Context-aware recommender systems (CARS) rest on a multidimensional rating function: Users × Items × Context → Ratings. This multidimensional modeling should improve the quality of the recommendation process, but unfortunately, it is rare or even impossible to have ratings for all possible cases of context. Our objective is therefore twofold: (i) to reduce the dimensionality of the contextual information (in order to reduce the sparsity), which leads to (ii) propose a technique for aggregating the ratings associated with the aggregated dimensions. To do this, we organize, in the CARS utility matrix, the contextual information according to hierarchical dimensions as is done in OLAP (OnLine Analytical Processing) and we use a regression-based approach for the rating aggregation according to previously defined hierarchies. Our approach supports multiple dimensions and hierarchical aggregation of ratings. It was validated on two real-world datasets.