Resistivity on a silicon wafer is influenced by several factors. The results of a 2⁴ factorial experiment performed during a critical processing step is shown in the following table:

 

(a) Estimate the factor effects. Plot the effect estimates on a normal probability plot and select a tentative model.

(b) Fit the model identified in part (a) and analyze the residuals. Is there any indication of model inadequacy?

(c) Repeat the analysis from parts (a) and (b) using In (y) as the response variable. Is there an indication that the transformation has been useful?

(d) Fit a model in terms of the coded variables that can be used to predict the resistivity.

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Run A B C D Resistivity 1 1.92 11.28 3 1.09 4 + 5.75 5 2.13 9.53 7 1.03 5.35 1.60 10 + 11.73 11 1.16 12 4.68 13 2.16 14 9.11 15 1.07 16 5.30 AIII IIII+ + + + + + + + UIII I + + + + IIII+ + + + AI | + +II + + II + + II + + 9.