Problem 13.24 The data in the following table come from an experiment to study the ef[1]fects of temperature (factor A), processing time (factor B), and the rate of temperature rise (factor C) on the amount dye (the response variable) left in the residue bath of a dyeing process. The experiment was run at two levels for each factor, with two replicates at each factor-level combination. Treatment Replicates Combination 1 19.9, 18.6 a 25.0, 22.8 b 17.4, 16.8 ab 19.5, 18.3 c 14.5, 16.1 ac 27.7, 18.0 bc 16.3, 14.6 abc 28.3, 26.2 McGraw-Hill, New York. Used with permission.)

(a) Prepare a table similar in format to Table 13.23 listing all the contrasts and estimates of the main effects and interactions.

(b) Using the results obtained in part

(a) compute the sums of squares for each main and interaction effect.

(c) Given the information that SST = 313.88 and SSE = 56.14 compute the proportion of the total variability explained by each main effect and interaction. Rank the effects in decreasing order of importance as measured by SS(effect)/SST.

(d) Using the information obtained in parts

(b) and

(c) compute the ANOVA table in a format similar to Table 13.24. Are your final results consistent with the preliminary con[1]clusions you obtained in part (c)? Comment.