Reconsider the drill data from Problem 13.16. Remove any regressors from the original model that you think might be unimportant and rework parts b-e of Problem 13.16. Comment on your findings.

Data From Problem 13.16

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).

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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