How many experiments are required to perform a 1/8 fractional factorial design o

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How many experiments are required to perform a 1/8 fractional factorial design of experiments with 6 factors at 2 levels each? If a model is fit using all of the main effects, how many degrees of freedom will there be for the error analysis assuming no other points were added to the design? b) Create a table showing the runs given by a 1/2 fractional factorial experimental design with 4 factors at 2 levels each using the design generator I = ABCD. Identify the high and low factor levels with + and respectively. Be very clear in your signs. c) A Central Composite Design is a factorial experimental design with the addition of star points. What terms in the 2ndorder model do these star points allow to be fit? d) If a linear model, f(A, B, C), is constructed to find a direction in order to MINIMIZE the output, in what direction or vector should one move from the current center of the factorial experiments? e) A Central Composite Design of experiments was performed on 6 factors in order to determine the optimum location to run the factors to get the highest production. It was later determined that only 4 of these factors are truly significant, but the report failed to mention Which factors were significant. From the data on the next page, determine Which 4 factors are significant. Explain your reasoning clearly.

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