In a closely coupled heterogeneous computing system the work is shared amongst all available computing resources. One challenge is to find an optimal division of work between the two or more very different kinds of processing units, each with their own optimal settings. We show that through the use of statistical techniques, a systematic search of the parameter space can be conducted. These techniques can be applied to variables that are categorical or continuous in nature and do not rely on the standard assumptions of linear models, mainly that the response variable can be described as a linear combination of the regression coefficients. Our search technique, when applied to the HPL benchmark, resulted in a performance gain of 14.5% over previously reported results.