2        0        36         0             0\n",
       "1   18           0     2        0        36         0             0\n",
       "2   18           0     2        0        36         0             0\n",
       "3   18           0     2        0        36         0             0\n",
       "4   18           0     2        0        36         0             0"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 501,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>GLM</td>            <td>AIC:</td>       <td>98317.8010</td>\n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Link Function:</td>           <td>log</td>            <td>BIC:</td>       <td>76157.5225</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>       <td>Cost</td>       <td>Log-Likelihood:</td>   <td>-49153.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2019-06-24 15:44</td>    <td>LL-Null:</td>       <td>-85044.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>        <td>1346</td>          <td>Deviance:</td>      <td>85812.</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>5</td>         <td>Pearson chi2:</td>   <td>8.69e+04</td> \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>          <td>1340</td>           <td>Scale:</td>        <td>1.0000</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "        <td>Method:</td>             <td>IRLS</td>              <td></td>              <td></td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>        <th>Coef.</th>  <th>Std.Err.</th>     <th>z</th>      <th>P>|z|</th> <th>[0.025</th>  <th>0.975]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>       <td>7.0666</td>   <td>0.0061</td>  <td>1158.4983</td> <td>0.0000</td> <td>7.0546</td>  <td>7.0785</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age</th>         <td>-0.0004</td>  <td>0.0000</td>   <td>-7.6673</td>  <td>0.0000</td> <td>-0.0005</td> <td>-0.0003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Experience</th>  <td>-0.0007</td>  <td>0.0001</td>   <td>-7.3690</td>  <td>0.0000</td> <td>-0.0009</td> <td>-0.0005</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Horse_power</th> <td>-0.0009</td>  <td>0.0001</td>   <td>-9.3601</td>  <td>0.0000</td> <td>-0.0010</td> <td>-0.0007</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Weight</th>      <td>-0.2826</td>  <td>0.0112</td>  <td>-25.2799</td>  <td>0.0000</td> <td>-0.3045</td> <td>-0.2607</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area</th>        <td>0.4473</td>   <td>0.0025</td>  <td>176.1924</td>  <td>0.0000</td> <td>0.4423</td>  <td>0.4522</td> \n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "               Results: Generalized linear model\n",
       "===============================================================\n",
       "Model:              GLM              AIC:            98317.8010\n",
       "Link Function:      log              BIC:            76157.5225\n",
       "Dependent Variable: Cost             Log-Likelihood: -49153.   \n",
       "Date:               2019-06-24 15:44 LL-Null:        -85044.   \n",
       "No. Observations:   1346             Deviance:       85812.    \n",
       "Df Model:           5                Pearson chi2:   8.69e+04  \n",
       "Df Residuals:       1340             Scale:          1.0000    \n",
       "Method:             IRLS                                       \n",
       "---------------------------------------------------------------\n",
       "               Coef.  Std.Err.     z     P>|z|   [0.025  0.975]\n",
       "---------------------------------------------------------------\n",
       "const          7.0666   0.0061 1158.4983 0.0000  7.0546  7.0785\n",
       "Age           -0.0004   0.0000   -7.6673 0.0000 -0.0005 -0.0003\n",
       "Experience    -0.0007   0.0001   -7.3690 0.0000 -0.0009 -0.0005\n",
       "Horse_power   -0.0009   0.0001   -9.3601 0.0000 -0.0010 -0.0007\n",
       "Weight        -0.2826   0.0112  -25.2799 0.0000 -0.3045 -0.2607\n",
       "Area           0.4473   0.0025  176.1924 0.0000  0.4423  0.4522\n",
       "===============================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 501,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "\n",
    "X_sm = sm.add_constant(X)\n",
    "\n",
    "binom_model = sm.GLM(y, X_sm, family=sm.families.Poisson())\n",
    "binom_results = binom_model.fit()\n",
    "binom_results.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 502,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(98317.80097471544, 76157.52249780388)"
      ]
     },
     "execution_count": 502,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binom_results.aic, binom_results.bic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [],
   "source": [
    "residuals = data.Claims - binom_results.predict(X_sm)*data.Exposed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    4982.000000\n",
       "mean       -0.044159\n",
       "std         0.480966\n",
       "min        -5.052779\n",
       "25%        -0.163809\n",
       "50%        -0.042634\n",
       "75%        -0.009531\n",
       "max         1.687435\n",
       "dtype: float64"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "residuals.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    4982.000000\n",
       "mean        0.148791\n",
       "std         0.401535\n",
       "min        -1.003124\n",
       "25%        -0.062062\n",
       "50%        -0.018052\n",
       "75%         0.527490\n",
       "max         1.867542\n",
       "dtype: float64"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "residuals.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.05687787, 0.75941225, 1.04287949, 0.7944082 , 1.15486655,\n",
