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 to NaOH used as a pretreatment chemical and time (min) for a batch of pulp.

x1 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 x 2 5 treatment x 1 5 %

y 5 specific surface area (cm2

/g)

bˆ

0 1 bˆ

1 1 bˆ

2 x 2 5 x 2 k 5 2, x 1 5 x s SSE 5 26.98 bˆ sbˆ 2 5 .3073 s 1 5 1.002, bˆ

0 5 .8522, bˆ b 2 5 22.3621, ˆ b 1 5 6.581, ˆ

0 5 41.7422, x 5 log 10 (added Mn)

y 5 plant 1025.1 1025.4 1024.7 1026.0 1025.3 1025.8 1026.8 1026.2 1026.7 1027.2 1027.1 1028.0 y 5 conductivity x 5 Li2O The accompanying Minitab output resulted from a request to fit the model .

The regression equation is Predictor Coef Stdev t-ratio p Constant 6.0483 0.5208 11.61 0.000 NAOH 0.14167 0.03301 4.29 0.005 TIME 0.016944 0.006601 2.57 0.043 Analysis of Variance SOURCE DF SS MS F p Regression 2 5.8854 2.9427 12.51 0.007 Error 6 1.4118 0.2353 Total 8 7.2972

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 of is .162. Calculate a prediction interval for the value of specific surface area to be observed when % and treatment .