Question

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.

Answer 1

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