please solve by hand and not with code

[Required for all; #5 from 2016 Midterm 2] An engineer suspects that the surface finish of a metal part is influenced by the eed rate and the depth of cut. He selects three feed rates and four depths of cut He then conducts a factorial experiment and obtains following data Depth of Feed rate (in/min) Cut in 3 4 82, 88, 92 99. 104,96 99. 108, 95 104, 110,99 108, 110,99 114, 111, 107 74, 64. 60 79. 68.73 92, 86.88 98, 104.88 99, 98, 102 104, 99.95 2 3 Some summary statistics are give below. Suppose the following statistical model is used to fit the data. Yijk = +T;+ B; + ():; + Gijk; k=1,2,3 a. where til 1, 2, 3) and B; G = 1,2,3,4) are the effects of feed rate and cut depth, and (73); are their interactions. For parameter estimation, we impose the following con- straints as in the lecture notes 2:1:= , 3; = :6B); -2,(TP).j = 0. The ANOVA of the data was done in SAS and the output is shown. What are the estimates of T, and (TB):22? b. Test if the interaction between feed rate and cut depth is significant To get full credits, give a test statistic, the corresponding p-value and your conclusion. If we plan to perform pairwise comparison for all treatment combinations, which procedure should we use? What is the corresponding critical difference (using a = 5%)? Use the Bonferroni method to compare the following treatments (i.e. the level combi- nations of speed and depth): (2,3), (2,4), (3.3) and (3,4), pairwisely (Use a = 6%). Calculate the critical difference and report your results of comparison. You can report the result as we have seen in SAS output by labeling significantly different combinations with different Latin letter. C. c Grana mean pa998 mean Teed mem depen 81 688 80.778 91 588 898 103 BBB 97880 104889 Teed depth mean 1 66.000 12 78.333 1 1 1 - 99667 88.667 G 2 1 2 3 96.667 100.667 104.333 99.667 F 199.833 G. ( 1 2 3 4 105.667 110.687 Depandant Variable: finish or source DP F Value Pe F 0001 Modal 11 Square 22. Bey 829 29 8632.000 Maan Squana 821.161818 28.7222022 Honor 24 Ca Total 05 DF olunda PARA Type ISS 3180,00 2010.101 GOY 066 Maan Squana Manual 1680.26 65.00 709.370 2.22 0.0001 4.0001 depth feedwdopche