Chapter 8.3, Problem 2E

The article “Experimental Design Approach for the Optimization of the Separation of Enantiomers in Preparative Liquid Chromatography” (S. Lai and Z. Lin. Separation Science and Technology, 2002: 847–875) describes an experiment involving a chemical process designed to separate enantiomers. A model was lit to estimate the cycle time (y) in terms of the flow rate (x₁), sample concentration (x₂), and mobile-phase composition (x₃). The results of a least-squares lit are presented in the following table. (The article did not provide the value of the t statistic for the constant term.)

Of the following, which is the best next step in the analysis?

1. i. Nothing needs to be done. This model is fine.
2. ii. Drop $x_1^2,x_2^2$, and $x_3^2$ from the model, and then perform an F test.
3. iii. Drop $x_1{x}_2,x_1{x}_3$, and $x_2{x}_3$ from the model, and then perform an F test.
4. iv. Drop $x_1$, and $x_1^2$ from the model, and then perform an F test.
5. v. Add cubic terms $x_1^3,x_2^3$, and $x_3^3$ to the model to try to improve the fit.