In the central composite design of Problem 11-14, two responses were obtained, the mean and variance of

Question:

In the central composite design of Problem 11-14, two responses were obtained, the mean and variance of an oxide thickness. Use the Box-Cox method to investigate the potential usefulness of transformation for both of these responses. Is the log transformation suggested in part (c) of that problem appropriate?

Problem 11-14

A central composite design is run in a chemical vapor deposition process, resulting in the experimental data shown on the next page. Four experimental units were processed simultaneously on each run of the design, and the responses are the mean and variance of thickness, computed across the four units.

X2 -1 -1 360.6 6.689 1 -1 445.2 14.230 -1 1 412.1 7.088 1 1 601.7 8.586 1.414 518.0 13.130 -1.414 411.4 6.644 1.414 497.6 7.649 -1.414 397.6 11.740 530.6 7.836 495.4 9.306 510.2 7.956 487.3 9.127