Chapter 13, Problem 76SE

The article “Chemithermomechanical Pulp from Mixed High Density Hardwoods” (TAPPI, July 1988: 145–146) reports on a study in which the accompanying data was obtained to relate y = specific surface area (cm²/g) to x₁ = % NaOH used as a pretreatment chemical and x₂ = treatment time (min) for a batch of pulp.

*1	X2	y
3	30	5.95
3	60	5.60
3	90	5.44
9	30	6.22
9	60	5.85
9	90	5.61
15	30	8.36
15	60	7.30
15	90	6.43

The accompanying Minitab output resulted from a request to fit the model $Y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\in$  e.

a. What proportion of observed variation in specific surface area can be explained by the model relationship?

b. Does the chosen model appear to specify a useful relationship between the dependent variable and the predictors?

c. Provided that % NaOH remains in the model, would you suggest that the predictor treatment time be eliminated?

d. Calculate a 95% CI for the expected change in specific surface area associated with an increase of 1% in NaOH when treatment time is held fixed.

e. Minitab reported that the estimated standard deviation ${\hat{\beta }}_0+{\hat{\beta }}_1(9)+{\hat{\beta }}_2(60)$ is .162. Calculate a prediction interval for the value of specific surface area to be observed when % NaOH = 9 and treatment time = 60.