The data in the table below are from an experiment designed to study the advance rate \(y\) of a drill. The four design factors are \(x_{1}=\) load, \(x_{2}=\) flow, \(x_{3}=\) drilling speed, and \(x_{4}=\) type of drilling mud (the original experiment is described by Cuthbert Daniel in his 1976 book on industrial experimentation).

a. Fit a generalized linear model to the advance rate response. Use a gamma response distribution and a log link, and include all four regressors in the linear predictor.
b. Find the model deviance for the GLM from part a. Does this indicate that the model is satisfactory?
c. Perform a type 3 partial deviance analysis of the model parameters. Does this indicate that any regressors could be removed from the model?
d. Compute Wald statistics for testing the contribution of each regressor to the model. Interpret the results of these test statistics.
e. Find approximate \(95 \%\) Wald confidence intervals on the model parameters.

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Observation 1 X1 X2 X3 X4 Advance Rate, y 1.68 2 + 1.98 3 + 3.28 4567 + 3.44 + + + + 8 + + 9 - +1 1 1 1 4.98 5.70 9.97 9.07 2.07 10 + 2.44 11 + + 4.09 12 + + + 4.53 13 + + 7.77 14 + 15 + 16 + + +++ + 9.43 + + 11.75 16.30