Quantitative predictions are typically obtained by characterizing a system in terms of algebraic relationships and then using these relationships to compute quantitative predictions from numerical data. For real-life systems, such as mainframe operating systems, an algebraic characterization is often difficult, if not intractable. This paper proposes a statistical approach to obtaining quantitative predictions from monotone relationships - non-parametric interpolative-prediction for monotone functions (NIMF). NIMF uses monotone relationships to search historical data for bounds that provide a desired level of statistical confidence. We evaluate NIMF by comparing its predictions to those of linear least-squares regression (a widely-used statistical technique that requires specifying algebraic relationships) for memory contention in an IBM computer system. Our results suggest that using an accurate monotone relationship can produce better quantitative predictions than using an approximate algebraic relationship.