R. D. Snee (“Experimenting with a Large Number of Variables,” in Experiments in Industry: Design, Analysis and Interpretation of Results, by R. D. Snee, L. D. Hare, and J. B.

Trout, eds., ASQC, 1985) describes an experiment in which a 251 design with I  ABCDE was used to investigate the effects of five factors on the color of a chemical product. The factors are A  solvent/reactant, B  catalyst/reactant, C  temperature, D  reactant purity, and E  reactant pH.

The results obtained are as follows:

e 0.63 d  6.79 a  2.51 ade  6.47 b 2.68 bde  3.45 abe 1.66 abd  5.68 c  2.06 cde  5.22 ace 1.22 acd  4.38 bce2.09 bcd  4.30 abc 1.93 abcde 4.05

(a) Write down the complete defining relation and the aliases from the design.

(b) Estimate the effects and prepare a normal probability plot of the effects. Which effects are active?

(c) Interpret the effects and develop an appropriate model for the response.

(d) Plot the residuals from your model against the fitted values. Also construct a normal probability plot of the residuals. Comment on the results.