Problem 4 (40 pts) In order to maximize the yield of a certain process, an engineer studied the impact of five factors A, B, C, D and E on yield using the following experimental design (with four replicates per trial). ABCDE + - - - + + - + - + + + - - + - + + + + - + + + - + + + + + (a) Write down a set of generators for this design. (b) What is the resolution of this design? (c) Which effects are clear? (d) How many points shall figure in each half-normal plot (one for location and one for disper- sion) ? Which factorial effects would they represent ? Clearly explain your answer.Problem 4 (40 pts) In order to maximize the yield of a certain process, an engineer studied the impact of five factors A, B, C, D and E on yield using the following experimental design (with four replicates per trial). ABCDE + - - - + + - + - + + + - - + - + + + + - + + + - + + + + + (a) Write down a set of generators for this design. (b) What is the resolution of this design? (c) Which effects are clear? (d) How many points shall figure in each half-normal plot (one for location and one for disper- sion) ? Which factorial effects would they represent ? Clearly explain your answer.Location Dispersion Effect IPSE Effect 1PSE A 7.82 B 5.95 -4.91 -1.87 E 2.15 - 1.24 -1.12 0.78 -0.92 -0.57 0.35 -0.29 0.24 0.08 The following table gives the tpse values for location ()) and dispersion (Ins') corresponding to different factorial effects. The values are arranged in descending order. The PSE values for location and dispersion are 0.132 and 0.079, respectively. The experimenter decides that the effects that are declared significant at level 0.05 by Lenth's test will be considered for optimization of the process. Because the experimenter considers missing an important factor much more serious than misidentifying an inert factor, he/she decides to use IER critical values for the Lenth's test. (e) Based on the above table and all the stated information, which effects would the experi- menter consider for fitting location and dispersion models? (Hint: With I =7,IERo.os = 2.30, IERo.025 = 3.43) (f) Based on the information above, is it possible to fit the complete regression models linking y and In(s') to the significant factor effects? If not, which term(s) would be missing? (g) Write down the regression models (as explicitly as possible) for y and Ins- in terms of the significant factor effects. (h) What settings of the significant factors would you recommend