       "       0.54593691, 0.69641952, 1.15836614, 1.21086008, 1.25285523,\n",
       "       1.19686169, 0.90289566, 0.069943  , 0.68942033, 0.76991103,\n",
       "       0.88189809, 1.22835806, 1.25635482, 0.72791589, 5.05694966,\n",
       "       1.09187383, 0.64392559, 1.23185765, 0.33946077, 0.57393368,\n",
       "       0.43744945, 0.76291184, 0.50394177, 1.15836614, 1.08487464,\n",
       "       0.34645996, 1.06737666, 0.68592074, 1.08137504, 1.25635482,\n",
       "       1.23885684, 0.70691831, 0.85390133, 1.23885684, 0.65092478,\n",
       "       1.25285523, 0.46194662, 0.93789162, 0.74541386, 1.12686978,\n",
       "       0.42345107, 1.24585603, 0.41295228, 0.37580169, 0.94122809])"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred = np.array(binom_results.predict(X_sm)*data.Exposed)\n",
    "pred[:50]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1,\n",
       "       1, 1, 2, 2, 1, 1])"
      ]
     },
     "execution_count": 264,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(data.Claims)[:50]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Sev</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 467,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_excel('data/Sev_statistics.xlsx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Horse_power</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Area</th>\n",
       "      <th>Exposed</th>\n",
       "      <th>Claims</th>\n",
       "      <th>Cost</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>78</td>\n",
       "      <td>0.74</td>\n",
       "      <td>2</td>\n",
       "      <td>0.827397</td>\n",
       "      <td>1</td>\n",
       "      <td>2043.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>79</td>\n",
       "      <td>0.82</td>\n",
       "      <td>2</td>\n",
       "      <td>0.594521</td>\n",
       "      <td>1</td>\n",
       "      <td>2162.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>0.74</td>\n",
       "      <td>2</td>\n",
       "      <td>0.816438</td>\n",
       "      <td>1</td>\n",
       "      <td>2153.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>80</td>\n",
       "      <td>0.83</td>\n",
       "      <td>2</td>\n",
       "      <td>0.621918</td>\n",
       "      <td>1</td>\n",
       "      <td>2209.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>86</td>\n",
       "      <td>0.84</td>\n",
       "      <td>2</td>\n",
       "      <td>0.904110</td>\n",
       "      <td>1</td>\n",
       "      <td>1634.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Age  Experience  Horse_power  Weight  Area   Exposed  Claims    Cost\n",
       "0   18           0           78    0.74     2  0.827397       1  2043.0\n",
       "1   18           0           79    0.82     2  0.594521       1  2162.0\n",
       "2   18           0           80    0.74     2  0.816438       1  2153.0\n",
       "3   18           0           80    0.83     2  0.621918       1  2209.0\n",
       "4   18           0           86    0.84     2  0.904110       1  1634.0"
      ]
     },
     "execution_count": 468,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 469,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Horse_power</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Area</th>\n",
       "      <th>Exposed</th>\n",
       "      <th>Claims</th>\n",
       "      <th>Cost</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1346.000000</td>\n",
       "      <td>1346.000000</td>\n",
       "      <td>1346.000000</td>\n",
       "      <td>1346.000000</td>\n",
       "      <td>1346.000000</td>\n",
       "      <td>1346.000000</td>\n",
       "      <td>1346.000000</td>\n",
       "      <td>1346.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>40.823180</td>\n",
       "      <td>6.738484</td>\n",
       "      <td>151.245914</td>\n",
       "      <td>1.310208</td>\n",
       "      <td>2.045319</td>\n",
       "      <td>0.697903</td>\n",
       "      <td>1.067608</td>\n",
       "      <td>1767.109212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>18.290711</td>\n",
       "      <td>9.166853</td>\n",
       "      <td>40.233571</td>\n",
       "      <td>0.327301</td>\n",
       "      <td>0.208081</td>\n",
       "      <td>0.233190</td>\n",
       "      <td>0.251165</td>\n",
       "      <td>464.660260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>18.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>75.000000</td>\n",
       "      <td>0.610000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.219178</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1001.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>23.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>116.000000</td>\n",
       "      <td>1.030000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.493836</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1438.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>38.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>159.000000</td>\n",
       "      <td>1.380000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.746575</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1737.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>58.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>190.000000</td>\n",
       "      <td>1.610000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.904110</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1992.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>70.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>199.000000</td>\n",
