An experiment was performed to improve the yield of a chemical process. Four factors were selected, and two replicates of a completely randomized experiment were run.

The results are shown in the following table:

Replicate Replicate Treatment Combination I II Treatment Combination I II

(1) 90 93 d 98 95 a 74 78 ad 72 76 b 81 85 bd 87 83 ab 83 80 abd 85 86 c 77 78 cd 99 90 ac 81 80 acd 79 75 bc 88 82 bcd 87 84 abc 73 70 abcd 80 80

(a) Estimate the factor effects.

(b) Prepare an analysis of variance table and determine which factors are important in explaining yield.

(c) Write down a regression model for predicting yield, assuming that all four factors were varied over the range from −1 to + 1 (in coded units).

(d) Plot the residuals versus the predicted yield and on a normal probability scale. Does the residual analysis appear satisfactory?

(e) Two three-factor interactions, ABC and ABD, apparently have large effects. Draw a cube plot in the factors A, B, and C with the average yields shown at each corner.
Repeat using the factors A, B, and D. Do these two plots aid in data interpretation? Wherewould you recommend that the process be run with respect to the four variables?