87. 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 (J.
Chem. Tech. Biotech., 2002: 933—943) carried out a multiple regression analysis to relate the dependent variable y  amount of b-carotene (g/dm3) to the three predictors: amount of linoleic acid, amount of kerosene, and amount of antioxidant (all g/dm3).

a. Fitting the complete second-order model in the three predictors resulted in R2  .987 and adjusted R2  .974, whereas tting the rst-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 based on the complete second-order model. Predict the amount of b-carotene that would result from a single experimental run with the designated values of the independent variables, and do so in a way that conveys information about precision and reliability.