       "      <td>1.790000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>1.775342</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>4445.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Age   Experience  Horse_power       Weight         Area  \\\n",
       "count  1346.000000  1346.000000  1346.000000  1346.000000  1346.000000   \n",
       "mean     40.823180     6.738484   151.245914     1.310208     2.045319   \n",
       "std      18.290711     9.166853    40.233571     0.327301     0.208081   \n",
       "min      18.000000     0.000000    75.000000     0.610000     2.000000   \n",
       "25%      23.000000     1.000000   116.000000     1.030000     2.000000   \n",
       "50%      38.000000     3.000000   159.000000     1.380000     2.000000   \n",
       "75%      58.000000     7.000000   190.000000     1.610000     2.000000   \n",
       "max      70.000000    48.000000   199.000000     1.790000     3.000000   \n",
       "\n",
       "           Exposed       Claims         Cost  \n",
       "count  1346.000000  1346.000000  1346.000000  \n",
       "mean      0.697903     1.067608  1767.109212  \n",
       "std       0.233190     0.251165   464.660260  \n",
       "min       0.219178     1.000000  1001.000000  \n",
       "25%       0.493836     1.000000  1438.250000  \n",
       "50%       0.746575     1.000000  1737.000000  \n",
       "75%       0.904110     1.000000  1992.000000  \n",
       "max       1.775342     2.000000  4445.000000  "
      ]
     },
     "execution_count": 469,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 504,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = data.Cost\n",
    "X = data.drop(['Claims', 'Cost', 'Exposed'], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 507,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>GLM</td>            <td>AIC:</td>       <td>19484.8668</td>\n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Link Function:</td>           <td>log</td>            <td>BIC:</td>       <td>-9603.2308</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>       <td>Cost</td>       <td>Log-Likelihood:</td>   <td>-9736.4</td> \n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2019-06-24 15:48</td>    <td>LL-Null:</td>       <td>-10257.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>        <td>1346</td>          <td>Deviance:</td>      <td>51.325</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>5</td>         <td>Pearson chi2:</td>     <td>48.2</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>          <td>1340</td>           <td>Scale:</td>       <td>0.035939</td> \n",
       "</tr>\n",
       "<tr>\n",
       "        <td>Method:</td>             <td>IRLS</td>              <td></td>              <td></td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>        <th>Coef.</th>  <th>Std.Err.</th>     <th>z</th>     <th>P>|z|</th> <th>[0.025</th>  <th>0.975]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>       <td>8.3613</td>   <td>0.0573</td>  <td>146.0400</td> <td>0.0000</td> <td>8.2491</td>  <td>8.4735</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age</th>         <td>0.0001</td>   <td>0.0004</td>   <td>0.2991</td>  <td>0.7649</td> <td>-0.0006</td> <td>0.0008</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Experience</th>  <td>-0.0010</td>  <td>0.0007</td>   <td>-1.3724</td> <td>0.1700</td> <td>-0.0025</td> <td>0.0004</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Horse_power</th> <td>-0.0012</td>  <td>0.0007</td>   <td>-1.6591</td> <td>0.0971</td> <td>-0.0026</td> <td>0.0002</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Weight</th>      <td>-0.2302</td>  <td>0.0889</td>   <td>-2.5893</td> <td>0.0096</td> <td>-0.4045</td> <td>-0.0560</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area</th>        <td>-0.2246</td>  <td>0.0250</td>   <td>-8.9907</td> <td>0.0000</td> <td>-0.2736</td> <td>-0.1756</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "               Results: Generalized linear model\n",
       "===============================================================\n",
       "Model:              GLM              AIC:            19484.8668\n",
       "Link Function:      log              BIC:            -9603.2308\n",
       "Dependent Variable: Cost             Log-Likelihood: -9736.4   \n",
       "Date:               2019-06-24 15:48 LL-Null:        -10257.   \n",
       "No. Observations:   1346             Deviance:       51.325    \n",
       "Df Model:           5                Pearson chi2:   48.2      \n",
       "Df Residuals:       1340             Scale:          0.035939  \n",
       "Method:             IRLS                                       \n",
       "---------------------------------------------------------------\n",
       "                Coef.  Std.Err.    z     P>|z|   [0.025  0.975]\n",
       "---------------------------------------------------------------\n",
       "const           8.3613   0.0573 146.0400 0.0000  8.2491  8.4735\n",
       "Age             0.0001   0.0004   0.2991 0.7649 -0.0006  0.0008\n",
       "Experience     -0.0010   0.0007  -1.3724 0.1700 -0.0025  0.0004\n",
       "Horse_power    -0.0012   0.0007  -1.6591 0.0971 -0.0026  0.0002\n",
       "Weight         -0.2302   0.0889  -2.5893 0.0096 -0.4045 -0.0560\n",
       "Area           -0.2246   0.0250  -8.9907 0.0000 -0.2736 -0.1756\n",
       "===============================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 507,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "offset = np.log(data.Claims.values)\n",
    "\n",
    "\n",
    "X_sm = sm.add_constant(X)\n",
    "\n",
    "binom_model = sm.GLM(y, X_sm, family=sm.families.Gamma(link=sm.genmod.families.links.log),\n",
    "                    offset = offset)\n",
    "binom_results = binom_model.fit()\n",
    "binom_results.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 499,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(19484.86675522325, -9603.230802597307)"
      ]
     },
     "execution_count": 499,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binom_results.aic, binom_results.bic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 500,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2100.828305\n",
       "1    2060.017555\n",
       "2    2095.788492\n",
       "3    2052.814025\n",
       "4    2033.389230\n",
       "5    2019.394817\n",
       "6    2028.511200\n",
       "7    2044.615031\n",
       "8    2023.442896\n",
       "9    2022.837087\n",
       "dtype: float64"
      ]
     },
     "execution_count": 500,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred = binom_results.predict(X_sm)*np.exp(offset)\n",
    "pred[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa7cbd17b00>"
      ]
     },
     "execution_count": 488,
     "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": [
    "seaborn.residplot(y, pred, lowess=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [],
   "source": [
    "residuals = data.Cost - binom_results.predict(X_sm)*data.Claims"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    1346.000000\n",
       "mean      -12.136119\n",
       "std       358.908099\n",
       "min     -1951.547273\n",
       "25%      -259.831222\n",
       "50%        13.634735\n",
       "75%       255.522518\n",
       "max       702.938371\n",
       "dtype: float64"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "residuals.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     1346.000000\n",
       "mean      -476.330331\n",
       "std       1792.345200\n",
       "min     -10919.776069\n",
       "25%       -371.977337\n",
       "50%        -98.700374\n",
       "75%        163.357091\n",
       "max        634.062292\n",
       "dtype: float64"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "residuals.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "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>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Claims</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1255.0</td>\n",
       "      <td>1702.274900</td>\n",
       "      <td>377.897499</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>1414.0</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>1942.5</td>\n",
       "      <td>2500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>91.0</td>\n",
       "      <td>2661.252747</td>\n",
       "      <td>608.177891</td>\n",
       "      <td>1501.0</td>\n",
       "      <td>2230.0</td>\n",
       "      <td>2651.0</td>\n",
       "      <td>3013.0</td>\n",
       "      <td>4445.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         count         mean         std     min     25%     50%     75%  \\\n",
       "Claims                                                                    \n",
       "1       1255.0  1702.274900  377.897499  1001.0  1414.0  1709.0  1942.5   \n",
       "2         91.0  2661.252747  608.177891  1501.0  2230.0  2651.0  3013.0   \n",
       "\n",
       "           max  \n",
       "Claims          \n",
       "1       2500.0  \n",
       "2       4445.0  "
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.groupby(['Claims']).Cost.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "metadata": {},
   "outputs": [],
   "source": [
    "pearson_res = residuals / (binom_results.predict(X_sm)*data.Claims)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    1346.000000\n",
       "mean       -0.000025\n",
       "std         0.000299\n",
       "min        -0.002467\n",
       "25%        -0.000094\n",
       "50%        -0.000029\n",
       "75%         0.000125\n",
       "max         0.001002\n",
       "dtype: float64"
      ]
     },
     "execution_count": 412,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pearson_res.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    1346.000000\n",
       "mean       -0.000025\n",
       "std         0.000299\n",
       "min        -0.002467\n",
       "25%        -0.000094\n",
       "50%        -0.000029\n",
       "75%         0.000125\n",
       "max         0.001002\n",
       "dtype: float64"
      ]
     },
     "execution_count": 413,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pearson_res.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40    1504.638426\n",
       "41    1513.247190\n",
       "42    2994.855871\n",
       "43    2869.846593\n",
       "44    2142.901780\n",
       "dtype: float64"
      ]
     },
     "execution_count": 414,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(binom_results.predict(X_sm)*data.Claims)[40:45]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40    1606.924674\n",
       "41    1625.376458\n",
       "42     802.764947\n",
       "43     748.475796\n",
       "44    2353.355496\n",
       "dtype: float64"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(binom_results.predict(X_sm)/data.Claims)[40:45]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40    1919.0\n",
       "41    1545.0\n",
       "42    1915.0\n",
       "43    1646.0\n",
       "44    2220.0\n",
       "Name: Cost, dtype: float64"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Cost[40:45]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Without offset</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 530,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_excel('data/Freq_statistics.xlsx')\n",
    "y = data.Claims\n",
