b) Calculate the proportion of variability explained by each of the principal components (use your (squared) answer to part a)iv) combined with the result that the k principal component explains 100 _* % of the variability, i.e. the ratio of the k" eigenvalue to the sum of all of the eigenvalues). Create a vector called proportions that contains the five proportions explained by the five principal components. c) Plot the scores on the first three principal components (PC2 vs. PC1), (PC3 vs. PC1), (PC3 vs. PC2). If you use par (mfrow=c (2 , 2) ) to create a 2 x 2 grid of plots, you can use the first three of these plot regions to create the three plots. For example, to plot PC2 against PC 1, use plot (met . pea$x [, 1] , met . pea$x [, 2] , xlab=paste (" FC1, (", 100* round (proportions [1] , 2) , " $ of variability) ", sep="") , ylab=paste ("PC2, ", 100 * round (proportions [ 2] , 2) , " variability) ", sep="") , main="pc2 against PC1") d) Repeat part a) using scale=TRUE as an argument to the prcomp ( ) function. How do your answers to parts iii) and iv) differ from part a)? What is the scaling used here, i.e. how are the variables scaled? Part a) used the covariance matrix. What matrix are we using here? Question 2 In this question we consider a two-variable system, and look at the effect of altering the correlation between the two variables on the proportion of variability explained by the first principal component. We are considering X, and X2, for which the correlation matrix is given by