An experiment to investigate the effects of a new technique for degumming of silk yarn was described in the article “Some Studies in Degumming of Silk with Organic Acids” (J. Society of Dyers and Colourists, 1992: 79–86). One response variable of interest was . The experimenters made observations on weight loss for various values of three independent variables: temperature ;

; tartaric acid concentration (g/L) 5 0,8,16. In the regression analyses, x x 2 5 time of teatment (min) 5 30, 75, 120 3 5 x 1 5 (8C) 5 90, 100, 110 y 5 weight loss(%)

x x 3 5 40 4 5 45 x 1 5 20, x s 2 5 25, Yˆ 5 7.46 b

ˆ b 4 ˆ

1 s 5 31.48 R-Sq 5 96.4% R-Sq(adj) 5 95.8%

237.4 water 1 7.64 paper 1 4.30 garbage enercont 5 2245 1 28.9 plastics Obs 9 10 11 12 13 14 15 x1 0 0 0 0 0 00 x2 1 1 1 1 0 00 x3 1 1 1 1 0 00 y 13.1 23.0 20.9 21.5 22.0 21.3 22.6 A multiple regression model with predictors—

, and

—was fit to the data, resulting in

, and .

a. Does this model specify a useful relationship? State and test the appropriate hypotheses using a significance level of .01.

b. The estimated standard deviation of when

(i.e., when ,

, and ) is 1.248. Calculate a 95% CI for expected weight loss when temperature, time, and concentration have the specified values.

c. Calculate a 95% PI for a single weight-loss value to be observed when temperature, time, and concentration have values 100, 75, and 8, respectively.

d. Fitting the model with only x1, x2, and x3 as predictors gave and . Does at least one of the second-order predictors provide additional useful information? State and test the appropriate hypotheses.