Insurance Charges_R_Project_KRC.Rmd

---
title: "Precision in Healthcare Costs: Modeling Individual Characteristics to Refine Insurance Charge Estimation"
author: "Kalyan Raj Chinigi"
date: "March 05,2024"

output:
  pdf_document: default
  html_document: default
  word_document: default
---
```{r}
# Load necessary libraries
library(dplyr)
library(Hmisc)

# Read the data
data <- read.csv("C:\\Users\\Kalya\\Downloads\\insurance.csv")

# View the first few rows and summary statistics of the data
head(data)
summary(data)

# Check the dimensions (rows and columns) of the dataframe
dimensions <- dim(data)
num_rows <- dimensions[1]
num_columns <- dimensions[2]

# Print the number of rows and columns
cat("Number of rows:", num_rows, "\n")
cat("Number of columns:", num_columns, "\n")

# Check the structure of the dataframe to identify variable types
str(data)
```
```{r}
# Check for null values in the dataframe
null_values <- is.na(data)

# Check if there are any null values overall
if (any(null_values)) {
  cat("There are null values in the dataset.\n")
  # Print the count of null values for each column
  print(colSums(null_values))
} else {
  cat("There are no null values in the dataset.\n")
}
```

```{r}
# Visualize the distribution of charges
hist(data$charges, main = "Distribution of Insurance Charges", xlab = "Charges", col = "skyblue")

# Explore the relationship between age and charges
plot(data$age, data$charges, main = "Age vs. Charges", xlab = "Age", ylab = "Charges", col = "blue")

# Explore the relationship between BMI and charges
plot(data$bmi, data$charges, main = "BMI vs. Charges", xlab = "BMI", ylab = "Charges", col = "green")

# Compare charges by gender
boxplot(charges ~ sex, data = data, main = "Charges by Gender", xlab = "Gender", ylab = "Charges", col = c("pink", "lightblue"))

# Compare charges by smoker status
boxplot(charges ~ smoker, data = data, main = "Charges by Smoker Status", xlab = "Smoker Status", ylab = "Charges", col = c("lightgreen", "orange"))

# Compare charges by region
boxplot(charges ~ region, data = data, main = "Charges by Region", xlab = "Region", ylab = "Charges", col = "yellow")

# Explore the relationship between the number of children and charges
plot(data$children, data$charges, main = "Number of Children vs. Charges", xlab = "Number of Children", ylab = "Charges", col = "purple")

# Identify outliers or anomalies in charges
boxplot(data$charges, main = "Charges Boxplot", ylab = "Charges", col = "red")

# Create a scatterplot matrix to visualize relationships between variables
pairs(data[, c("age", "bmi", "children", "charges")], main = "Scatterplot Matrix", col = "blue")

# Add Q-Q plots
par(mfrow = c(2, 2)) # Set the layout to 2x2 for Q-Q plots
for (variable in c("age", "bmi", "charges")) {
  if (is.numeric(data[[variable]])) {
    qqnorm(data[[variable]], main = paste("Q-Q Plot of", variable), col = "green")
    qqline(data[[variable]], col = "red")
  }
}


```
```{r}
# Load necessary library
library(Hmisc)

# Load the dataset (update the path as needed)
insurance_data <- read.csv("insurance.csv")  # Make sure the file path is correct

# Check for missing values
sum(is.na(insurance_data))

# Remove rows with missing values (if any)
insurance_data <- na.omit(insurance_data)

# Convert non-numeric columns to numeric if possible
insurance_data <- type.convert(insurance_data, as.is = TRUE)

# Convert categorical variables to factors
insurance_data$sex <- as.factor(insurance_data$sex)
insurance_data$smoker <- as.factor(insurance_data$smoker)
insurance_data$region <- as.factor(insurance_data$region)

# Identify categorical columns
categorical_cols <- c("sex", "smoker", "region") 

# Convert categorical columns to numerical using one-hot encoding
encoded_data <- model.matrix(~ 0 + ., data = insurance_data[, categorical_cols])

# Combine the encoded columns with the original dataframe
insurance_data_numeric <- cbind(insurance_data[, !names(insurance_data) %in% categorical_cols], encoded_data)

# Compute Spearman's correlation
cor_matrix <- rcorr(as.matrix(insurance_data_numeric), type = "spearman")

# Print the correlation matrix
print(cor_matrix$r)

