2.16 In a study in collaboration with the Engineering Sciences and Me- chanics Department at Virginia Tech, personnel at the Statistics Consulting Center were called upon to analyze a data set dealing with cathodic debonding of elastomeric metal bonds. A model relating the amount of debonding as a function of time (x1), voltage (x2), pH at time of bonding (x3), and temperature (x4) was sought. The following data were collected. y (cm) x (min) X2 (volts) x3 (pH) x4 (F) 2.240 24.00 1000 8.47 299 3.581 43.00 1000 8.55 299 5.131 84.00 1000 8.53 299 5.715 159.00 1000 8.60 297 0.889 3.79 1100 7.72 300

(a) Fit a standard multiple linear regression model to these data and comment on model adequacy.

(b) Use a Box-Cox power transformation on the response, and find the appropriate transform y\

(c) Does a confidence interval estimate on λ indicate whether or not there is a need to work with a transformed response rather than the natural metric yl Explain.

(d) If transformation is needed, fit a new regression using y x as the new response and indicate further evidence of the improved regression.