Question

An article in Technometrics (1974, Vol. 16, pp. 523-531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss (the amount of ammonia escaping) were measured with air flow X1, temperature x2, and acid concentration x3. y 21 .22 X3 42 80 27 89 37 80 27 88 37 75 25 90 28 62 24 87 18 62 22 87 18 62 23 87 62 24 93 19 20 62 24 93 15 58 23 87 14 58 18 80 14 58 18 89 13 58 17 88 11 58 18 82 12 58 19 93 8 50 18 89 7 50 18 86 8 50 19 72 8 19 79 9 50 50 56 20 80 15 20 82 15 70 20 91

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.956
R Square	0.914
Adjusted R Square	0.898
Standard Error	3.243
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	3	1890.408	630.136	59.902	0.000
Residual	17	178.830	10.519
Total	20	2069.238
	Coefficients	Standard Error	t Stat	P-value
Intercept	-39.920	11.896	-3.356	0.004
x1	0.716	0.135	5.307	0.000
x2	1.295	0.368	3.520	0.003
x3	-0.152	0.156	-0.973	0.344

a) y = -39.92 + 0.72x1 + 1.30x2 - 0.15x3

b) SS Total = 2069.24

c) x1 = 62, x2 = 26, x3 = 84

y = -39.92 + 0.72x1 + 1.30x2 - 0.15x3 = -39.92 + 0.72*62 + 1.30*26 - 0.15*84 = 25.92