    "offset = - np.log(data.Exposed)\n",
    "X = data.drop(['Claims', 'Exposed', 'Horse_power', 'Weight'], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 531,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Experience</th>\n",
       "      <th>Area</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Age  Experience  Area\n",
       "0   18           0     2\n",
       "1   18           0     2\n",
       "2   18           0     2\n",
       "3   18           0     2\n",
       "4   18           0     2"
      ]
     },
     "execution_count": 531,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 532,
   "metadata": {},
   "outputs": [],
   "source": [
    "X['Age*Exp'] = X.Age*X.Experience\n",
    "X['Age*Area'] = X.Age*X.Area\n",
    "X['Exp*Area'] = X.Experience*X.Area\n",
    "X['Age*Exp*Area'] = X.Age*X.Experience*X.Area\n",
    "X_sm = sm.add_constant(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 533,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>GLM</td>            <td>AIC:</td>        <td>4693.8465</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Link Function:</td>           <td>log</td>            <td>BIC:</td>       <td>-40416.5809</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>      <td>Claims</td>      <td>Log-Likelihood:</td>   <td>-2338.9</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2019-06-24 16:03</td>    <td>LL-Null:</td>       <td>-3286.7</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>        <td>4982</td>          <td>Deviance:</td>      <td>1930.0</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>7</td>         <td>Pearson chi2:</td>   <td>1.74e+03</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>          <td>4974</td>           <td>Scale:</td>        <td>1.0000</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "        <td>Method:</td>             <td>IRLS</td>              <td></td>              <td></td>      \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>        <th>Coef.</th>  <th>Std.Err.</th>    <th>z</th>     <th>P>|z|</th> <th>[0.025</th>  <th>0.975]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>        <td>-2.4278</td>  <td>0.3990</td>  <td>-6.0844</td> <td>0.0000</td> <td>-3.2099</td> <td>-1.6458</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age</th>          <td>-0.0529</td>  <td>0.0098</td>  <td>-5.4163</td> <td>0.0000</td> <td>-0.0721</td> <td>-0.0338</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Experience</th>   <td>-0.7046</td>  <td>0.1068</td>  <td>-6.5993</td> <td>0.0000</td> <td>-0.9139</td> <td>-0.4954</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area</th>         <td>1.2248</td>   <td>0.1857</td>  <td>6.5943</td>  <td>0.0000</td> <td>0.8607</td>  <td>1.5888</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age*Exp</th>      <td>0.0114</td>   <td>0.0016</td>  <td>7.0524</td>  <td>0.0000</td> <td>0.0082</td>  <td>0.0146</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age*Area</th>     <td>0.0188</td>   <td>0.0046</td>  <td>4.1114</td>  <td>0.0000</td> <td>0.0098</td>  <td>0.0277</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Exp*Area</th>     <td>0.2299</td>   <td>0.0490</td>  <td>4.6883</td>  <td>0.0000</td> <td>0.1338</td>  <td>0.3260</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age*Exp*Area</th> <td>-0.0038</td>  <td>0.0007</td>  <td>-5.0546</td> <td>0.0000</td> <td>-0.0052</td> <td>-0.0023</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "               Results: Generalized linear model\n",
       "================================================================\n",
       "Model:              GLM              AIC:            4693.8465  \n",
       "Link Function:      log              BIC:            -40416.5809\n",
       "Dependent Variable: Claims           Log-Likelihood: -2338.9    \n",
       "Date:               2019-06-24 16:03 LL-Null:        -3286.7    \n",
       "No. Observations:   4982             Deviance:       1930.0     \n",
       "Df Model:           7                Pearson chi2:   1.74e+03   \n",
       "Df Residuals:       4974             Scale:          1.0000     \n",
       "Method:             IRLS                                        \n",
       "----------------------------------------------------------------\n",
       "                  Coef.  Std.Err.    z    P>|z|   [0.025  0.975]\n",
       "----------------------------------------------------------------\n",
       "const            -2.4278   0.3990 -6.0844 0.0000 -3.2099 -1.6458\n",
       "Age              -0.0529   0.0098 -5.4163 0.0000 -0.0721 -0.0338\n",
       "Experience       -0.7046   0.1068 -6.5993 0.0000 -0.9139 -0.4954\n",
       "Area              1.2248   0.1857  6.5943 0.0000  0.8607  1.5888\n",
       "Age*Exp           0.0114   0.0016  7.0524 0.0000  0.0082  0.0146\n",
       "Age*Area          0.0188   0.0046  4.1114 0.0000  0.0098  0.0277\n",
       "Exp*Area          0.2299   0.0490  4.6883 0.0000  0.1338  0.3260\n",
       "Age*Exp*Area     -0.0038   0.0007 -5.0546 0.0000 -0.0052 -0.0023\n",
       "================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 533,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.GLM(y, X_sm, family=sm.families.Poisson())\n",
    "model_results = model.fit()\n",
    "model_results.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 534,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0    0.774699\n",
       " 1    0.774699\n",
       " 2    0.774699\n",
       " 3    0.774699\n",
       " 4    0.774699\n",
       " dtype: float64, 0    0.936308\n",
       " 1    1.303065\n",
       " 2    0.948876\n",
       " 3    1.245661\n",
