. In their book Empirical Model Building and Response Surfaces (John Wiley, 1987), G. E. P. Box and N. R. Draper describe an experiment with three fre-

tors. The data shown in the following table are a variation of the original experiment on p. 247 of their book, Suppose that these data were collected in a semiconductor manufacturing process.

(a) The response yj is the average of three readings on resistivity for a single wafer. Fit a quadratic model to this response.

(b) The response y2 is the standard deviation of the three resistivity measurements. Fit a first-order model to this response.

(e) Where would you recommend that we set x1. x2, and xy if the objective is to hold mean resistivity at 500 and minimize the standard deviation?

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x2 22 -1 -1 0 -1 1- -1 -1 -1 0 0 0 1 0 -1 1 0 1 1 77777777T 24.00 12.49 -1 120.33 8.39 213.67 42.83 -1 86.00 3.46. -1 136.63 80.41 -1 340.67 16.17 112.33 27.57 256.33 4.62 -1 271.67 23.63