The article "Drying of Pulps in Sprouted Bed: Effect of Composition on Dryer Performance" (M. Medeiros, S. Rocha, et al., Drying Technology, 2002:865-881) presents measurements of pH, viscosity (in kg/m · s), density (in g/cm3), and BRIX (in percent). The following MINITAB output presents the results of fitting the model
pH = β0 + β1 Viscosity + β2 Density + β3 BRIX + ε

a. Predict the pH for a pulp with a viscosity of 1500 kg/m · s, a density of 1.04 g/cm3, and a BRIX of 17.5%.
b. If two pulps differ in density by 0.01 g/cm3, by how much would you expect them to differ in pH, other things being equal?
c. The constant term β0 is estimated to be negative. But pulp pH must always be positive. Is something wrong? Explain.
d. Find a 95% confidence interval for the mean pH of pulps with viscosity 1200 kg/m · s, density 1.08 g/cm3, and BRIX 18.0%.
e. Find a 95% prediction interval for the pH of a pulp with viscosity 1000 kg/m · s, density 1.05 g/cm3, and BRIX 19.0%.
f. Pulp A has viscosity 2000, density 1.03, and BRIX 20.0. Pulp B has viscosity 1000, density 1.05, and BRIX 19.0. Which pulp will have its pH predicted with greater precision? Explain.

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The regression equation is pH1.79 0.000266 Viscosity 9.82 Density 0.300 BRIX Predictor Constant Viscosity Density BRIX Coef -1.7914 0.00026626 9.8184 -0.29982 SE Coef 6.2339 0.00011517 5.7173 0.099039 -0.29 2.31 1.72 .03 0.778 0.034 0.105 0.008 S 0.379578 R-Sq 50.0% R-Sq ( adj ) 40.6% Predicted VaTues for New Observations New Obs Fit 95% PI SE Fit 0.1351 (2.8010. 3.3740 (2.2333. 3.9416) 0.1483 (3.4207. 4.0496) (2.8712. 4.5990) 95% CI 3.0875 3.7351 2.8576 0.2510 (2.3255. 3.3896) (1.8929. 3.8222) alues of Predictors for New Observations New Obs Viscosity Density BRIX 1.05 19.0 1.08 18.0 1.03 20.0 1000 1200 2000