Discuss your key findings:

1. Did dimensionality reduction improve performance or interpretation?
2. Which classifier performed best and why?
3. What did the clusters reveal about your data?
4. Were there any surprises or inconsistencies in the results?

Dimensionality Reduction with PCA Technique: PCA Why: Principal Component Analysis reduces the dimensionality of the data, which simplifies it and helps identify the main directions in the variability. import matplotlib. pyplot as plt import seaborn as sns # Use PCA for visualization from sklearn . decomposition import PCA pca = PCA(n_components=2) components = pca. fit_transform(X) pit. figure(figsize=(10, 6)) sns. scatterplot (x=components[:, 0], y=components[:, 1], hue=labels, palette="viridis') pit. title('K-Means Clusters' ) pit . show( )\fpca = PCA(n_components=2) pca_components = pca. fit_transform(X) # Explained variance explained_var = pca . explained_variance_ratio_ print (f' Explained Variance: {explained_var}' ) Explained Variance: [0.17425319 0.10443189] pit. figure(figsize=(10, 6)) sns. scatterplot(x=pca_components [:, 0], y=pca_components[:, 1], hue=df[ 'grade' ], palette='coolwarm' ) pit. title('PCA of Student Data' ) pit . show( )Objective 4: Clustering for Pattern Detection Question: Can clustering techniques (e.g., k-means) identify natural groupings of students with similar attributes, and how do these clusters correlate with their end-of-term grades? # Drop irrelevant columns df . drop([ 'studentid', 'course id'], axis=1, inplace=True)\f