Configurable software systems allow stakeholders to derive program variants by selecting features. Understanding the correlation between feature selections and performance is important for stakeholders to be able to derive a program variant that meets their requirements. A major challenge in practice is to accurately predict performance based on a small sample of measured variants, especially when features interact. We propose a variability-aware approach to performance prediction via statistical learning. The approach works progressively with random samples, without additional effort to detect feature interactions. Empirical results on six real-world case studies demonstrate an average of 94 % prediction accuracy based on small random samples. Furthermore, we investigate why the approach works by a comparative analysis of performance distributions. Finally, we compare our approach to an existing technique and guide users to choose one or the other in practice.