lab3

simulate_student_features <- function(n = 100) {
  # 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
  )
  
  # Return the data frame
  return(student_features)
}

# Load required library
library(ggplot2)

# Generate simulated student features data
student_data <- simulate_student_features()

# Perform k-means clustering
set.seed(123) # for reproducibility
kmeans_result <- kmeans(student_data[, -1], centers = 3)  # excluding student_id for clustering

# Add cluster labels to the data
student_data$cluster <- as.factor(kmeans_result$cluster)

# Visualize the clusters
ggplot2::ggplot(student_data, ggplot2::aes(x = student_engagement, y = student_performance, color = cluster)) +
  ggplot2::geom_point() +
  ggplot2::labs(title = "K-Means Clustering of Student Features",
                x = "Student Engagement",
                y = "Student Performance",
                color = "Cluster") +
  ggplot2::theme_minimal()

# Load required library
library(ggplot2)

# Simulate student features
simulate_student_features <- function(n = 100) {
  # 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
  )
  
  # Return the data frame
  return(student_features)
}

# Generate simulated student features data
student_data <- simulate_student_features()

# Perform PCA
pca_result <- prcomp(student_data[, -1], scale. = TRUE)

# Extract the PC scores
pc_scores <- as.data.frame(pca_result$x)

# Add cluster labels to student data
student_data$cluster <- as.factor(kmeans(pca_result$x, centers = 3)$cluster)

# Visualize PCA
ggplot(pc_scores, aes(x = PC1, y = PC2, color = student_data$cluster)) +
  geom_point() +
  labs(title = "PCA of Student Features",
       x = "Principal Component 1",
       y = "Principal Component 2",
       color = "Cluster") +
  theme_minimal()