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 y = weight loss (%). The experimenters made observations on weight loss for various values of three independent variables: x₁ = (?C) = 90, 100, 110temperature ; x₂ = time of teatment (min) = 30, 75, 120; x₃ = tartaric acid concentration (g/L) = 0,8,16. In the regression analyses, the three values of each variable were coded as –1, 0, and 1, respectively, giving the accompanying data (the value y₈ = 19.3 was reported, but our value y₈ = 20.3 results in regression output identical to that appearing in the article).

  

      

  

      

 

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 x₁ =………….. = x₉ 5 0 (i.e., when  temperature = 100, time = 75, and concentration = 8) 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
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Does at least one of the second-order predictors provide additional useful information? State and test the appropriate hypotheses.

temperature (C) = 90, 100, 110;