A collaborative filtering technique with transparency using linear regression is proposed. In this study, the transparency is assumed as a role which users can know how the score is calculated. The proposed linear regression model presents regression coefficients to users. This study evaluates application of regularization and dimensionality reduction to estimate regression coefficient, and performs a score prediction experiment which analyze prediction accuracy, computing time, and obtained regression coefficients using five benchmark datasets for collaborative filtering. According to the experimental results, the proposed linear regression model with L2 regularization achieves the best prediction accuracy in the nine estimation methods considered for the regression coefficients. In addition, its prediction accuracy is similar level to Factorization Machines. The learning time of the proposed linear regression model is 24.9 to 1584 times faster than Factorization Machines. In the analysis of regression coefficients, variety in regression coefficient values are found in without regression and with L2 regression cases, and this suggests possibility of which the learned models are personalized.