An engineer is interested in the effect of cutting speed (A), metal hardness (B), and cutting angle (C) on the life of a cutting tool. Two levels of each factor are chosen, and two replicates of a 2³factorial design are run. The tool life data (in hours) are shown in the following table.

(a) Analyze the data from this experiment.

(b) Find an appropriate regression model that explains tool life in terms of the variables used in the experiment.

(c) Analyze the residuals from this experiment.

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Replicate Treatment Combination П (1) 221 311 325 435 a 354 348 ab 552 472 440 453 406 377 ac bc 605 500 abc 392 419