Question

# A B C D E RESPONSE -1 -1 -1 -1 1 38.9 1 -1 -1 -1...

 A B C D E RESPONSE -1 -1 -1 -1 1 38.9 1 -1 -1 -1 -1 35.3 -1 1 -1 -1 -1 36.7 1 1 -1 -1 1 45.5 -1 -1 1 -1 -1 35.3 1 -1 1 -1 1 37.8 -1 1 1 -1 1 44.3 1 1 1 -1 -1 34.8 -1 -1 -1 1 -1 34.4 1 -1 -1 1 1 38.4 -1 1 -1 1 1 43.5 1 1 -1 1 -1 35.6 -1 -1 1 1 1 37.1 1 -1 1 1 -1 33.8 -1 1 1 1 -1 36 1 1 1 1 1 44.9

If B high (ie +) was 30 volts and B low (ie -) was 40 volts, determine from the model equation the expected output at 32 volts if all other factors are set to nominal (ie 0).

for B- in the chart the input would be 40 and B+ would be 30 all others are 0 thats all the question has.

encoding the results for B -ve is 40 and +ve is 30 so

 RESPONSE B 38.9 40 35.3 40 36.7 30 45.5 30 35.3 40 37.8 40 44.3 30 34.8 30 34.4 40 38.4 40 43.5 30 35.6 30 37.1 40 33.8 40 36 30 44.9 30

we train a regression response = a + bB as all other factors are set to 0.

using solver in excel we get

 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 51.525 6.407893953 8.040863407 1.29053E-06 37.78143435 65.26856565 37.78143435 65.26856565 B -0.37875 0.181242611 -2.089740368 0.055373531 -0.767476739 0.009976739 -0.767476739 0.009976739
 Regression Statistics Multiple R 0.487610495 R Square 0.237763994 Adjusted R Square 0.183318565 Standard Error 3.624852214 Observations 16

so response = 51.525-.3875B

at B =32

response = 39.405

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