This paper offers a local distributed algorithm for multivariate regression in large peer-to-peer environments. The algorithm is designed for distributed inferencing, data compaction, data modeling and classification tasks in many emerging peer-to-peer applications for bioinformatics, astronomy, social networking, sensor networks and web mining. