# Problem

We have data of medical insurance of patients. We will use the independent data to create a machine learning model which will estimate the Insurance charges. The medical charge is a numeric value so this problem is a regression problem.

Charge is dependent variable and these are independent variable:

• age: Integer indicating the age of the patients

• sex: patients gender ,either male or female

• bmi: Body Mass Index(BMI) ,BMI is equal to weight( in kilograms) divided by height(in meter) squared.It provides a sense of how over or under weight a person is relative to their height.

• children: An integer indicating the number of children/dependent covered by the insurance plan.

• smoker : Patients regularly smokes tobacco

• region : Patients place of residence in U.S

• charges: charge of the health insurance to patient yearly.

# Load Library and data

library(dplyr)
library(caret)

insurance <- readRDS("insurance.rds")

# Exploratory Data Analysis (EDA)

It is already done in data analysis section.

knitr::kable(head(insurance))
age sex bmi children smoker region charges
19 female 27.900 0 yes southwest 16884.924
39 male 33.770 1 no southeast 1725.552
28 male 33.000 3 no southeast 4449.462
33 male 22.705 0 no northwest 21984.471
32 male 28.880 0 no northwest 3866.855
31 female 25.740 0 no southeast 3756.622
str(insurance)
## 'data.frame':    1338 obs. of  7 variables:
##  $age : int 19 39 28 33 32 31 46 37 37 60 ... ##$ sex     : Factor w/ 2 levels "female","male": 1 2 2 2 2 1 1 1 2 1 ...
##  $bmi : num 27.9 33.8 33 22.7 28.9 ... ##$ children: int  0 1 3 0 0 0 1 3 2 0 ...
##  $smoker : Factor w/ 2 levels "no","yes": 2 1 1 1 1 1 1 1 1 1 ... ##$ region  : Factor w/ 4 levels "northeast","northwest",..: 4 3 3 2 2 3 3 2 1 2 ...
##  \$ charges : num  16885 1726 4449 21984 3867 ...

## Algorithm

As this problem is regression problem we will use Multiple Linear Regression Algorithm to make Medical insurance Predictive Model.

### Simple Linear Regression

simple linear regression is a simple method for predicting the quantitative value and study relationships between two continuous variables suppose X and Y. Mathematically, simple linear regression can be written as:

$Y=a+b∗X+e$

Where $$Y$$ is dependent variable, $$X$$ is independent variable, $$a$$ is the intercept , $$b$$ is the slope of $$X$$ and $$e$$ is the error term in equation.

Linear regression method’s main task is to find the best-fitting straight line through the Y and X points

### Multiple Linear Regression

Multiple linear regression attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data.

Multiple Linear regression uses multiple predictors. The equation for multiple linear regression looks like:

$Y = \beta0 + \beta1x1+ \beta2x2+ ...+e$

where:

$$Y$$ is Response or dependent variable $$\beta0$$ is intercept $$x1$$ and $$x2$$ are predictors or independent variable $$\beta1$$ and $$\beta2$$ are coefficeints for the $$x1$$ and $$x2$$ respectively and $$e$$ is error term in equation.