The article “Simultaneous Optimization of Mechanical

Chapter 8, Problem 5E

(choose chapter or problem)

The article “Simultaneous Optimization of Mechanical Properties of Steel by Maximizing Exponential Desirability Functions” (K. J. Kim and D. K. J. Lin, Journal of the Royal Statistical Society Series C, Applied Statistics, 2000: 311–325) presents measurements on 72 steel plates. The following MINITAB output presents the results of a study to determine the relationship between yield strength (in \(\mathrm{kg} / \mathrm{mm}^{2}\)), and the proportion of carbon, manganese, and silicon, each measured in percent. The model fit is

     \(\text { Yield strength }=\beta_{0}+\beta_{1} \text { Carbon }+\beta_{2} \text { Manganese }+\beta_{3} \text { Silicon }+\varepsilon\)

Of the following, which is the best next step in the analysis? Explain your reasoning.

i. Add interaction terms \(\text { Carbon } \cdot \text { Manganese and Manganese } \cdot \text { Silicon }\) to try to find more variables to put into the model.

ii. Add the interaction term \(\text { Carbon - Silicon }\) to try to find another variable to put into the model.

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

iv. Drop Carbon and Silicon, and then perform an F test.

v. Drop Manganese, and then perform an F test.

Equation Transcription:

Text Transcription:

kg/mm^2

Yield strength=beta_0+beta_1 Carbon+beta_2 Manganese+beta_3 Silicon+varepsilon

Carbon{cdot}Manganese and Manganese{cdot}Silicon

Carbon{cdot}Silicon