In distributional semantics studies, there is a growing attention in compositionally determining the distributional meaning of word sequences. Yet, compositional distributional models depend on a large set of parameters that have not been explored. In this paper we propose a novel approach to estimate parameters for a class of compositional distributional models: the additive models. Our approach leverages on two main ideas. Firstly, a novel idea for extracting compositional distributional semantics examples. Secondly, an estimation method based on regression models for multiple dependent variables. Experiments demonstrate that our approach outperforms existing methods for determining a good model for compositional distributional semantics.