---
title: "Insurance-Analysis-using-R"
author: "Adebola Alaba"
date: "`r Sys.Date()`"
output: 
  flexdashboard::flex_dashboard:
    orientation: rows
    vertical_layout: fill
    social: menu
    source_code: embed
---

```{r setup, Import Libraries, message=FALSE, warning=FALSE, paged.print=FALSE, include=FALSE}

# **Library Import**

library(flexdashboard)
library(ggplot2) #EDA plot
library(ggpubr) #ggplot customization
library(corrplot) #Correlation Matrix Plot
library(dplyr) #Data manipulation
library(tidyverse) #Data Interaction
library(rmarkdown) #Knitting report to Word/pdf
library(e1071) #Skewness Check
library(forcats)

```


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Sidebar {.sidebar}
=======================================================================

### **Description**

This summary captures the application of statistical techniques on a dataset for accurate insights and inferences. The statistical technique used are Normality tests, non-parametric test, correlation. The  Github repository for this project is available  [here](https://github.com/adebola-alaba/Health-Insurance-Analysis-using-R).

Author: [Adebola Alaba](https://mavenanalytics.io/profile/siraug)

Data sources: [Yash Gupta](https://www.kaggle.com/datasets/yashgupta011/insurance), Kaggle


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# **Exploratory Data Analysis**

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```{r Import Dataset, warning=FALSE}
Insurance <- read.csv("insurance.csv")
#head(Insurance)

#sprintf("Dataset size: [%s]", toString(dim(Insurance)))
```


```{r Check for Null Values, warning=FALSE}
# Check for null values in the Insurance object
null <- is.null(Insurance)
#sprintf("Any null values? - %s", null)
```

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### **Regional Distribution**

```{r Regional Distribution}
ggplot(Insurance, aes(x = fct_infreq(region))) + 
  geom_bar(fill = "green",
          color = "black") +
  labs(x = "Region",
       y = "Frequency",
       title = "Count by Region")

```



### **Region by Charges**

```{r Region by Charges}



# Summarize total charges by region and sex
charges_summary <- Insurance %>%
  group_by(region, sex) %>%
  summarise(total_charges = sum(charges), .groups = "drop")

# Reorder region by total charges (sum over both sexes)
charges_summary <- charges_summary %>%
  group_by(region) %>%
  mutate(region_total = sum(total_charges)) %>%
  ungroup() %>%
  mutate(region = fct_reorder(region, region_total, .desc = TRUE))

# Plot
ggplot(charges_summary, aes(x = region, y = total_charges, fill = sex)) + 
  geom_bar(stat = "identity", position = "stack") +
  #coord_flip() +
  labs(title = "Total Charges by Region and Sex",
       x = "Region", y = "Total Charges")


#regionbycharges <- ggplot(Insurance, aes(x = region, y = charges, fill = sex)) + 
 # geom_bar(data = subset(Insurance, sex == "female"), stat = "identity") + 
  #geom_bar(data = subset(Insurance, sex == "male"), stat = "identity") +
  #coord_flip()

#regionbycharges

```

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### **Age Distribution**

```{r Age Distribution}
ggplot(Insurance, aes(x = age)) + 
  geom_density(aes(y = ..count..), fill = "yellow") +
  geom_vline(aes(xintercept = mean(age)), 
             linetype = "dashed", linewidth = 0.6,
             color = "#FC4E07")
```


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# **Statistical Analysis**


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### **BMI Skewness**

```{r Skewness, warning=FALSE}

sprintf("Skewness: [%s]", toString(skewness(Insurance$bmi)))
```



### **Shapiro Wilk's Test**

```{r "Shapiro Wilk's Test for BMI Normality", warning=FALSE}


#Research Question: is the BMI variable normally distributed?

