Exercise Solution 3.21

1. The correlation matrix has determinant |ρ| = .009314.
2. Based upon item (a), Z is multicollinear.
3. The eigenvalues λ₁, λ₂ and λ₃ are 33.0548, 15.6856 and 0.0759 respectively. The corresponding eigenvectors form the columns of

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4. 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.

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