       " 4    0.856864\n",
       " dtype: float64)"
      ]
     },
     "execution_count": 534,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frequency = model_results.predict(X_sm)\n",
    "frequency[:5], (frequency * np.exp(offset))[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 535,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4693.846490630964, -40416.580947526374)"
      ]
     },
     "execution_count": 535,
     "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": [
    "seaborn.residplot(y, frequency*np.exp(offset))\n",
    "model_results.aic, model_results.bic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 542,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>GLM</td>            <td>AIC:</td>        <td>4986.8226</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Link Function:</td>           <td>log</td>            <td>BIC:</td>       <td>-40123.6048</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>      <td>Claims</td>      <td>Log-Likelihood:</td>   <td>-2485.4</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2019-06-24 16:04</td>    <td>LL-Null:</td>       <td>-3286.7</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>        <td>4982</td>          <td>Deviance:</td>      <td>2223.0</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>7</td>         <td>Pearson chi2:</td>   <td>2.39e+03</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>          <td>4974</td>           <td>Scale:</td>        <td>1.0000</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "        <td>Method:</td>             <td>IRLS</td>              <td></td>              <td></td>      \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>        <th>Coef.</th>  <th>Std.Err.</th>    <th>z</th>     <th>P>|z|</th> <th>[0.025</th>  <th>0.975]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>        <td>-2.9914</td>  <td>0.3964</td>  <td>-7.5465</td> <td>0.0000</td> <td>-3.7684</td> <td>-2.2145</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age</th>          <td>-0.0510</td>  <td>0.0097</td>  <td>-5.2508</td> <td>0.0000</td> <td>-0.0701</td> <td>-0.0320</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Experience</th>   <td>-0.6372</td>  <td>0.1068</td>  <td>-5.9673</td> <td>0.0000</td> <td>-0.8464</td> <td>-0.4279</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area</th>         <td>1.2536</td>   <td>0.1846</td>  <td>6.7906</td>  <td>0.0000</td> <td>0.8918</td>  <td>1.6154</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age*Exp</th>      <td>0.0105</td>   <td>0.0016</td>  <td>6.5080</td>  <td>0.0000</td> <td>0.0073</td>  <td>0.0136</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age*Area</th>     <td>0.0179</td>   <td>0.0046</td>  <td>3.9317</td>  <td>0.0001</td> <td>0.0090</td>  <td>0.0268</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Exp*Area</th>     <td>0.1892</td>   <td>0.0493</td>  <td>3.8356</td>  <td>0.0001</td> <td>0.0925</td>  <td>0.2858</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age*Exp*Area</th> <td>-0.0032</td>  <td>0.0007</td>  <td>-4.3110</td> <td>0.0000</td> <td>-0.0047</td> <td>-0.0017</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "               Results: Generalized linear model\n",
       "================================================================\n",
       "Model:              GLM              AIC:            4986.8226  \n",
       "Link Function:      log              BIC:            -40123.6048\n",
       "Dependent Variable: Claims           Log-Likelihood: -2485.4    \n",
       "Date:               2019-06-24 16:04 LL-Null:        -3286.7    \n",
       "No. Observations:   4982             Deviance:       2223.0     \n",
       "Df Model:           7                Pearson chi2:   2.39e+03   \n",
       "Df Residuals:       4974             Scale:          1.0000     \n",
       "Method:             IRLS                                        \n",
       "----------------------------------------------------------------\n",
       "                  Coef.  Std.Err.    z    P>|z|   [0.025  0.975]\n",
       "----------------------------------------------------------------\n",
       "const            -2.9914   0.3964 -7.5465 0.0000 -3.7684 -2.2145\n",
       "Age              -0.0510   0.0097 -5.2508 0.0000 -0.0701 -0.0320\n",
       "Experience       -0.6372   0.1068 -5.9673 0.0000 -0.8464 -0.4279\n",
       "Area              1.2536   0.1846  6.7906 0.0000  0.8918  1.6154\n",
       "Age*Exp           0.0105   0.0016  6.5080 0.0000  0.0073  0.0136\n",
       "Age*Area          0.0179   0.0046  3.9317 0.0001  0.0090  0.0268\n",
       "Exp*Area          0.1892   0.0493  3.8356 0.0001  0.0925  0.2858\n",
       "Age*Exp*Area     -0.0032   0.0007 -4.3110 0.0000 -0.0047 -0.0017\n",
       "================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 542,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_off = sm.GLM(y, X_sm, family=sm.families.Poisson(), offset=offset)\n",
    "model_off_results = model_off.fit()\n",
    "model_off_results.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 543,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0    0.468414\n",
       " 1    0.468414\n",
       " 2    0.468414\n",
       " 3    0.468414\n",
       " 4    0.468414\n",
       " dtype: float64, 0    0.566129\n",
       " 1    0.787885\n",
       " 2    0.573728\n",
       " 3    0.753176\n",
       " 4    0.518094\n",
       " dtype: float64)"
      ]
     },
     "execution_count": 543,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frequency_off = model_off_results.predict(X_sm)\n",