#H0: The BMI variable is normally distributed\
#HA: The BMI variable is not normally distributed\

#Confidence Interval: If the p-value is greater than 0.05, the null hypothesis will fail to be rejected and if it is lower than 0.05, the null hypothesis will be rejected.\


shapiro.test(Insurance$bmi)
```



### **Charges Skewness**

```{r Skewness_Charges, warning=FALSE}

sprintf("Skewness: [%s]", toString(skewness(Insurance$charges)))
```



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### **Skewness Check for BMI**

```{r Skewness Check for BMI, warning=FALSE}
ggplot(Insurance, aes(x=bmi)) + 
    geom_density(alpha=.3, fill="blue", color="blue", size=1)+
    geom_vline(aes(xintercept=mean(bmi)), size=1, color ="black")+
    ggtitle("Distribution density of BMI") +
    theme(text = element_text(size = 15))
    
```


### **QQPlot for BMI Normality**

```{r QQPlot Check for BMI Normality, warning=FALSE}

qqnorm(Insurance$bmi, main = "Normal QQPlot of BMI",)
qqline(Insurance$bmi)

```


### **Histogram Plot for BMI Normality**

```{r Histogram for BMI Normality, warning=FALSE}

hist(Insurance$bmi, main = "Histogram of BMI", prob = TRUE, ylim = c(0, 0.07))
lines (density(Insurance$bmi))

```


### **BMI Boxplot Check**


```{r BMI Boxplot Check}

boxplot(Insurance$bmi,
        ylab = "bmi",
        main = "Boxplot of BMI",
        col= "blue",
        outcol="blue")
```


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### **Skewness Check for Charges**


```{r Skewness Check for Charges, warning=FALSE}

ggplot(Insurance, aes(x=charges)) + 
    geom_density(alpha=.3, fill="red", color="red", size=1)+
    geom_vline(aes(xintercept=mean(charges)), size=1, color ="black")+
    ggtitle("Distribution density of Charges") +
    theme(text = element_text(size = 15))

```



### **QQPlot Check for charges Normality**


```{r QQPlot Check for charges Normality, warning=FALSE}

qqnorm(Insurance$charges, main = "Normal QQPlot of Charges",)
qqline(Insurance$charges)

```


### **Histogram Plot for charges Normality**


```{r Histogram Check for charges Normality, warning=FALSE}

hist(Insurance$charges, main = "Histogram of Charges", prob = TRUE)
lines (density(Insurance$charges))

```


### **Charges Boxplot Check**

```{r Charges Boxplot Check, warning=FALSE}
boxplot(Insurance$charges,
        ylab = "charges",
        main = "Boxplot of Insurance Charges",
        col= "red",
        outcol="red")

```


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# **Non-Parametric Tests**

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### **Two Sample Independent T-test: Hypothesis One**

```{r}
library(grid)

grid.newpage()
grid.text("Hypothesis:
H0: The median BMI of smokers > non smokers
HA: The median BMI of smokers <  non smokers

Inference: 
The p-value of [0.5321] > significant level of 0.05, 
there is enough evidence for the null hypothesis 
to fail to be rejected. 
The non-smokers mean bmi isn't within the ideal range.", 
          x = 0.5, y = 0.5,
          gp = gpar(col = "black", fontsize = 16, fill = "lightblue"))


#grid.rect(x = 0.5, y = 0.5, width = 0.6, height = 0.2, gp = gpar(fill = "lightblue"))
#grid.text("This is a textbox", x = 0.5, y = 0.5)

```

### **SOLUTION TO HYPOTHESIS ONE**


```{r Hypothesis One, warning=FALSE}

smoker_bmi <- Insurance$bmi[Insurance$smoker == 'yes'] # extract bmi where smoker equals yes
non_smoker_bmi <- Insurance$bmi[Insurance$smoker == 'no'] # extract bmi where smoker equals no


wilcox.test(smoker_bmi,non_smoker_bmi, alternative = "less", conf.int = TRUE)

```




```{r Hypothesis OneA, warning=FALSE}
#To Confirm what the exact values are:
#cat("Mean & Median BMI by Smoking Status:\n\n")

group_by(Insurance,smoker) %>%
  summarise(
            median = median(bmi, na.rm = TRUE),
            mean = mean(bmi, na.rm = TRUE))

```


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### **Two Sample Independent T-test: Hypothesis Two**


```{r}
library(grid)

grid.newpage()
grid.text ("Hypothesis Formulation:
HO: The insurance claims of smokers and non-smokers are similar
HA: The insurance claims of smokers and non-smokers are not similar

