Step 3: perform Principal component analysis (PCA) to generate a number of Principal Components (PCs) capturing >85% of total data variance.

d) Compute the covarion matrix of the P PC variables (this should be P-by-P matrix), and compute the total variance of PCs ( sum of diagonal elements of covariance matrix ), compare this value with the total variance of data in Step2_b, what % variance kept in PCs (5 points),

e) compute correlation (Pearsons correlation) between new variable PC1 and new variable PC2 (5 points),

f) Plot the PC coefficients (or projection direction) of N components you selected (5 points)