Problem 2 (110 Pts) for a metal cutting process, an engineer suspects that the surface finish quality of a metal part is influenced by the feed rate and depth of cut. He selects two depths of cut and three feed rates for study and obtain the following experimental results (surface finish index) given in the table: Depth of cut Feed Rate FR (inch/min) (DC) in inch 1.0 1.5 2.0 0.1 74 79 82 64 68 88 0.2 92 98 99 86 104 108 (a) Let yijk be the experimental result (surface finish index). Subscript i represents the level i for DC; j represents the level j for FR; k represents the replicative number. Give the statistical model for the observation of experimental result yijk, as well as the possible values for subscripts i, j, k. (10 points) (b) Give y112=? y212=? y1..=? y2..=? y.1.=? y.2.=? y.3.=? y...=? CF=? y...=? (20 points) (c) Complete the ANOVA table below (Note: SST is already given in the table so you don't need to calculate it) (40 points) : Analysis of Variance for Surface finish Source DF SS MS Fo FR DC FR*DC Error Total 2169. 67 (d) Test which factors and interactions are significant at a=0.05. (15 points) (e) Draw the response curve for the interaction effect FR*DC as below (15 points) Response 100 80 60 1.0 1.5 2.0 FR (inch/min) (f) If you use Minitab (or SPSS) to develop the ANOVA table in (c), write down the steps how to do it (no more than 30 words)