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. of Chem. Tech. and 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 lineolic 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 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 y^ = .66573, sY^ = .01785, based on the complete second-order model. Predict the amount of β-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.

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