PLease answer all, I would really appreciate it.

Suppose you design a 2""2 fractional factorial for your upcoming DOE project (assume the factors are named A, B, C, D, E and F). a) How many runs does that experiment have? b) What are the generator(s) of that design? c) What is the defining relationship ofthat design? d) What is the main effect D aliased/confounded with? What about the 2-factor interaction B*C? e) Suppose the coefficient for the B*C term in the model is significant (i.e., its 95% confidence interval does not contain zero). Keeping the aliasing you found in d) in mind, what reasonable conclusion can you make? Create a 23 full factorial design investigating the effects of three factors (A = temperature, B = pH, and C = agitation rate) on the yield, y, from a chemical reaction. The yields are reported here, in standard order: y = [67, 71, 84, 73, 66, 62, 94, 97]. a) Calculate the 8 regression coefficients (intercept, 3 main effects, 3 two-factor interactions, and the threefactor interaction) by hand. Although you need to calculate and state all 8 coefficients, you only have to show your work for the intercept, one main effect, one two-factor interaction, and the three-factor interaction. b) Describe how you would identify the significant effects in the model, knowing that we currently have no degrees of freedom for error as we used all 8 data points to estimate the 8 coefficients. Note that you don't need to do this, just describe how you would do it given what we learned in this chapter. c) Assume that only the factors (could be main effect, 2-factor or 3factor interaction) with the two largest coefficients ended up being significant. Write out the final regression model dropping the terms that should no longer be there. Number of factors, k 3 4 5 6 7 23-1 CO 2III 4 +C=AB 23 2 TV 25-2 2III 26-3 4III 7-4 8 2III +D=AB +D=AB LE=AC Number of runs +D=AB full E=AC +D=ABC +F=BC 123 LE=AC +F=BC 25-1 G=ABC 24 26-2 210 16 2IV +E=BCD E=ABC +F=ACD twice +E=ABC full +F=BCD 23 +E=ABCD +G=ABC +F=BCD +G=ACD 24 25 +H=ABD 26-1 27-2 28-3 32 +F=ABC 4 times +F=ABCD twice full +G=ABD 23 #F=ABCDE +G=ABDE 24 +H=BCDE 25 26 2VII 28-2 64 8 times 4 times G=ABCD twice full G=ABCDEF +H=ABEF