Industrial engineers at the University of Florida used regression modeling as a tool to reduce the time and cost associated with developing new metallic alloys (Modelling and Simulation in Materials Science and Engineering, Vol. 13, 2005). To illustrate, the engineers build a regression model for the tensile yield strength (y) of a new steel alloy. The potential important predictors of yield strength are listed in the following table.
x1 = Carbon amount 1% weight2
x2 = Manganese amount 1% weight2
x3 = Chromium amount 1% weight2
x4 = Nickel amount 1% weight2
x5 = Molybdenum amount 1% weight2
x6 = Copper amount 1% weight2
x7 = Nitrogen amount 1% weight2
x8 = Vanadium amount 1% weight2
x9 = Plate thickness 1millimeters2
x10 = Solution treating 1millimeters2
x11 = Ageing temperature 1degrees Celsius2
a. The engineers used stepwise regression to search for a parsimonious set of predictor variables. Do you agree with this decision? Explain.
b. The stepwise regression selected the following independent variables: x1 = Carbon, x2 = Manganese, x3 = Chromium, x5 = Molybdenum, x6 = Copper, x8 = Vanadium, x9 = Plate thickness, x10 = Solution treating, and x11 = Ageing temperature. On the basis of this information, determine the total number of first-order models that were fit in the stepwise routine.
c. Refer to part b. All the variables listed there were statistically significant in the stepwise model, with R2 = .94. Consequently, the engineers used the estimated stepwise model to predict yield strength. Do you agree with this decision? Explain.