Predicting_Insurance_Costs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7d7a3092",
   "metadata": {},
   "source": [
    "# Predicting Insurance Costs\n",
    "For this project we will be looking at the Medical Costs dataset from kaggle. This dataset contains information on individual medical insurance bills. Each bill is associated with some demographic and personal characteristics of the person who received it.\n",
    "\n",
    "For our regression problem, we are interested in how these different characteristics relate to the total medical costs. We want to construct the best possible predictive model for the cost, given some information about the patient.\n",
    "\n",
    "Let us get started by importing the required Python Libraries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "8a198d20",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c68dd9f2",
   "metadata": {},
   "source": [
    "We can now read in our **insurance** dataset using pandas Library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1086cbdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>smoker</th>\n",
       "      <th>region</th>\n",
       "      <th>charges</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19</td>\n",
       "      <td>female</td>\n",
       "      <td>27.900</td>\n",
       "      <td>0</td>\n",
       "      <td>yes</td>\n",
       "      <td>southwest</td>\n",
       "      <td>16884.92400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>male</td>\n",
       "      <td>33.770</td>\n",
       "      <td>1</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>1725.55230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28</td>\n",
       "      <td>male</td>\n",
       "      <td>33.000</td>\n",
       "      <td>3</td>\n",
       "      <td>no</td>\n",
       "      <td>southeast</td>\n",
       "      <td>4449.46200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33</td>\n",
       "      <td>male</td>\n",
       "      <td>22.705</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>21984.47061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>32</td>\n",
       "      <td>male</td>\n",
       "      <td>28.880</td>\n",
       "      <td>0</td>\n",
       "      <td>no</td>\n",
       "      <td>northwest</td>\n",
       "      <td>3866.85520</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age     sex     bmi  children smoker     region      charges\n",
       "0   19  female  27.900         0    yes  southwest  16884.92400\n",
       "1   18    male  33.770         1     no  southeast   1725.55230\n",
       "2   28    male  33.000         3     no  southeast   4449.46200\n",
       "3   33    male  22.705         0     no  northwest  21984.47061\n",
       "4   32    male  28.880         0     no  northwest   3866.85520"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Read in insurance dataset\n",
    "df = pd.read_csv(r\"D:\\Work_Shop\\Data_Analytics_Project_3\\insurance.csv\")\n",
    "\n",
    "# Display the first five rows\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89c5d78f",
   "metadata": {},
   "source": [
    "## Explore and Prepare the Data\n",
    "\n",
    "### Check for Missing Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "7e12440f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age         0\n",
       "sex         0\n",
       "bmi         0\n",
       "children    0\n",
       "smoker      0\n",
       "region      0\n",
       "charges     0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37cd17e9",
   "metadata": {},
   "source": [
    "Our dataset does not have missing data\n",
    "\n",
    "### Check for Duplicates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "efb0c4f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.duplicated().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58eec36d",
   "metadata": {},
   "source": [
    "Our dataset has got **1** duplicate. Let us remove the duplicate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "38309346",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.drop_duplicates(inplace = True)\n",
    "\n",
    "# Check for duplicates again\n",
    "df.duplicated().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97676a6f",
   "metadata": {},
   "source": [
    "Our dataset is now without duplicates and missing data. \n",
    "\n",
    "### Display correlation between variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "aea160f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>charges</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.109344</td>\n",
       "      <td>0.041536</td>\n",
       "      <td>0.298308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bmi</th>\n",
       "      <td>0.109344</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.012755</td>\n",
       "      <td>0.198401</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>children</th>\n",
       "      <td>0.041536</td>\n",
       "      <td>0.012755</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.067389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>charges</th>\n",
       "      <td>0.298308</td>\n",
       "      <td>0.198401</td>\n",
       "      <td>0.067389</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               age       bmi  children   charges\n",
       "age       1.000000  0.109344  0.041536  0.298308\n",
       "bmi       0.109344  1.000000  0.012755  0.198401\n",
       "children  0.041536  0.012755  1.000000  0.067389\n",
       "charges   0.298308  0.198401  0.067389  1.000000"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr(numeric_only = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c80d8997",
   "metadata": {},
   "source": [
    "From the Table we can see that there are no two variables with strong correlation. However, the correlation between **charges** and **age** which is about **30%** will need further inspection as it is trying to tell us something. Let us observe the corretion between **charges** and categorical variables. \n",
    "\n",
    "**NB**: We are comparing other variables to **charges** because **charges** has been choosen to be a dependent variable.\n",
    "\n",
    "Let us display the distribution of charges as we may get some insights as to whether there are no attributes that are making our charges column to show weak correlation with other variables or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9ef547cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a Histogram\n",
