Consider the Hald cement data in Table B.21.

a. From the matrix of correlations between the regressors, would you suspect that multicollinearity is present?
b. Calculate the variance inflation factors.
c. Find the eigenvalues of \(\mathbf{X}^{\prime} \mathbf{X}\).
d. Find the condition number of \(\mathbf{X}^{\prime} \mathbf{X}\).

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Observation i Yi Xil X12 11 13 123456 67896122 78.5 7 26 74.3 1 29 104.3 11 56 658 60 52 20 87.6 11 31 8 47 95.9 7 52 6 33 109.2 11 55 102.7 3 71 72.5 1 31 93.1 2 54 10 115.9 21 47 83.8 1 40 113.3 11 66 109.4 10 68 97264390 22 17 6 22 44 18 22 26 34 12 8 12