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In their book Empirical Model Building and Response Surfaces (John Wiley, 1987), Box and Draper described an experiment with three factors. The data in the following table are a variation of the original experiment from their book. Suppose that these data were collected in a semiconductor manufacturing process.

(a) The response y_{1} is the average of three readings on resistivity for a single wafer. Fit a quadratic model to this response.

(b) The response y_{2} is the standard deviation of the three resistivity measurements. Fit a linear model to this response.

(c) Where would you recommend that we set x_{1}, x_{2}, and x_{3} if the objective is to hold mean resistivity at 500 and minimize the standard deviation?

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