Exercise Solution 3.21
 The correlation matrix has determinant ρ = .009314.
 Based upon item (a), Z is multicollinear.
 The eigenvalues λ_{1}, λ_{2} and λ_{3} are 33.0548, 15.6856 and 0.0759 respectively. The corresponding eigenvectors form the columns of
[s1]
 The principal components of Z are the normalized eigenvectors of the covariance matrix Σ_{Z}. The eigenvectors we presented for item (c) are normalized, so they are the principal components of Z.

[s2]
[s3]
[s4]

[s5]

[s6]
[s7]
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