2. Reconsider part (c) of Problem #1. Use the regression model to generate response surface and contour plots of the tool life response. Interpret these plots. Do they provide insight regarding the desirable operating conditions for this process?

3. Find the standard error of the factor effects and approximate 95 percent confidence limits for the factor effects in Problem #1. Do the results of this analysis agree with the conclusions from the analysis of variance?

PS## us Minitabe for Problem 1-3

1. An engineer is interested in the effects of cutting speed A, tool geometry B, and cutting angle c on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 23 factorial design are run. The results are as follows: Replicate Treatment Combination ABC I II III - - | | (1) 22 31 25 + + - | a 32 43 29 + b 35 34 50 + + ab 55 47 46 + 44 45 38 + + + + ac 40 37 36 - + + 1 be 60 50 54 + + + abc 39 41 47 a. Estimate the factor effects. Which effects appear to be large? b. Use the analysis of variance to confirm your conclusions for part (a). c. Write down a regression model for predicting tool life (in hours) based on the results of this experiment. d. Analyze the residuals. Are there any obvious problems? e. On the basis of an analysis of main effect and interaction plots, what coded factor levels of A, B, and C would you recommend using? 1. An engineer is interested in the effects of cutting speed A, tool geometry B, and cutting angle c on the life (in hours) of a machine tool. Two levels of each factor are chosen, and three replicates of a 23 factorial design are run. The results are as follows: Replicate Treatment Combination ABC I II III - - | | (1) 22 31 25 + + - | a 32 43 29 + b 35 34 50 + + ab 55 47 46 + 44 45 38 + + + + ac 40 37 36 - + + 1 be 60 50 54 + + + abc 39 41 47 a. Estimate the factor effects. Which effects appear to be large? b. Use the analysis of variance to confirm your conclusions for part (a). c. Write down a regression model for predicting tool life (in hours) based on the results of this experiment. d. Analyze the residuals. Are there any obvious problems? e. On the basis of an analysis of main effect and interaction plots, what coded factor levels of A, B, and C would you recommend using