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

Question

5. 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 x2, and acid concentration x Predictor Constant X1 X2 Coeff 39.9197 0.7156 1.2953 -0.1521 SE Coef 11.8960 0.1846 0.1526 0.1563 S 3.243 sq R-sq (Adj) = 89.83% Analysis of Variance Source Regression Residual Error Total DF MS 1890.41 20 2069.24 Fill in the missing quantities. You may use bounds for the P-values What conclusions can you draw about the overall model significance 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? Write the out the linear regression equation Predict the stack loss when x = 60, x,-26, and x,-85 a. b. c. d. e.

Explanation / Answer

b) since p-value of F is 3*10^(-9) << 0.05

the model is significant

c)

if p-value is less than 0.05

the regressor is significant

here x1 and x2 are significant , but x3 is not

d)

Y^ = -39.9197 + 0.7156 *x1 + 1.2953 *x2 - 0.1521 *x3

e)

when x1 = 60 ,x2 = 26 , x3 = 85

y^ = -39.9197 + 0.7156 *60 + 1.2953 *26 - 0.1521 *85

=23.7656

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coeff se coeff t p constant -39.9197 11.896 -3.35572 0.003750297 x1 0.7156 0.1846 3.87649 0.001211966 x2 1.2953 0.1526 8.488204 1.61445E-07 x3 -0.1521 0.1563 -0.97313 0.344133539 R^2 0.913577 df SS MS F p regression 3 1890.41 630.1367 59.90227218 3.01631E-09 error 17 178.83 10.51941 total 20 2069.24

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