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 (Modeling and Simulation in Materials Science and Engineering, Vol. 13. 2005). To illustrate, the engineers built a regression model for the tensile yield strength (y) of a new steel alloy. The potentially important predictors of yield strength are listed in the accompanying table.

a. The engineers discovered that the variable Nickel (x4) was highly correlated with the other potential independent variables. Consequently. Nickel was dropped from the model. Do you agree with this decision? Explain.
b. The engineers used stepwise regression on the remaining 10 potential independent variables in order to search for a parsimonious set of predictor variables. Do you agree with this decision? Explain.

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Xi = Carbon amount (% weight) x2 = Manganese amount (% weight) = Chromium amount (% weight) x4 Nickel amount (% weight) X5 = Molybdenum amount (% weight) X5 = Copper amount (% weight) Nitrogen amount (% weight) xs = Vanadium amount (% weight) Plate thickness (millimeters) x10 = Solution treating (milliliters) 1 Aging temperature (degrees, Celsius)