Many large-scale clusters now have hundreds of thousands of processors, and processor counts will be over one million within a few years. Computational scientists must scale their applications to exploit these new clusters. Time-constrained scaling, which is often used, tries to hold total execution time constant while increasing the problem size along with the processor count. However, complex interactions between parameters, the processor count, and execution time complicate determining the input parameters that achieve this goal. In this paper we develop a novel gray-box, focused regression-based approach that assists the computational scientist with maintaining constant run time on increasing processor counts. Combining application-level information from a small set of training runs, our approach allows prediction of the input parameters that result in similar per-processor execution time at larger scales. Our experimental validation across seven applications showed that median prediction errors are less than 13%.