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

a. Use the ridge trace to select an appropriate value of \(k\). Is the final model a good one?
b. How much inflation in the residual sum of squares has resulted from the use of ridge regression?
c. Compare the ridge regression model with the two-regressor model involving \(x_{1}\) and \(x_{2}\) developed by all possible regressions in Example 9.1.

Example 9.1

Observation i Yi Xil X2 X3 Xi4 1234567 78.5 7 26 74.3 1 29 104.3 11 56 658 60 15 52 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