Reconsider the drill data from Problem 13.16. Fit a GLM using the log link and the gamma distribution, but expand the linear predictor to include all six of the two-factor interactions involving the four original regressors. Compare the model deviance for this model to the model deviance for the "main effects only model" from Problem 13.16. Does adding the interaction terms seem useful?

Data From Problem 13.16

The data in the table below are from an experiment designed to study the advance rate y$\mathrm{????}$ of a drill. The four design factors are x1=${\mathrm{????}}_1=$ load, x2=${\mathrm{????}}_2=$ flow, x3=${\mathrm{????}}_3=$ drilling speed, and x4=${\mathrm{????}}_4=$ type of drilling mud (the original experiment is described by Cuthbert Daniel in his 1976 book on industrial experimentation).

Observation X1 X2 X3 X4 Advance Rate, y 1.68 1 2 + 1.98 3 + - 3.28 4 + 5 + 6 + 7 + + 8 + + 9 - + | | | | 1 3.44 4.98 5.70 9.97 9.07 2.07 10 + + 2.44 11 + + 4.09 12 + + + 4.53 13 14 + 15 16 + || ++ + 7.77 + + + +++ 9.43 11.75 16.30