    "frequency_off[:5], (frequency_off * np.exp(offset))[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 544,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4986.8226392935485, -40123.604798863795)"
      ]
     },
     "execution_count": 544,
     "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": [
    "seaborn.residplot(y, frequency_off*np.exp(offset))\n",
    "model_off_results.aic, model_off_results.bic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 545,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td>Model:</td>               <td>GLM</td>            <td>AIC:</td>        <td>4856.9889</td> \n",
       "</tr>\n",
       "<tr>\n",
       "    <td>Link Function:</td>           <td>log</td>            <td>BIC:</td>       <td>-40253.4385</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <td>Dependent Variable:</td>      <td>Claims</td>      <td>Log-Likelihood:</td>   <td>-2420.5</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "         <td>Date:</td>        <td>2019-06-24 16:04</td>    <td>LL-Null:</td>       <td>-3286.7</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "   <td>No. Observations:</td>        <td>4982</td>          <td>Deviance:</td>      <td>2093.1</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "       <td>Df Model:</td>              <td>7</td>         <td>Pearson chi2:</td>   <td>2.16e+03</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "     <td>Df Residuals:</td>          <td>4974</td>           <td>Scale:</td>        <td>1.0000</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "        <td>Method:</td>             <td>IRLS</td>              <td></td>              <td></td>      \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "        <td></td>        <th>Coef.</th>  <th>Std.Err.</th>    <th>z</th>     <th>P>|z|</th> <th>[0.025</th>  <th>0.975]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th>        <td>-2.1315</td>  <td>0.4020</td>  <td>-5.3029</td> <td>0.0000</td> <td>-2.9193</td> <td>-1.3437</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age</th>          <td>-0.0507</td>  <td>0.0098</td>  <td>-5.1834</td> <td>0.0000</td> <td>-0.0699</td> <td>-0.0316</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Experience</th>   <td>-0.7665</td>  <td>0.1068</td>  <td>-7.1790</td> <td>0.0000</td> <td>-0.9757</td> <td>-0.5572</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Area</th>         <td>1.2571</td>   <td>0.1871</td>  <td>6.7184</td>  <td>0.0000</td> <td>0.8904</td>  <td>1.6238</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age*Exp</th>      <td>0.0122</td>   <td>0.0016</td>  <td>7.5157</td>  <td>0.0000</td> <td>0.0090</td>  <td>0.0153</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age*Area</th>     <td>0.0175</td>   <td>0.0046</td>  <td>3.8269</td>  <td>0.0001</td> <td>0.0085</td>  <td>0.0264</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Exp*Area</th>     <td>0.2668</td>   <td>0.0488</td>  <td>5.4632</td>  <td>0.0000</td> <td>0.1711</td>  <td>0.3626</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age*Exp*Area</th> <td>-0.0042</td>  <td>0.0007</td>  <td>-5.6858</td> <td>0.0000</td> <td>-0.0057</td> <td>-0.0028</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary2.Summary'>\n",
       "\"\"\"\n",
       "               Results: Generalized linear model\n",
       "================================================================\n",
       "Model:              GLM              AIC:            4856.9889  \n",
       "Link Function:      log              BIC:            -40253.4385\n",
       "Dependent Variable: Claims           Log-Likelihood: -2420.5    \n",
       "Date:               2019-06-24 16:04 LL-Null:        -3286.7    \n",
       "No. Observations:   4982             Deviance:       2093.1     \n",
       "Df Model:           7                Pearson chi2:   2.16e+03   \n",
       "Df Residuals:       4974             Scale:          1.0000     \n",
       "Method:             IRLS                                        \n",
       "----------------------------------------------------------------\n",
       "                  Coef.  Std.Err.    z    P>|z|   [0.025  0.975]\n",
       "----------------------------------------------------------------\n",
       "const            -2.1315   0.4020 -5.3029 0.0000 -2.9193 -1.3437\n",
       "Age              -0.0507   0.0098 -5.1834 0.0000 -0.0699 -0.0316\n",
       "Experience       -0.7665   0.1068 -7.1790 0.0000 -0.9757 -0.5572\n",
       "Area              1.2571   0.1871  6.7184 0.0000  0.8904  1.6238\n",
       "Age*Exp           0.0122   0.0016  7.5157 0.0000  0.0090  0.0153\n",
       "Age*Area          0.0175   0.0046  3.8269 0.0001  0.0085  0.0264\n",
       "Exp*Area          0.2668   0.0488  5.4632 0.0000  0.1711  0.3626\n",
       "Age*Exp*Area     -0.0042   0.0007 -5.6858 0.0000 -0.0057 -0.0028\n",
       "================================================================\n",
       "\n",
       "\"\"\""
      ]
     },
     "execution_count": 545,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_off = sm.GLM(y, X_sm, family=sm.families.Poisson(), offset=-offset)\n",
    "model_off_results = model_off.fit()\n",
    "model_off_results.summary2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 546,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0    1.103246\n",
       " 1    1.103246\n",
       " 2    1.103246\n",
       " 3    1.103246\n",
       " 4    1.103246\n",
       " dtype: float64, 0    0.912823\n",
       " 1    0.655903\n",
       " 2    0.900733\n",
       " 3    0.686129\n",
       " 4    0.997456\n",
       " dtype: float64)"
      ]
     },
     "execution_count": 546,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frequency_off = model_off_results.predict(X_sm)\n",
