Many applied scientific domains are increasingly relying on largescale parallel computation. Consequently, many large clusters now have thousands of processors. However, the ideal number of processors to use for these scientific applications varies with both the input variables and the machine under consideration, and predicting this processor count is rarely straightforward. Accurate prediction mechanisms would provide many benefits, including improving cluster efficiency and identifying system configuration or hardware issues that impede performance. We explore novel regression-based approaches to predict parallel program scalability. We use several program executions on a small subset of the processors to predict execution time on larger numbers of processors. We compare three different regression-based techniques: one based on execution time only; another that uses per-processor information only; and a third one based on the global critical path. These techniques provide accurate scaling predictions, with median prediction errors between 6.2% and 17.3% for seven applications.