83. 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. Chem. Tech. Biotech., 1994:

161—170).

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 request to the SAS package to t b0  b1x1 

b2x2  b3x3, where x3  x1x2 (an interaction predictor)

yielded the accompanying output.

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

c. Does there appear to be a useful 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 signi cance level of .01.

e. The estimated standard deviation of when mole contents is 2.0 and calcination temperature is 500 is . Calculate a 95% con dence interval for the mean value of surface area under these circumstances.

f. Based on appropriate diagnostic plots, is there any reason to question the regression model assumptions?