Question

Consider the following output from R, where I carry out a principal components anal ysis based on the correlation matrix associated with ability.cov. For a description of the data, type ?ability.cov in R round cov2cor (ability.covScov),3) general picture blocks maze reading vocab general .000 0.466 0.552 0.340 0.576 0.514 picture 0.466 1.000 0.572 0.193 0.263 0.239 blocks 0.552 0.572 1.000 0.445 0.354 0.356 0.340 0.193 0.445 1.000 0.184 0.219 reading 0.576 0.263 0.354 0.184 1.000 0.791 vocab > #Eigenvalues 0.514 0.239 0.356 0.219 0.791 1.000 round oigon(cov2cor (ability.covscov))Svalues,3) 1 3.077 1.140 0,817 0.411 0.355 0.200 > #Eigenvectors roundCoigon(cov2cor (ability.covscov))Svectors,3) [1, -0.471 0.002 0.072 0.863 0.037 -0.164 2,-0.358 0.408 0.593 -0.268 0.531 0.002 [3, -0.434 0.404 0.064 -0.201 -0.775 0.051 [4,] -0.288 0.404 -0.794 -0.097 0.334 0.052 5,1 -0.440 -0.507 -0.015 -0.100 0.056 0.733 (6, -0.430 -0.501 -0.090 -0.352 0.021 -0.657 (a) What is the sum of the variances of the principal components and what is the sum of the diagonal clemets of the correlation matrix? (b) For each principal component, caleulate the proportion of the total variation in the data that it explains. (c) Interpret this principal componients analysis. Do this in two steps: i. Decide how many principal components to use in your analysis of these data i. Then give an interprotation, in terms of the data, for each of the components you use.

Answer 1