The article “Experimental Design Approach for the

Chapter 8, Problem 2E

(choose chapter or problem)

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 fit to estimate the cycle time \((y)\) in terms of the flow rate \((x_1)\), sample concentration \((x_2)\), and mobile-phase composition \((x_3)\). 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 \(x_1^2,x_2^2,\text{ and }x_3^2\) from the model, and then perform an F test.

iii. Drop \(x_1x_2,x_1x_3,\text{ and }x_2x_3\) from the model, and then perform an F test.

iv. Drop \(x_1\text{ and }x_1^2\) from the model, and then perform an F test.

v. Add cubic terms \(x_1^3,x_2^3,\text{ and }x_3^3\) to the model to try to improve the fit.

Equation Transcription:

Text Transcription:

(y)

(x_1)

(x_2)

(x_3)

x_1

x_2

x_3

x_1^2

x_2^2

x_3^2

x_1x_2

x_1x_3

x_2x_3

x_1^2,x_2^2, and x_3^2

x_1x_2,x_1x_3, and x_2x_3

x_1 and x_1^2

x_1^3,x_2^3, and x_3^3