An experiment carried out to study the effect of the mole contents of cobalt (x1) and the calcination temperature (x2)

on the surface area of an iron–cobalt hydroxide catalyst (y)

resulted in the accompanying data (“Structural Changes and Surface Properties of CoxFe3xO4 Spinels,” J. of Chemical Tech. and Biotech., 1994: 161–170). A request to the SAS package to fit 0 1x1 2x2 3 x3, where x3
x1x2 (an interaction predictor) yielded the output below.

x1 | .6 .6 .6 .6 .6 1.0 1.0 x2

| 200 250 400 500 600 200 250 y | 90.6 82.7 58.7 43.2 25.0 127.1 112.3 x1 | 1.0 1.0 1.0 2.6 2.6 2.6 2.6 x2 | 400 500 600 200 250 400 500 y | 19.6 17.8 9.1 53.1 52.0 43.4 42.4 x1 | 2.6 2.8 2.8 2.8 2.8 2.8 x2 | 600 200 250 400 500 600 y | 31.6 40.9 37.9 27.5 27.3 19.0

a. Predict the value of surface area when cobalt content is 2.6 and temperature is 250, and calculate the value of the corresponding residual.

b. Since ˆ

1
46.0, is it legitimate to conclude that if cobalt content increases by 1 unit while the values of the other predictors remain fixed, surface area can be expected to decrease by roughly 46 units? Explain your reasoning.

c. Does there appear to be a useful linear relationship between y and the predictors?

d. Given that mole contents and calcination temperature remain in the model, does the interaction predictor x3 provide useful information about y? State and test the appropriate hypotheses using a significance level of .01.

e. The estimated standard deviation of Y

ˆ when mole contents is 2.0 and calcination temperature is 500 is sYˆ
4.69. Calculate a 95% confidence interval for the mean value of surface area under these circumstances.