Utilization of sucrose as a carbon source for the production of chemicals is uneconomica...

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 β-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 , 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.