Inference: 
The p-value is below 0.05. 
Therefore, there is no sufficient evidence to fail to reject 
the claim that the charges of those who smoke, 
and non-smokers are the same. 
The null hypothesis is hereby rejected as result 
shows that the claims are indeed different.", 

          x = 0.5, y = 0.5,
          gp = gpar(col = "black", fontsize = 16, fill = "lightblue"))


#grid.rect(x = 0.5, y = 0.5, width = 0.6, height = 0.2, gp = gpar(fill = "lightblue"))
#grid.text("This is a textbox", x = 0.5, y = 0.5)

```

### **SOLUTION TO HYPOTHESIS TWO**

```{r Hypothesis Two, warning=FALSE}
charges_smoking <- Insurance$charges[Insurance$smoker == 'yes'] # extract charges where smoker equals yes
charges_no_smoking <- Insurance$charges[Insurance$smoker == 'no'] # extract charges where smoker equals no

# Calculate and print the sums
sum_smokers <- sum(charges_smoking)
sum_nonsmokers <- sum(charges_no_smoking)

#cat("Total charges for smokers: ", sum_smokers, "\n")
#cat("Total charges for non-smokers: ", sum_nonsmokers, "\n")

# Perform Wilcoxon test
wilcox.test(charges_smoking, charges_no_smoking, conf.int = TRUE)

```

```{r Hypothesis TwoA, warning=FALSE}
#To Confirm what the exact values are:
#cat("Total Charges by Smoking Status:\n\n")

Insurance %>%
  group_by(smoker) %>%
  summarise(total_charges = sum(charges), .groups = "drop")


```



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### **Barplot of Region and Smoker Status,**

```{r barplot of Region and Smoker status, warning=FALSE}
#barplot of Region and Smoker status

ggplot(Insurance) +
  aes(x = region, fill = smoker) +
  geom_bar()
```



### **Pearson Chi-Squared Test**

```{r}
library(grid)

grid.newpage()
grid.text ("Hypothesis Formulation:
H0: Region and smoking status are independent\
HA: Region and smoking status are dependent\

Inference: 
The chi-squared test shows that region and smoker 
are independent as the p-value is greater than the 
significance level of 0.05 thus 
the null hypothesis fails to be rejected.", 

          x = 0.5, y = 0.5,
          gp = gpar(col = "black", fontsize = 16, fill = "lightblue"))


#grid.rect(x = 0.5, y = 0.5, width = 0.6, height = 0.2, gp = gpar(fill = "lightblue"))
#grid.text("This is a textbox", x = 0.5, y = 0.5)

```


```{r Chi Squared Test: Table and Plot, warning=FALSE}

#Create a Contingency table of the variables Region and Smoker Status

region_smoker <- table(Insurance$region, Insurance$smoker)

#region_smoker

```


### **Chi Squared Test Result**

```{r Chi Squared Test, warning=FALSE}
chisq_reg_smk <- chisq.test(region_smoker)

chisq_reg_smk

```



### **Pearson Chi-Squared Test - Residual Plot**

```{r Residual Plot, warning=FALSE}
corrplot(chisq_reg_smk$residuals, is.cor = FALSE)
```








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# **Correlation Test**


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### **Correlation Hypothesis**

```{r}
library(grid)

grid.newpage()
grid.text ("Research Question: 

Are any of the variables correlated?

Inference:

The results show that some variables are positively correlated.

Smoker and Charges variables have a correlation coefficient of 0.66 

Age and Charges also have a correlation coefficient of 0.53.",

x = 0.5, y = 0.5,
          gp = gpar(col = "black", fontsize = 14, fill = "lightblue"))

# Result Interpretation:

#-   Strong negative correlation (-1) means that whenever x rises, y falls.\
#-   0 indicates no correlation exists between the two variables (x and y).\
#-   A strong positive correlation of 1 means that y rises as x does.\
# Age, BMI, Children and Charges are all numerical while sex, smoker and region are categorical.\

