Estimate model parameters for the Hald cement data (Table B.21) using principal-component regression.

a. What is the loss in \(R^{2}\) for this model compared to least squares?b. How much shrinkage in the coefficient vector has resulted?
c. Compare the principal-component model with the ordinary ridge model developed in Problem 9.17. Comment on any apparent differences in the models.

Data From Problem 9.17

Apply ridge regression to the Hald cement data in Table B.21.

Observation i Yi Xil x2 X3 Xi4 1234561 78.5 7 26 6 60 74.3 1 29 15 52 104.3 11 56 8 20 87.6 11 31 8 47 95.9 7 52 6 33 109.2 11 55 9 22 7 102.7 3 71 17 6 8 72.5 1 31 22 44 9 93.1 2 54 18 22 10 115.9 21 47 4 26 11 83.8 1 40 23 34 12 113.3 11 66 9 12 13 109.4 10 68 8 12