    "frequency_off[:5], (frequency_off * np.exp(-offset))[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 547,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4856.98891532077, -40253.43852283657)"
      ]
     },
     "execution_count": 547,
     "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": [
    "seaborn.residplot(y, frequency_off*np.exp(-offset))\n",
    "model_off_results.aic, model_off_results.bic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa7b7584dd8>"
      ]
     },
     "execution_count": 342,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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f7sc5uX/u0mP2BpH3Z36SvwfQAWCXpCT/ksxsOuTdw0/Se0leA+AFksslVV5kjnUA1uWGfSSrJ1HbAgCdk1iuGEq5NqC06yvl2oDSrm+ytV0/mckoZfNOneRXAYxJ+l5G85VJWpHFXFkr5dqA0q6vlGsDSru+rGvLp43XtSQX5n6+CsDdAGqyKszMCiufo/3zAewgOQfjLyL/JekX2ZQFINfqu0SVcm1AaddXyrUBpV1fprVl9rbfzN5YfIafWaAcfrNAOfxmgSq58JPcQbKbZMnd/ovkdSR/S7KKZAXJ1cWu6XwkryG5L3cDlQMk1xe7pguRvJrkEZKbi13L+UiOnHfzmZI76Edyae5amqrc3/Ytec9Zagf8SL4PwDwAayV9tNj1nI/kOwAskpTkvubcD+CvLnWD0umWu8biKklDJK8GUAngVkknilxaiuQmADcCaJa0odj1nEOyS9KfF7uOSyH5MoDHJL1K8m0A+iSN5DNnye35Je0G0F/sOi5GUvu5U5gldQA4CeBtxa3qjySNShrKDecCeBNK6K5KJG8E8E4AO4tdyxsJyb8FcFbSqwAg6WS+wQdKMPxvFCTfA2CWpJZi13I+km8lWQ6gFcB3JXUVu6bzbAbwaLGLuIRrSf6B5O9I3lnsYi5wI4ABki+R3E/y37KY1OG/AiTfDuCnAD5b7FouJKlH0rsALAXwSZKLil0TAJD8EIA6SXXFruUSrs/djv4hAD8leW2xCzrPmwGsBPAvAG4H8AGSH8h3Uod/inKnMu8A8G1Jvy92PZci6TiACgCril1LzgoAnyDZhPF3AOtLqQGMpKO5/ysBVAH4y+JWNEErgH2SWiSdxvjHpnfnO6nDPwUkCeAnAH4j6dkil/MnSC46t8fK/b8KQG1xqxon6VFJ10m6HsAGAFskfbPIZQEASP5Z7kX93K3n/wZAKbVl3gdgUa7OWRj/u07mytjXVXI37SD5KwC3AHgLyVYAH5a0r8hlnXMHgI8DqCD5QO6xByUdKGJN51sC4Ee5FykCeFpSRZFreiP4awD/SXIM4w1p/lXSySLXlJI0kvuc/wrG/67/I+m/85235L7qM7Pp4bf9ZoFy+M0C5fCbBcrhNwuUw28WKIffLFAOv1mg/h+fcCTjDyR3/AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 280x210 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "w = 4\n",
    "h = 3\n",
    "d = 70\n",
    "plt.figure(figsize=(w, h), dpi=d)\n",
    "x = numpy.array([1, 2, 3, 4, 5, 6])\n",
    "y = numpy.array([2, 1, 6, 13, 10, 13])\n",
    "\n",
    "seaborn.residplot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa7b65e9ba8>"
      ]
     },
     "execution_count": 347,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+4motWVATW5/nvRVjZs9IumSERfe7+3/m2pGZBZICSZo7d27OBQJAsVuyoCbWIB/uvMHu7jdF0ZG7r5e0XpLq6uo8in0CQDGob2nXuoZWHens1pyqCi1fXBtr0HMrBgBiVN/SrlVbm9V+skczp5Wp/WSPVm1tVn1Le2x95vu448fNrE3StZJ+YmY/i6YsAEiGdQ2tKkuZKspLZZZ5LUuZ1jW0xtZnXo87uvsWSVsiqgUAEudIZ7dSJrV2dKk3PaDyVIlmzShXW2d3bH1yKwYAYjSjPKVXj5/Wqd60+tKuU71pvXr8tKaXp2Lrk2AHgBiNdmXOFTsAFKmu3oExtUeBYAeAhCHYASBhCHYASBiCHQAShmAHgIQh2AEgYQh2AEgYgh0AYlRiY2uPpM/4dg0AqCgfOWanj9IeBYIdAGL0+5dVaea00sEr9BKTZk4r1VWXVZ17wzwQ7AAQo+WLa/WOaeWaP2u6rnr3OzR/1nS9Y1q5li+uja1Pgh0AYrRkQY0eWrZQNZVT9cbpPtVUTtVDyxZO7HeeAgDyU+jvPOWKHQAShmAHgIQh2AEgYQh2AEgYgh0AEsbcvfCdmnVIenWcm8+SdCzCcqJCXWNDXWNDXWOT1Lre4+7V51tpQoI9H2bW6O51E13HcNQ1NtQ1NtQ1Nhd6XdyKAYCEIdgBIGGKMdjXT3QBo6CusaGusaGusbmg6yq6e+wAgHMrxit2AMA5TKpgN7OlZnbQzA6Z2b0jLJ9iZt8Ll+82s3lZy+4L2w+a2UcLXNc/mNmvzGyfmf23mb0na1nazF4If7YWuK47zKwjq/+7spbdbma/Dn9uL3BdX8+q6SUzO5G1LJbjZWaPm1m7me0fZbmZ2WNhzfvM7ANZy+I8Vuer6y/DevaZ2S4zuzpr2WEzezE8Vo0FrmuJmb2R9btalbXsnL//mOu6J6um/eH5dHG4LM7jNcfMnjWzA2bWbGZfGGGdwp1j7j4pfiSlJL0sqVZSuaS9kq4cts7dktaG07dJ+l44fWW4/hRJ88P9pApY142SKsLpvztbVzjfNYHH6w5Ja0bY9mJJreFrVThdVai6hq3/eUmPF+B4LZb0AUn7R1l+s6SfSjJJfyBpd9zHKse6rjvbn6SPna0rnD8sadYEHa8lkn6c7+8/6rqGrfunknYW6HhdKukD4XSlpJdG+PtYsHNsMl2xXyPpkLu3unuvpM2Sbh22zq2SvhVOPyXpj8zMwvbN7n7G3V+RdCjcX0Hqcvdn3b07nH1e0uyI+s6rrnP4qKSn3f24u3dKelrS0gmq61OSNkXU96jcvUHS8XOscqukb3vG85JmmtmlivdYnbcud98V9isV7tzK5XiNJp/zMuq6CnJuSZK7v+7ue8Lpk5IOSLps2GoFO8cmU7BfJulI1nyb3n5gBtdx935Jb0h6Z47bxllXtjuV+Vf5rKlm1mhmz5vZn0VU01jq+ovwv31PmdmcMW4bZ10Kb1nNl7Qzqzmu43U+o9Ud57Eaq+HnlkvaYWZNZhZMQD3XmtleM/upmS0M2ybF8TKzCmXC8QdZzQU5Xpa5RbxI0u5hiwp2jk2mL9oY6Tu7hz+yM9o6uWw7Xjnv28w+LalO0h9mNc9199fMrFbSTjN70d1fLlBd2yRtcvczZvZZZf638+Ect42zrrNuk/SUu6ez2uI6XuczEedWzszsRmWC/Yas5uvDY1Uj6WkzawmvaAthjzIfb+8ys5sl/UjS5Zokx0uZ2zD/6+7ZV/exHy8zm6HMPyZfdPc3hy8eYZNYzrHJdMXeJmlO1vxsSa+Nto6ZlUq6SJn/luWybZx1ycxuknS/pGXufuZsu7u/Fr62SqpX5l/ygtTl7r/LquVfJX0w123jrCvLbRr2X+UYj9f5jFZ3nMcqJ2b2PkkbJN3q7r872551rNolbVF0tx/Py93fdPeucHq7pDIzm6VJcLxC5zq3YjleZlamTKh/191/OMIqhTvH4ngjYZxvPpQq86bBfL31psvCYev8vYa+efr9cHqhhr552qro3jzNpa5FyrxhdPmw9ipJU8LpWZJ+rYjeSMqxrkuzpj8u6Xl/682aV8L6qsLpiwtVV7jee5V5M8sKcbzCfc7T6G8G3qKhb2z9Iu5jlWNdc5V5z+i6Ye3TJVVmTe+StLSAdV1y9nenTED+Jjx2Of3+46orXH72gm96oY5X+Gf/tqTV51inYOdYZAc7ooNzszLvJr8s6f6w7SFlroIlaaqkJ8MT/ReSarO2vT/c7qCkjxW4rmck/VbSC+HP1rD9Okkvhif3i5LuLHBd/yypOez/WUkLsrb9m/A4HpL014WsK5z/J0lfGbZdbMdLmau31yX1KXOFdKekz0r6bLjcJH0zrPlFSXUFOlbnq2uDpM6sc6sxbK8Nj9Pe8Hd8f4Hr+lzWufW8sv7hGen3X6i6wnXuUOZhiuzt4j5eNyhz+2Rf1u/q5ok6x/jkKQAkzGS6xw4AiADBDgAJQ7ADQMIQ7ACQMAQ7ACQMwY7EMbNLzGyzmb1smVE3t5vZFaONCJi13bvN7KlC1QnEZTINKQDkLRwUboukb7n7bWHb+yW963zbeuaTiZ+It0IgflyxI2lulNTn7mvPNrj7C8oaZMnM5pnZ/5jZnvDnuqz2/eH0HWb2IzPbZmavmNnnLDPu/i/DAcrOjvG9wt4ai39zYf+owMi4YkfSXCWp6TzrtEv6iLv3mNnlynyasW6UfS1S5hPPhyR92d0XmdnXJf2VpNWS7pU03zMDrc2M6g8B5INgx4WoTNKa8BZNWtIVo6z3rGfG1j5pZm8oM1qmlPk4+PvC6X2SvmtmP1JmhENgwnErBknTrLdGsRzNSmXG9rlamSv18lHWO5M1PZA1P6C3LopuUWb8jw9KagpHHQUmFMGOpNkpaYqZ/e3ZBjP7kKT3ZK1zkaTX3X1A0meU+Tq3MTOzEklz3P1ZSV+SNFPSjPEWDkSFYEeieGZUu49L+kj4uGOzMiNJZo9v/S+Sbjez55W5DXNqnN2lJH3HzF6U9EtJX3f3E+fZBogdozsCQMJwxQ4ACUOwA0DCEOwAkDAEOwAkDMEOAAlDsANAwhDsAJAwBDsAJMz/A72/U1XhdIfaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "seaborn.residplot(y, frequency_off)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  1,  6, 13, 10, 13])"
      ]
     },
     "execution_count": 344,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}