    "df['charges'].plot.hist()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9dc0e9d7",
   "metadata": {},
   "source": [
    "The distribution is skewed to the right, an indication that there are more extremely high **charges** than they are extremely low charges. This has the ability of affecting how residual values are offseting each other. There is no balance. The expectation is for the residual values to cancel each other from both sides of the a regression line. Let us add a new column to our dataset. The new column will be the **log** of charges column. We will display the distribution of our new column and we will recalculate the correlation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "f24177ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Add a log_charges column\n",
    "import numpy as np\n",
    "df['log_charges'] = np.log2(df['charges'])\n",
    "\n",
    "# Display the distribution of our new column\n",
    "df['log_charges'].plot.hist()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85e7e583",
   "metadata": {},
   "source": [
    "We now have a distribution that is almost **normal**. This distribution is more likely to produce less residual values than the previous one. Let us display the correlations now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "118b26f0",
   "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>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>charges</th>\n",
       "      <th>log_charges</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.109344</td>\n",
       "      <td>0.041536</td>\n",
       "      <td>0.298308</td>\n",
       "      <td>0.526927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bmi</th>\n",
       "      <td>0.109344</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.012755</td>\n",
       "      <td>0.198401</td>\n",
       "      <td>0.132822</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>children</th>\n",
       "      <td>0.041536</td>\n",
       "      <td>0.012755</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.067389</td>\n",
       "      <td>0.160336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>charges</th>\n",
       "      <td>0.298308</td>\n",
       "      <td>0.198401</td>\n",
       "      <td>0.067389</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.893084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>log_charges</th>\n",
       "      <td>0.526927</td>\n",
       "      <td>0.132822</td>\n",
       "      <td>0.160336</td>\n",
       "      <td>0.893084</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  age       bmi  children   charges  log_charges\n",
       "age          1.000000  0.109344  0.041536  0.298308     0.526927\n",
       "bmi          0.109344  1.000000  0.012755  0.198401     0.132822\n",
       "children     0.041536  0.012755  1.000000  0.067389     0.160336\n",
       "charges      0.298308  0.198401  0.067389  1.000000     0.893084\n",
       "log_charges  0.526927  0.132822  0.160336  0.893084     1.000000"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation Table\n",
    "df.corr(numeric_only = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48a31ae4",
   "metadata": {},
   "source": [
    "We can now see that correlation between **log_charges** and **age** (**50%**)is now higher than that of **charges** and **age**. We are going to use **log_charges** for our predictions. \n",
    "\n",
    "Let us now check the correlation between the **log_charges** with categorical variables in our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "2631abde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Boxplot of log_charges and sex\n",
    "df.boxplot(column = ['log_charges'], by = 'sex')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56026c7b",
   "metadata": {},
   "source": [
    "There is a wider distribution of charges for **male** patients. However, we cannot explicitly tell the relationship between **log_charges** and **sex** columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "b0afe5ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# \"log_charges\" and \"smoker\"\n",
    "df.boxplot(column = 'log_charges', by = 'smoker')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c589b16f",
   "metadata": {},
   "source": [
    "There is an explicit relationship between **log_charges** and **smoker**. It seems those who smoke are charged higher. We will use his column in our prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "5090977c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# log_charges and region\n",
    "df.boxplot(column = 'log_charges', by = 'region')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77b9fc2e",
   "metadata": {},
   "source": [
    "There is also no visisble relationship between **log_charges** and **region**,therefore we are not going to use this column.\n",
    "\n",
    "Let us now **feature engineer** smoker column. The intention is to convert the variable make it suitable for regression analysis. We are going to convert **yes** to **1** and **no** to **0**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "aa3b2d0d",
   "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>sex</th>\n",
       "      <th>bmi</th>\n",
       "      <th>children</th>\n",
       "      <th>region</th>\n",
       "      <th>charges</th>\n",
       "      <th>log_charges</th>\n",
       "      <th>smoker_no</th>\n",
       "      <th>smoker_yes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>19</td>\n",
       "      <td>female</td>\n",
       "      <td>27.900</td>\n",
       "      <td>0</td>\n",
       "      <td>southwest</td>\n",
       "      <td>16884.92400</td>\n",
       "      <td>14.043448</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>18</td>\n",
       "      <td>male</td>\n",
       "      <td>33.770</td>\n",
       "      <td>1</td>\n",
       "      <td>southeast</td>\n",
       "      <td>1725.55230</td>\n",
       "      <td>10.752842</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28</td>\n",
       "      <td>male</td>\n",
       "      <td>33.000</td>\n",
       "      <td>3</td>\n",
       "      <td>southeast</td>\n",
       "      <td>4449.46200</td>\n",
       "      <td>12.119415</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33</td>\n",
       "      <td>male</td>\n",
       "      <td>22.705</td>\n",