# For this test, all categorical will be changed to numerical.

# **For sex:**\
# - male becomes 1\
# - female becomes 2\

# **For smoker:**\
# - no becomes 0\
# - yes becomes 1\

# **For region:**\
# - southeast becomes 1\
# - southwest becomes 2\
# - northeast becomes 3\
# - northwest becomes 4\

          


#grid.rect(x = 0.5, y = 0.5, width = 0.6, height = 0.2, gp = gpar(fill = "lightblue"))
#grid.text("This is a textbox", x = 0.5, y = 0.5)

```



```{r Correlation, warning=FALSE}
## Make a copy of the data
insurance_copy = Insurance
#head(insurance_copy)

## Replacing values for sex
insurance_copy['sex'][insurance_copy['sex'] == 'male'] <- 1
insurance_copy['sex'][insurance_copy['sex'] == 'female'] <- 2

## Replacing values for smoker
insurance_copy['smoker'][insurance_copy['smoker'] == 'no'] <- 0
insurance_copy['smoker'][insurance_copy['smoker'] == 'yes'] <- 1

## Replacing values for region
insurance_copy['region'][insurance_copy['region'] == 'southeast'] <- 1
insurance_copy['region'][insurance_copy['region'] == 'southwest'] <- 2
insurance_copy['region'][insurance_copy['region'] == 'northeast'] <- 3
insurance_copy['region'][insurance_copy['region'] == 'northwest'] <- 4

## Print Changes
#head(insurance_copy)

# check the datatype of the variables
#class(insurance_copy$age)
#class(insurance_copy$sex)
#class(insurance_copy$bmi)
#class(insurance_copy$children)
#class(insurance_copy$smoker)
#class(insurance_copy$region)
#class(insurance_copy$charges)
```



```{r Correlation Data, warning=FALSE}
## Converting variables to lists
age <- c(insurance_copy$age)
sex <- as.integer(c(insurance_copy$sex))
bmi <- c(insurance_copy$bmi)
children <- c(insurance_copy$children)
smoker <- as.integer(c(insurance_copy$smoker))
region <- as.integer(c(insurance_copy$region))
charges <- as.integer(c(insurance_copy$charges))

## binding the variables
insurance_cor <- cbind(age,sex,bmi,children,smoker,region,charges)

#head(insurance_cor)
```




### **Correlation Matrix**

```{r Correlation Matrix, warning=FALSE}
insurance_cor_result <- round (cor(insurance_cor, method = 'spearman'),3)
insurance_cor_result
```




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### **Correlation Plot**

```{r Correlation Plot, warning=FALSE}
corrplot(insurance_cor_result, method = 'number')
```







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# **Multiple Linear Regression**


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### **Research Question**

```{r}
library(grid)

grid.newpage()
grid.text ("Model Variables:
Predictors: Age and Smoker      Response: Charges

Hypothesis Formulation:
H0: There is no relationship between the predictors and response variables\
HA: There is a relationship between the predictors and response variables\

Inference: 
Statistical summary indicates that smoking status and charges are related.
The R-squared (multiple and adjusted) are within a good range at 0.72. 
This suggests that the model is a good fit and 
can possibly explain 72% of the total variability.",

x = 0.5, y = 0.5,
          gp = gpar(col = "black", fontsize = 13, fill = "lightblue"))

```


### **Multiple Regression Model**

```{r Multiple Regression, warning=FALSE}
model <- lm(charges ~ smoker+age, data = Insurance)
summary(model)

### Confidence Interval of the Model Coefficient
confint(model)
```





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### **Model Prediction**

```{r Multiple Linear Regression: Model Prediction, warning=FALSE}

new <- data.frame(age=c(35), smoker=c('yes'))

predict(model, newdata=new)

```





### **Prediction**

```{r}
library(grid)

grid.newpage()
grid.text ("Mathematically, multiple regression is represented as 

y = a +(b1)(x1) +......+ (bn)(xn).

In this model, this means the charges for a 35-year-old smoker
will be calculated as 

Charges = (-2391.63) + (23855.30) + (274.87*35) = $31,084.

The model accurately predicted the charges for a 35 year-old smoker.",

x = 0.5, y = 0.5,
          gp = gpar(col = "black", fontsize = 14, fill = "lightblue"))

```