Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
9th Edition
ISBN: 9798214004020
Author: Jay L. Devore
Publisher: Cengage Learning US
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Chapter 13.4, Problem 52E
Utilization of sucrose as a carbon source for the production of chemicals is uneconomical. Beet molasses is a readily available and low-priced substitute. The article “Optimization of the Production of b-Carotene from Molasses by Blakeslea Trispora” β. of Chem. Tech. and Biotech., 2002: 933–943) carried out a multiple regression analysis to relate the dependent variable y = amount of β-carotene (g/dm3) to the three predictors amount of lineolic acid, amount of kerosene, and amount of antioxidant (all g/dm3).
| Obs | Linoleic | Kerosene | Antiox | Betacaro |
| 1 | 30.00 | 30.00 | 10.00 | 0.7000 |
| 2 | 30.00 | 30.00 | 10.00 | 0.6300 |
| 3 | 30.00 | 30.00 | 18.41 | 0.0130 |
| 4 | 40.00 | 40.00 | 5.00 | 0.0490 |
| 5 | 30.00 | 30.00 | 10.00 | 0.7000 |
| 6 | 13.18 | 30.00 | 10.00 | 0.1000 |
| 7 | 20.00 | 40.00 | 5.00 | 0.0400 |
| 8 | 20.00 | 40.00 | 15.00 | 0.0065 |
| 9 | 40.00 | 20.00 | 5.00 | 0.2020 |
| 10 | 30.00 | 30.00 | 10.00 | 0.6300 |
| 11 | 30.00 | 30.00 | 1.59 | 0.0400 |
| 12 | 40.00 | 20.00 | 15.00 | 0.1320 |
| 13 | 40.00 | 40.00 | 15.00 | 0.1500 |
| 14 | 30.00 | 30.00 | 10.00 | 0.7000 |
| 15 | 30.00 | 46.82 | 10.00 | 0.3460 |
| 16 | 30.00 | 30.00 | 10.00 | 0.6300 |
| 17 | 30.00 | 13.18 | 10.00 | 0.3970 |
| 18 | 20.00 | 20.00 | 5.00 | 0.2690 |
| 19 | 20.00 | 20.00 | 15.00 | 0.0054 |
| 20 | 46.82 | 30.00 | 10.00 | 0.0640 |
a. Fitting the complete second-order model in the three predictors resulted in R2 = .987 and adjusted R2 = .974, whereas fitting the first-order model gave R2 = .016. What would you conclude about the two models?
b. For x1 = x2 = 30, x3 = 10, a statistical software package reported that
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Chapter 13 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
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