• You are required to justify your choice of number of clusters by doing a proper elbow analysis and including the code for generating the elbow plot as part of the submitted R script. • Use the k-means method since it makes the “total within sum of squares’ ’ metric readily available as part of the model output. • Reuse the same datasets and script/solution from assignment 2 in order to produce the dataframe that contains 2018 data on healthcare spending and life expectancy (this should be the starting point for this assignment).

Sure, I can help you with that! Here's how you can perform an elbow analysis to determine the optimal number of clusters for your k-means model:

1. Load the necessary libraries and data:

library(tidyverse)
library(cluster)
df <- read.csv("healthcare_data.csv", header = TRUE)

2. Clean and prepare the data by selecting only the relevant columns and removing any missing values:

df_clean <- df %>% select(Life.Expectancy, Healthcare.Spending) %>% drop_na()

3. Scale the data to ensure that both variables have equal influence on the clustering:

df_scaled <- scale(df_clean)

4. Run the k-means algorithm for a range of cluster values (e.g. 1 to 10) and calculate the total within-cluster sum of squares (WSS) for each:

wss <- sapply(1:10, function(k){
  kmeans(df_scaled, k, nstart = 10)$tot.withinss
})

5. Plot the WSS values against the number of clusters and identify the "elbow" point where adding more clusters does not significantly reduce the WSS:

plot(1:10, wss, type = "b", pch = 19, frame = FALSE, 
     xlab = "Number of clusters K", ylab = "Total within-clusters sum of squares")

6. Based on the plot, select the optimal number of clusters for your k-means model. The "elbow" point is usually where the curve starts to flatten out, indicating diminishing returns from adding more clusters.

Here's the complete R code for performing an elbow analysis on the healthcare spending and life expectancy data:

library(tidyverse)
library(cluster)

# Load data
df <- read.csv("healthcare_data.csv", header = TRUE)

# Clean and prepare data
df_clean <- df %>% select(Life.Expectancy, Healthcare.Spending) %>% drop_na()
df_scaled <- scale(df_clean)

# Elbow analysis
wss <- sapply(1:10, function(k){
  kmeans(df_scaled, k, nstart = 10)$tot.withinss
})
plot(1:10, wss, type = "b", pch = 19, frame = FALSE, 
     xlab = "Number of clusters K", ylab = "Total within-clusters sum of squares")

I hope this helps you determine the optimal number of clusters for your k-means model!