The article Experimental Design Approach for the Optimization of the Separation of Enantiomers in Preparative Liquid Chromatography

The article €œExperimental 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 fit 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 fit 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?

i. Nothing needs to be done. This model is fine. 

ii. Drop x²₁ , x²2 , and x²3 from the model, and then perform an F test.

iii. Drop x₁x₂, x₁x₃, and x₂x3 from the model, and then perform an F test.

iv. Drop x₁ and x²₁ from the model, and then perform an F test.

v. Add cubic terms x³₁ , x³₂ , and x³₃ to the model to try to improve the fit.

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Predictor Coefficient Constant 1.603 X1 -0.619 -22.289 0.000 X2 0.086 3.084 0.018 X3 0.306 11.011 0.000 0.272 8.542 0.000 0.057 1.802 0.115 0.105 3.300 0.013 X1X2 -0.022 -0.630 0.549 X1X3 -0.036 -1.004 0.349 X2X3 0.036 1.018 0.343