An article in Industrial and Engineering Chemistry

(“More on Planning Experiments to Increase Research Efficiency,”

1970, pp. 60–65) uses a 25−2 design to investigate the effect of A = condensation temperature, B = amount of material 1, C = solvent volume, D = condensation time, and E = amount of material 2 on yield. The results obtained are as follows:

e = 23.2 ad = 16.9 cd = 23.8 bde = 16.8 ab = 15.5 bc = 16.2 ace = 23.4 abcde = 18.1

(a) Verify that the design generators used were I = ACE and I = BDE.

(b) Write down the complete defining relation and the aliases for this design.

(c) Estimate the main effects.

(d) Prepare an analysis of variance table. Verify that the AB and AD interactions are available to use as error.

(e) Plot the residuals versus the fitted values. Also construct a normal probability plot of the residuals. Comment on the results.