a. The correlation matrix has determinant
= .009314.
b. Based upon item (a), Z is multicollinear.
c. The eigenvalues
are 33.0548, 15.6856 and 0.0759 respectively. The corresponding eigenvectors
form the columns of
[s1]
d. The principal components of Z are the
normalized eigenvectors of the covariance matrix
.
The eigenvectors we presented for item (c) are normalized, so they are the
principal components of Z.