For questions 1-4: A single replicate 2 4 experiment is designed. The experiment

Question

For questions 1-4:

A single replicate 24 experiment is designed. The experiment has factors A, B, C, and D, each of which can be set to +1 or -1. We conduct a single replicate of this experiment, collecting the response for each possible combination of factor settings. This data is in the file HW_DOEInterp_171.csv (attached below) .

We compute the factorial and interaction effects from this data, and determine that the following effects are significant:

Factorial Effect B = 10.622

Factorial Effect D = 10.387

Interaction Effect BD = -15.538

Give the values of the following coefficients in a regression model that only includes the significant factorial and interaction effects.

1) Coefficient 0

2) Coefficient 2

3) Coefficient 4

4) Coefficient 24

Treatment Combination Factor A Factor B Factor C Factor D Response -1 -1 -1 -1 -1 -13.68 d -1 -1 -1 1 10.41 c -1 -1 1 -1 -14.25 cd -1 -1 1 1 13.54 b -1 1 -1 -1 10.73 bd -1 1 -1 1 5.77 bc -1 1 1 -1 12.74 bcd -1 1 1 1 8.05 a 1 -1 -1 -1 -13.83 ad 1 -1 -1 1 11.19 ac 1 -1 1 -1 -13.98 acd 1 -1 1 1 12.82 ab 1 1 -1 -1 12.79 abd 1 1 -1 1 6.71 abc 1 1 1 -1 12.64 abcd 1 1 1 1 7.77

Explanation / Answer

Term Effect Coef
Constant 4.339
A 0.350 0.175
B 10.623 5.311
C 1.155 0.578
D 10.388 5.194
A*B 0.305 0.152
A*C -0.558 -0.279
A*D -0.170 -0.085
B*C 0.145 0.073
B*D -15.538 -7.769
C*D 0.870 0.435
A*B*C -0.288 -0.144
A*B*D -0.155 -0.077
A*C*D -0.123 -0.061
B*C*D -0.500 -0.250
A*B*C*D 0.358 0.179

(I HAVE CALCULATED THE CALCULATION IN MINITAB SOFTWARE)

the two columns are contains effect and coefficient of each of the factor combinations

we need to report coefficient of

b0=4.339

b2=5.311

b4=5.194

b24=-7.769

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