The kanga data in faraway R package contains 148 observations with 20 variables on the skulls of historical kangaroo specimens.

(a.) Please eliminate observations with missing values and compute PCA on its 18 measurements. What percentage of variation is explained by the first principal component?

(b.) Provide the loadings for the first principal component. What variables are prominent? Can you give an interpretation of the first principal component?

(c.) Repeat the PCA but with the variables all scaled to the same standard deviation. How do the percentage of variation explained and the first principal component differ from those found in the previous PCA?

(d.) Give an interpretation of the second principal component.

(e.) Compute the Mahalanobis distances and draw a appropriate plot to check for outliers.

(f.) Make a scatterplot of the first and second principal components using a different plotting symbol depending on the sex of the specimen. Do you think these two components would be effective in determining the sex of a skull?