The data in the following  come from a complete 23 factorial experiment to study the effect of cutting speed (A), tool geometry (B), and cutting angle (C) on the life of a machine tool. Two levels of each factor were chosen and there were three replicates for each factor-level combination.

(Source: D. C. Montgomery (1984), Design and Analysis of Experiments, 2nd ed. p. 292, John Wiley Press, Inc. Used with permission.) (a) Given that SSE = 482.67, SST = 2095.33 analyze the data by computing the ANOVA  and determine which main effects and interactions are significant at the level α = 0.05. (b) Using the results in part (a) 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.