Solution

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.

e.

[s2]

[s3]
[s4]

f.

[s5]

g.

[s6]

 

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