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15.11 In Myers, Montgomery, and Anderson-Cook (2009), a data set is discussed in which a 2" factorial is used by an engineer to study the effects of cutting speed (A), tool geometry (B), and cutting angle (O) on the life (in hours) of a machine tool. Two levels of each factor are chosen, and duplicates are run at each design point with the order of the runs being random. The data are presented here. A B C Life (1) - - 22. 31 32. 43 35. 34 ab + 35, 47 C + 44. 45 ac + 40. 37 +1+1 bc + + 60. 50 abc + + 39, 41 (a) Calculate all seven effects. Which appear, based on their magnitude, to be important? (b) Do an analysis of variance and observe P-values. (c) Do your results in (a) and (b) agree?treatment influence magnesium uptake. (d) Fit the appropriate regression model with treat- ment as a categorical variable. Include interaction in the model. (e) Is interaction significant in the regression model?14.13 In Myers, Classical and Modern Regression with Applications (Duxbury Classic Series, 2nd edition, 1990), an experiment is described in which the Envi- ronmental Protection Agency seeks to determine the effect of two water treatment methods on magnesium uptake. Magnesium levels in grams per cubic centime- ter (cc) are measured, and two different time levels are incorporated into the experiment. The data are as fol- lows: Treatment Time (hr) 1 2 2.19 2.15 2.16 203 2.01 2.04 2 2.01 2.03 2.04 1.88 1.86 1.91 (a) Do an interaction plot. What is your impression? (b) Do an analysis of variance and show tests for the main effects and interaction. (c) Give scientific findings regarding how time andwhat is learned and let your answer be couched the context of any significant interaction. (d) Do an interaction plot that illustrates the effect interaction. (e) Do a test comparing methods 1 and 2 at laborato I and do the same test at laboratory 7. Commer on what these results illustrate