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

    [s1]

  4. The principal components of Z are the normalized eigenvectors of the covariance matrix ΣZ. The eigenvectors we presented for item (c) are normalized, so they are the principal components of Z.
  5. [s2]

    [s3]

    [s4]

  6. [s5]

  7. [s6]

    [s7]

 

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