       "      <td>0</td>\n",
       "      <td>northwest</td>\n",
       "      <td>21984.47061</td>\n",
       "      <td>14.424197</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>32</td>\n",
       "      <td>male</td>\n",
       "      <td>28.880</td>\n",
       "      <td>0</td>\n",
       "      <td>northwest</td>\n",
       "      <td>3866.85520</td>\n",
       "      <td>11.916945</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age     sex     bmi  children     region      charges  log_charges  \\\n",
       "0   19  female  27.900         0  southwest  16884.92400    14.043448   \n",
       "1   18    male  33.770         1  southeast   1725.55230    10.752842   \n",
       "2   28    male  33.000         3  southeast   4449.46200    12.119415   \n",
       "3   33    male  22.705         0  northwest  21984.47061    14.424197   \n",
       "4   32    male  28.880         0  northwest   3866.85520    11.916945   \n",
       "\n",
       "   smoker_no  smoker_yes  \n",
       "0          0           1  \n",
       "1          1           0  \n",
       "2          1           0  \n",
       "3          1           0  \n",
       "4          1           0  "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Feature Engineering smoker column\n",
    "df = pd.get_dummies(df, columns = ['smoker'])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46260fc5",
   "metadata": {},
   "source": [
    "We have introduced two new columns in our dataset: **smoker_no** and **smoker_yes**. We are going to use **smoker_yes** column.\n",
    "\n",
    "Our model will consist of three variables from the dataset: **log_charges**, **age**, and **smoker_yes**.\n",
    "\n",
    "## Dividing the dataset\n",
    "\n",
    "We will first divid our dataset into a **target** variable and **feature** variables. \n",
    "\n",
    "Our target (dependent) variable is **log_charges** and the rest will be **feature** variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "a2f77aff",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Target variable\n",
    "y = df['log_charges']\n",
    "\n",
    "# Feature variables\n",
    "X = df.drop(['log_charges'], axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "443a6b71",
   "metadata": {},
   "source": [
    "### Spliting our Dataset into Training sets and Testing sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "5e118d74",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1069, 8)\n",
      "(268, 8)\n",
      "(1069,)\n",
      "(268,)\n"
     ]
    }
   ],
   "source": [
    "# Spliting data\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=674)\n",
    "\n",
    "# Display the chape of our new datasets\n",
    "print(X_train.shape, X_test.shape, y_train.shape, y_test.shape, sep = \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4767d790",
   "metadata": {},
   "source": [
    "### Creating Subsets "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "b700bf54",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(268, 2)\n",
      "(1069, 2)\n"
     ]
    }
   ],
   "source": [
    "# X_train subset\n",
    "X_train_subset = X_train[['age', 'smoker_yes']]\n",
    "\n",
    "# X_test subset\n",
    "X_test_subset = X_test[['age', 'smoker_yes']]\n",
    "\n",
    "# Display the shape of subsets\n",
    "print(X_test_subset.shape, X_train_subset.shape, sep = \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d90d3e59",
   "metadata": {},
   "source": [
    "### Fitting the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "dbab18a8",
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Instantiating the Linear Regression object\n",
    "model = LinearRegression()\n",
    "\n",
    "# Fitting the model\n",
    "model.fit(X_train_subset, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6391dd41",
   "metadata": {},
   "source": [
    "Now that we have our model, we can use it for making predictions. Before we use our model for prediction, let us display the estimated **intercept** and **coefficients** of our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "bf042637",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Coeffients of our model are: [0.04946947 2.2216724 ]\n",
      "The Intercept for our model is: 10.757583699081843\n"
     ]
    }
   ],
   "source": [
    "# Intercept\n",
    "intercept = model.intercept_\n",
    "\n",
    "# coefficients\n",
    "coefficients = model.coef_\n",
    "\n",
    "print(f\"The Coeffients of our model are: {coefficients}\")\n",
    "print(f\"The Intercept for our model is: {intercept}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d5eb0bb",
   "metadata": {},
   "source": [
    "We will not yet interpret the coefficients untill we run some test to make sure our model is a good model and ready for use. We will use **R Squared** goodness of fit measure. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "475184bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.72193160925696\n",
      "0.7997280587908229\n"
     ]
    }
   ],
   "source": [
    "# R_squared for Training data\n",
    "r_square_training_data = model.score(X_train_subset, y_train)\n",
    "\n",
    "# R_squared for Testing data\n",
    "r_square_testing_data = model.score(X_test_subset, y_test)\n",
    "\n",
    "# Display the R_squares scores\n",
    "print(r_square_training_data, r_square_testing_data, sep = \"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "938ce726",
   "metadata": {},
   "source": [
    "As determined by the **Goodness of Fit** (R Squares) above, our model is somewhat a good model to be used for prediction. However, our model may still need some touch up because we have only used two features as determinants of insurance charges while in real sense there are many variables determing insurance charges. There are also many Machine Learning models that can be used to predict insurance cost.\n",
    "\n",
    "### Interpretation of Coefficients\n",
    "\n",
    "1. A one year increase in a patient's age results into **5%** increase in insurance charges.\n",
    "2. If a patient is a smoker, his or her insurance charges will increase by **822%**\n",
    "\n",
    "## Conclusion\n",
    "\n",
    "We can go ahead and use the model for prediction. The above figures are supposed to be tested for significance, however, the main purpose of this project was to predict the model. "
   ]
  }
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