Calculate the three eigenvectors and eigenvalues of the unstandardized 2006Stock data (i. e., use the covariance matrix instead of the correlation matrix).
a. How do the eigenvector weights change when the data are not standardized?
b. Provide an interpretation of the first eigenvalue. In other words, does the first eigenvalue using the unstandardized data indicate that PC1 will explain more or less of the variability than when the data were standardized?
c. Use the covariance matrix of X to compare the variances of the original data [Var(x1), Var(x2), and Var(x3)] to the variances of the principal components [Var(PC1), Var(PC2), and Var(PC3)].