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This research is an extension to the research conducted by K. Leka and G. Barnes of the Colorado Research Associates Division, Northwest Research Associates, Inc. in Boulder, Colorado (CORA) in which they established no single photospheric solar parameter could sufficiently identify a flare-producing active region (AR). Their research then explored the possibility a linear combination of parameters used in a multivariable discriminant function (DF) could adequately predict solar activity. The purpose of this research is to extend the DF research conducted by Leka and Barnes by refining the method of statistical discriminant analysis (DA) with the goal of selecting those photospheric magnetic parameters most capable of identifying flare-producing active regions in hopes of increasing the reliability of short term flare warnings and the understanding of flare production. The data for this research were photospheric vector magnetograms captured by the Imaging Vector Magnetograph (IVM) at the University of Hawai`i Mees Solar Observatory at Haleakala and provided by CORA.