For questions 6-9: A single replicate 2 4 experiment is designed. The experiment

Question

For questions 6-9:

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_886.csv (chart attached right below) .

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

Factorial Effect B = 8.855

Factorial Effect C = 9.367

Interaction Effect BC = 10.013

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 3

4) Coefficient 23

Treatment Combination Factor A Factor B Factor C Factor D Response -1 -1 -1 -1 -1 -13.91 d -1 -1 -1 1 -15.04 c -1 -1 1 -1 -13.26 cd -1 -1 1 1 -16.63 b -1 1 -1 -1 -13.96 bd -1 1 -1 1 -15 bc -1 1 1 -1 3.9 bcd -1 1 1 1 3.71 a 1 -1 -1 -1 -13.28 ad 1 -1 -1 1 -14.61 ac 1 -1 1 -1 -13.7 acd 1 -1 1 1 -15.83 ab 1 1 -1 -1 -16.03 abd 1 1 -1 1 -16.48 abc 1 1 1 -1 4.98 abcd 1 1 1 1 3.46

Explanation / Answer

Let us assume the regression model which having this coefficients

Response = B0 + B2 FactorB + B3 FactorC + B23 FactorB*FactorC + e

We use excel to find the coefficients of this model

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -10.105 0.278774 -36.248 1.24E-13 -10.7124 -9.4976 Factor B 4.4275 0.278774 15.88205 2.02E-09 3.820104 5.034896 Factor C 4.68375 0.278774 16.80125 1.06E-09 4.076354 5.291146 Factor B &C 5.00625 0.278774 17.95811 4.88E-10 4.398854 5.613646

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