Current ILP systems that perform numerical reasoning, se- lect the best hypothesis using exclusively the scored value of the cost function. The cost function, by itself, cannot guarantee the goodness-of- fit of the induced hypotheses in numerical domains. Consequently the induced theory may not capture the overall structure of the underlying process that generated data. This paper proposes a statistical-based cri- terion for hypotheses acceptance, called model validation, that assess the goodness-of-fit of the induced hypotheses in numerical domains. We have found this extension essential to improve on results over ML and statistical-based algorithms used in the empirical evaluation study.