EXTRA CREDIT (5 points): An article in Technometrics (1974, Vol. 16, pp. 523-531

Question

EXTRA CREDIT (5 points): 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 ow x,, temperature x, and acid concentration x Predictor Constant X1 X2 X3 S = 3.243 Coeff 39.9197 11.8960 0.7156 1.2953 0.1521 SE Coef 0.1846 0.1526 0.1563 R-sq = R-sq (Adj) 89.83% Analysis of Variance Source Regression Residual Error Total DF MS 1890.41 20 2069.24 a. Fill in the missing quantities. You may use bounds for the P-values. hat conclusions can you draw about thc ovcrall modcl significancc of regression? Is the overall model significant at = 0.05? at 0.01 ? What conclusions can you draw about the contributions of the individual regressors to the model? c. d. Write the out the linear regression equation e. Predict the stack loss when x 60, x, 26, and x,-85

Explanation / Answer

a)

r^2adj=1-[(1-r^2){n-1/n-k-1}]

0.8983=1-[(1-r^2){21-1/21-3-1}]

0.8983=1-[(1-r^2){20/17}]

0.8983=1-[(1-r^2){1.1764}]

0.8983=1-[(1.1764- 1.1764r^2}]

1.1764- 1.1764r^2=1-0.8983

r^2=0.91354981

b)

Model is significant at both 0.05 and 0.01.

c)

Looking at the p-value, only X3 is not significant. Rest both are significant.

d)

y=-39.9197+0.7156X1+1.2953X2-0.1521X3

e)

y=-39.9197+0.7156(60)+1.2953(26)-0.1521(85)

y=23.7656

Coefficients Standard Error t Stat P-value Constant -39.9197 11.896 -3.355724613 0.003520081 X1 0.7156 0.1846 3.876489707 0.001105864 X2 1.2953 0.1526 8.488204456 1.0436E-07 X3 -0.1521 0.1563 -0.973128599 0.343386233 ANOVA df SS MS F Significance F Regression 3 1890.41 630.1366667 59.90227218 < .00001 Residual 17 178.83 10.51941176 Total 20 2069.24

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