People rely on their trusted circle of friends for advice and recommendations on everything from travel destinations to purchase decisions. With the extensive use of social networks these relationships are now taken to an electronic platform, where they manifest as likes, comments, wall posts, etc., on social media networks. This paper explores the novel idea that such user relationships can be extracted to significantly improve the accuracy of commercial recommendation systems by identifying otherwise hidden relationships between users. A multiple linear regression based model capable of extracting such user relationships and their corresponding strength efficiently is introduced under this research and the above hypothesis is tested by integrating the predictive model to an existing social media based travel recommendation system. Finally, experimental results of the proposed model are produced, proving the capability of the model in achieving a significant increase in accuracy in travel recommendations, affirming the considered hypothesis.