In their book, Empirical Model Building and Response Surfaces (Hoboken, NJ: John Wiley & Sons, 1987), G. E. P. Box and N. R. Draper describe an experiment with three factors. The data shown in the following table are a variation of the original experiment on page 247 of their book.

Suppose that these data were collected in a semiconductor manufacturing process.

(a) The response y1 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 linear model to this response.

(c) Where would you recommend that we set x1, x2, and x3 if the objective is to hold mean resistivity at 500 and minimize the standard deviation?

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x1 -1 0 x2 -1 0 0 0 * y Y2 24.00 12.49 120.33 8.39 213.67 42.83 86.00 3.46 136.63 80.41