Consider a famous experiment reported by O. L. Davies

(ed.), The Design and Analysis of Industrial Experiments

(London: Oliver and Boyd, 1956). The following data were collected from an unreplicated experiment in which the investigator was interested in determining the effect of four factors on the yield of an isatin derivative used in a fabric-dying process. The four factors are each run at two levels as indicated: (A) acid strength at 87 and 93%, (B) reaction time at 15 and 30 min, (C)

amount of acid 35 and 45 ml, and (D) temperature of reaction 60 and 70C. The response is the yield of isatin in grams per 100 grams of base material. The data are as follows:

(a) Estimate the effects and prepare a normal plot of the effects. Which interaction terms are negligible? Use t-ratios to confirm your findings.

(b) Based on your results in part (a), construct a model and analyze the residuals.

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b = (1) = 6.08 a 9D = 6.04 d = 6.79 ad = 6.68 6.53 bd = 6.73 ab = 6.43 abd = 6.08 C = 6.31 cd = 6.77 bc = 6.09 = 6.12 abc - 6.36 acd = 6.38 bcd = 6.49 abcd = 6.23