This work demonstrates a novel computational approach combining flux balance modeling with statistical methods to identify correlations among fluxes in a metabolic network, providing insight as to how the fluxes should be redirected to achieve maximum product yield. The procedure is demonstrated using the example of amino acid production from an industrial Escherichia coli production strain and a hypothetical engineered strain overexpressing two heterologous genes. Regression analysis based on a random sampling of 5000 points within the feasible solution space of the E. coli stoichiometric network suggested that increased activity of the glyoxylate cycle or PEP carboxylase and elimination of malic enzyme will improve lysine and arginine synthesis.