lab3

# Load necessary libraries
library(ggplot2)
library(stats)

simulate_student_features <- function(n = 100, clusters = 3) {
  # Set the random seed
  set.seed(260923)
  
  # Generate unique student IDs
  student_ids <- seq(1, n)
  
  # Simulate student engagement
  student_engagement <- rnorm(n, mean = 50, sd = 10)
  
  # Simulate student performance
  student_performance <- rnorm(n, mean = 60, sd = 15)
  
  # Combine the data into a data frame
  student_features <- data.frame(
    student_id = student_ids,
    student_engagement = student_engagement,
    student_performance = student_performance
  )
  
  # Perform PCA for dimensionality reduction
  pca_result <- prcomp(student_features[, -1], scale. = TRUE)
  student_features_pca <- data.frame(student_id = student_ids, pca_result$x)
  colnames(student_features_pca) <- c("student_id", paste0("PC", 1:ncol(pca_result$x)))
  
  # Perform K-means clustering
  kmeans_result <- kmeans(pca_result$x, centers = clusters)
  
  # Add cluster labels to the data
  student_features_pca$cluster <- as.factor(kmeans_result$cluster)
  
  # Return the data frame
  return(student_features_pca)
}

# Generate student features data with dimensionality reduction and clustering
student_data <- simulate_student_features()
head(student_data)

##   student_id        PC1         PC2 cluster
## 1          1 -0.4415374 -1.64338014       2
## 2          2  0.2737353 -0.08332113       1
## 3          3  1.9391244 -0.26845756       1
## 4          4 -1.0635415 -1.05927303       2
## 5          5  1.0139706  0.23352365       1
## 6          6  0.8785119  0.03787004       1

# Plot clusters
ggplot(student_data, aes(x = PC1, y = PC2, color = cluster)) +
  geom_point() +
  labs(title = "K-means Clustering of Student Features with PCA",
       x = "Principal Component 1",
       y = "Principal Component 2",
       color = "Cluster") +
  theme_minimal()