# Sample data creation
set.seed(0)
data <- matrix(runif(300), nrow=100, ncol=3)  # 100 samples with 3 features
# Standardize the data
data_scaled <- scale(data)
# Perform PCA
pca <- prcomp(data_scaled, center = TRUE, scale. = TRUE)
# Determine the number of components to retain 95% of the variance
explained_variance <- pca$sdev^2 / sum(pca$sdev^2)
cumulative_variance <- cumsum(explained_variance)
num_components <- which(cumulative_variance >= 0.95)[1]
# Create a data frame with the selected principal components
principal_components <- data.frame(pca$x[, 1:num_components])
colnames(principal_components) <- paste0("PC", 1:num_components)
# Plot the principal components
library(ggplot2)
ggplot(principal_components, aes_string(x = colnames(principal_components)[1], y = colnames(principal_components)[2])) +
  geom_point() +
  ggtitle("PCA with 95% Variance Retained") +
  xlab("Principal Component 1") +
  ylab("Principal Component 2")
# Explained variance and number of components
print(explained_variance)
print(paste("Number of components selected:", num_components))