Yield strength of steel alloy. 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.

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.

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= X1 Carbon amount (% weight) X2 X3 X4 X5 = = = Manganese amount (% weight) Chromium amount (% weight) Nickel amount (% weight) Molybdenum amount (% weight) Copper amount (% weight) Nitrogen amount (% weight) X8 Vanadium amount (% weight) X9 = Plate thickness (millimeters) Solution treating (millimeters) X6 x7 = X10 X11 = = - Ageing temperature (degrees Celsius)