```
```{r}
# Load the corrplot library
library(corrplot)

# Visualize the Spearman correlation matrix using a heatmap
corrplot(cor_matrix$r, method = "color", 
         main = "Spearman Correlation Matrix", 
         type = "upper", 
         tl.col = "black", 
         tl.cex = 0.8, 
         addCoef.col = "black")
```

```{r}
# Filter all numerical columns (excluding the target variable 'charges')
numeric_cols <- data %>%
  select_if(is.numeric)

# Exclude the target variable 'charges'
numeric_cols <- numeric_cols %>%
  select(-charges)

# Filter encoded numerical columns (if you've encoded categorical variables)
encoded_numeric_cols <- data %>%
  select(starts_with("encoded_"))  # Adjust this based on the column names after encoding

# Combine all numerical columns
all_numeric_cols <- cbind(numeric_cols, encoded_numeric_cols)

# Define a function to binarize numeric variables
binarize_numeric <- function(x) {
  ifelse(x >= median(x), "high", "low")
}

# Perform t-tests for each numeric column
t_test_results <- lapply(all_numeric_cols, function(col) {
  # Binarize the numeric variable
  binarized_col <- binarize_numeric(col)
  # Perform t-test
  t_test_result <- t.test(data$charges ~ binarized_col, data = data)
  return(t_test_result)
})

# Print t-test results
names(t_test_results) <- names(all_numeric_cols)
t_test_results

```
```{r}

# Perform chi-square tests for each categorical column
chi_square_results <- lapply(categorical_cols, function(col) {
  chi_square_result <- chisq.test(table(data[[col]], data$charges > median(data$charges)))
  return(chi_square_result)
})

# Print chi-square test results
names(chi_square_results) <- categorical_cols
chi_square_results


```
```{r}
# Perform Shapiro-Wilk test for normality
shapiro_test_result <- shapiro.test(data$charges)

# Print the test result
shapiro_test_result

```
```{r}
# Filter categorical and numerical variables
categorical_vars <- c("sex", "smoker", "region")
numeric_vars <- c("age", "bmi", "children")

# Perform Kruskal-Wallis test for categorical variables
kruskal_cat <- lapply(categorical_vars, function(var) {
  kruskal.test(charges ~ get(var), data = data)
})

# Perform Kruskal-Wallis test for numerical variables
kruskal_num <- lapply(numeric_vars, function(var) {
  kruskal.test(data$charges ~ data[[var]])
})

# Print results for categorical variables
cat_results <- data.frame(
  Variable = categorical_vars,
  Statistic = sapply(kruskal_cat, function(x) x$statistic),
  P_Value = sapply(kruskal_cat, function(x) x$p.value)
)
print("Kruskal-Wallis test results for categorical variables:")
print(cat_results)

# Print results for numerical variables
num_results <- data.frame(
  Variable = numeric_vars,
  Statistic = sapply(kruskal_num, function(x) x$statistic),
  P_Value = sapply(kruskal_num, function(x) x$p.value)
)
print("Kruskal-Wallis test results for numerical variables:")
print(num_results)

```

```{r}
# Fit a linear regression model
linear_model <- lm(charges ~ age + bmi + children + sex + smoker + region, data = data)

# Summary of the linear regression model
summary(linear_model)

```
```{r}
# Fit a multiple regression model
multiple_model <- lm(charges ~ ., data = data)

# Summary of the multiple regression model
summary(multiple_model)

```
```{r}
# Convert 'charges' to a binary variable based on a threshold (e.g., median)
data$charges_binary <- ifelse(data$charges > median(data$charges), 1, 0)

# Fit a logistic regression model
logistic_model <- glm(charges_binary ~ age + bmi + children + sex + smoker + region, data = data, family = binomial)

# Summary of the logistic regression model
summary(logistic_model)

```

```{r}
# Linear Regression
# Simple Linear Regression
simple_lm <- lm(charges ~ age, data = data)
r_squared_simple <- summary(simple_lm)$r.squared

# Multiple Linear Regression
multiple_lm <- lm(charges ~ ., data = data)
r_squared_multiple <- summary(multiple_lm)$r.squared

# Combine R-squared values with model names
model_names <- c("Simple Linear Regression", "Multiple Linear Regression")
r_squared_values <- c(r_squared_simple, r_squared_multiple)

# Create a bar plot to visualize R-squared values
barplot(r_squared_values, 
        names.arg = model_names,
        ylab = "R-squared", main = "Comparison of R-squared Values",
        col = c("skyblue", "salmon"), ylim = c(0, 1))

# Add text labels for R-squared values
text(x = 1:2, y = r_squared_values + 0.05, round(r_squared_values, 3), pos = 3, cex = 0.8, col = "black")



```
```{r}

# Fit a multiple linear regression model
lm_multiple <- lm(charges ~ ., data = data)

# Obtain residuals from the model
residuals_multiple <- residuals(lm_multiple)

# Create residual plot with color
plot(fitted(lm_multiple), residuals_multiple, 
     xlab = "Fitted values", 
     ylab = "Residuals", 
     main = "Residual Plot (Multiple Regression)",
     col = "blue")  # Specify color here

# Add a horizontal line at y = 0 for reference
abline(h = 0, col = "red", lty = 2)
```