Question

A 2^4-1  experiment was performed to improve the yield of a chemical process. Four factors were selected, and two replicates were run. Due to raw materials constraints, it was possible to run only 8 runs. Thus, the design generator D = ABC was selected. The data are shown in the following table. Create the standard order fractional factorial design in Minitab. Analyze the fractional factorial design and, following the principle of hierarchical order, remove all interaction terms then main effects that are not statistically significant at p = 0.05. Analyze the reduced factorial design and output a normal probability plot, fitted values plot, and plots of the residuals versus each factor. State the final model and comment on its adequacy based on its R-square values and residuals analyses. What settings of the final model predictors maximize yield?

RUN	A	B	C	D	YIELD
1	-1	-1	-1	-1	97
2	1	-1	-1	1	74
3	-1	1	-1	1	81
4	1	1	-1	-1	71
5	-1	-1	1	1	92
6	1	-1	1	-1	81
7	-1	1	1	-1	88
8	1	1	1	1	83
9	-1	-1	-1	-1	98
10	1	-1	-1	1	72
11	-1	1	-1	1	87
12	1	1	-1	-1	80
13	-1	-1	1	1	99
14	1	-1	1	-1	79
15	-1	1	1	-1	87
16	1	1	1	1	85

Answer 1

ANSWER:

Factorial Fit: Y versus A, B, C, D

Estimated Effects and Coefficients for Y (coded units)

Term Effect Coef SE Coef T P
Constant 84.625 0.8385 100.92 0.000
A -13.000 -6.500 0.8385 -7.75 0.000
B -3.750 -1.875 0.8385 -2.24 0.056
C 4.250 2.125 0.8385 2.53 0.035
D -1.000 -0.500 0.8385 -0.60 0.567
A*B 7.000 3.500 0.8385 4.17 0.003
A*C 3.500 1.750 0.8385 2.09 0.070
A*D 1.750 0.875 0.8385 1.04 0.327

S = 3.35410 PRESS = 360
R-Sq = 92.21% R-Sq(pred) = 68.85% R-Sq(adj) = 85.40%

Analysis of Variance for Y (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 808.50 808.500 202.125 17.97 0.000
A 1 676.00 676.000 676.000 60.09 0.000
B 1 56.25 56.250 56.250 5.00 0.056
C 1 72.25 72.250 72.250 6.42 0.035
D 1 4.00 4.000 4.000 0.36 0.567
2-Way Interactions 3 257.25 257.250 85.750 7.62 0.010
A*B 1 196.00 196.000 196.000 17.42 0.003
A*C 1 49.00 49.000 49.000 4.36 0.070
A*D 1 12.25 12.250 12.250 1.09 0.327
Residual Error 8 90.00 90.000 11.250
Pure Error 8 90.00 90.000 11.250
Total 15 1155.75

so here at 5% significance AC ,AD, B ,D are having statistically insignificant result( as there p-value >0.05).

also i cannot perform test lefting the effect has no effect as A and C has significant result but AC has insignificant result. so while including A and C i cannot ignore AC.

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