3. (25 points) n engineer is interested in the effects of cutting speed (A), tool geometry (8], and cutting angle (C) on the life (in hours] ofa machine tool. Two levels of each factor are chosen, and four replicates of a 23 factorial desigr are run. The results are as follows. Treatment Replicates B C Combination | II III IV (1} 30.82 26.79 23.98 30.92 + - - a 28.89 28.71 27.77 33.91 b 8.22 39.58 16.96 33.09 + + ab 38.08 38.21 23.92 31.13 + c 23.95 31.06 27.83 33.20 + + ac 29.06 24.23 30.38 30.36 + + bc 17.12 23.74 30.70 14.20 + + + abc 34.29 35.88 39.65 34.21 1) (7 points] Estimate the factor effects? Which effects appear to be large? 2) (6 points] Use the analysis ofyariance to confirm your conclusions for part (1]. (a = 0.01} 3) (6 points] Write down a regression model for predicting tool life (in hours] based on the results of the experiment. Based on the regression model, factor levels of 71, I3, and C would you recommend using? 4) (3 points] On the basis an analysis of the main effect and interaction plots, what coded factor levels of A, B, and C would you recommend using? 5) (3 points] Analyze the residuals from the experiment. re there any obvious problems