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 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 (% weight)
x2 = Manganese amount (% weight)
x3 = Chromium amount (% weight)
x4 = Nickel amount (% weight)
x5 = Molybdenum amount (% weight)
x6 = Copper amount (% weight)
x7 = Nitrogen amount (% weight)
x8 = Vanadium amount (% weight)
x9 = Plate thickness (millimeters)