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 kg/mm2), and the proportion of carbon, manganese, and silicon, each measured in percent. The model fit is Yield strength = ????0 + ????1 Carbon + ????2 Manganese + ????3 Silicon + ????

The regression equation is Yield Strength = 24.677 - 19.402 Carbon + 14.720 Manganese + 70.720 Silicon Predictor Coef StDev T P Constant 24.677 5.8589 4.21 0.000 Carbon -19.402 28.455 -0.68 0.498 Manganese 14.720 5.6237 2.62 0.011 Silicon 70.720 45.675 1.55 0.126 Of the following, which is the best next step in the analysis? Explain your reasoning.

i. Add interaction terms Carbon ⋅ Manganese and Manganese ⋅ Silicon to try to find more variables to put into the model.

ii. Add the interaction term 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.