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/cm), and BRIX (in percent). The following MINITAB output presents the results of fitting the model pH = 6, +6, Viscosity + B, Density + ß, BRIX +€ The regression equation is pH - -1.79 + 0.000266 Viscosity + 9.82 Density - 0.300 BRIX Predictor Coef SE Coef Constant -1.7914 6.2339 -0.29 0.778 Viscosity 0.00026626 0.00011517 2.31 0.034 Density 9.8184 5.7173 1.72 0.105 BRIX -0.29982 0.099039 -3.03 0.008 S - 0.379578 R-Sq - 50.0% R-Sq(adj) - 40.6% Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 3.0875 0.1351 (2.8010, 3.3740) (2.2333, 3.9416) (3.4207, 4.0496) (2.3255, 3.3896) 2 3.7351 0.1483 (2.8712, 4.5990) з 2.8576 0.2510 (1.8929, 3.8222) Values of Predictors for New Observations New Obs Viscosity Density BRIX 1000 1.05 19.0 1200 1.08 18.0 2000 1.03 20.0 Predict the pH for a pulp with a viscosity of 1500 kg/m - s, a density of 1.04 g/cm?, and a BRIX of 17.5%. a. If two pulps differ in density by 0.01 g/cm², by how much would you expect them to differ in pH, other things being equal? ъ. The constant term Bo is estimated to be negative. But pulp pH must always be positive. Is something wrong? Explain. 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%. Find a 95% prediction interval for the pH of a pulp with viscosity 1000 kg/m - s, density 1.05 g/cm?, 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. C. d. e.

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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/cm), and BRIX (in percent). The
following MINITAB output presents the results of fitting the model
pH = 6, +6, Viscosity + B, Density + ß, BRIX +€
The regression equation is
pH - -1.79 + 0.000266 Viscosity + 9.82 Density - 0.300 BRIX
Predictor
Coef
SE Coef
Constant
-1.7914
6.2339
-0.29
0.778
Viscosity
0.00026626
0.00011517
2.31
0.034
Density
9.8184
5.7173
1.72
0.105
BRIX
-0.29982
0.099039
-3.03
0.008
S - 0.379578
R-Sq - 50.0%
R-Sq(adj) - 40.6%
Predicted Values for New Observations
New
Obs
Fit
SE Fit
95% CI
95% PI
3.0875
0.1351
(2.8010, 3.3740)
(2.2333, 3.9416)
(3.4207, 4.0496)
(2.3255, 3.3896)
2
3.7351
0.1483
(2.8712, 4.5990)
з
2.8576
0.2510
(1.8929, 3.8222)
Values of Predictors for New Observations
New
Obs
Viscosity
Density
BRIX
1000
1.05
19.0
1200
1.08
18.0
2000
1.03
20.0
Predict the pH for a pulp with a viscosity of 1500 kg/m - s, a density of 1.04 g/cm?,
and a BRIX of 17.5%.
a.
If two pulps differ in density by 0.01 g/cm², by how much would you expect them to
differ in pH, other things being equal?
ъ.
The constant term Bo is estimated to be negative. But pulp pH must always be positive.
Is something wrong? Explain.
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%.
Find a 95% prediction interval for the pH of a pulp with viscosity 1000 kg/m - s,
density 1.05 g/cm?, 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.
C.
d.
e.
Transcribed Image Text: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/cm), and BRIX (in percent). The following MINITAB output presents the results of fitting the model pH = 6, +6, Viscosity + B, Density + ß, BRIX +€ The regression equation is pH - -1.79 + 0.000266 Viscosity + 9.82 Density - 0.300 BRIX Predictor Coef SE Coef Constant -1.7914 6.2339 -0.29 0.778 Viscosity 0.00026626 0.00011517 2.31 0.034 Density 9.8184 5.7173 1.72 0.105 BRIX -0.29982 0.099039 -3.03 0.008 S - 0.379578 R-Sq - 50.0% R-Sq(adj) - 40.6% Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 3.0875 0.1351 (2.8010, 3.3740) (2.2333, 3.9416) (3.4207, 4.0496) (2.3255, 3.3896) 2 3.7351 0.1483 (2.8712, 4.5990) з 2.8576 0.2510 (1.8929, 3.8222) Values of Predictors for New Observations New Obs Viscosity Density BRIX 1000 1.05 19.0 1200 1.08 18.0 2000 1.03 20.0 Predict the pH for a pulp with a viscosity of 1500 kg/m - s, a density of 1.04 g/cm?, and a BRIX of 17.5%. a. If two pulps differ in density by 0.01 g/cm², by how much would you expect them to differ in pH, other things being equal? ъ. The constant term Bo is estimated to be negative. But pulp pH must always be positive. Is something wrong? Explain. 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%. Find a 95% prediction interval for the pH of a pulp with viscosity 1000 kg/m - s, density 1.05 g/cm?, 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. C. d. e.
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