This paper introduces a novel collaborative filtering recommender system for ecommerce which copes reasonably well with the ratings sparsity issue through the use of the notion of selective predictability and the use of the information theoretic measure known as entropy to estimate the same. It exploits the predictable portion(s) of apparently complex relationships between users when picking out mentors for an active user. The potential of the proposed approach in providing novel as well as good quality recommendations have been demonstrated through comparative experiments on popular datasets such as MovieLens and Jester. The approach’s additional capability to come up with explanations for its recommendations will enhance the user’s comfort level in accepting the personalized recommendations.