The usual numerical learning methods, that are primarily concerned with finding a good numerical fit to the data, often make predictions that do not correspond to the qualitative mechanisms in the domain of modelling or a domain expert's intuition. Consistency of numerical predictions with a given qualitative model is helpful when a numerical model is used for explanation of phenomena in the modelled domain, but can also considerably improve numerical accuracy. In this paper we present a novel approach to numerical machine learning called Qfilter. Qfilter is a numerical regression method that can take into account qualitative background knowledge to give qualitatively faithful numerical prediction. The results on a set of domains including population dynamics show considerable prediction accuracy improvements compared to the usual numerical learners. As qualitative domain knowledge is often available in practice, Qfilter's ability to exploit such knowledge should be beneficial in many applications.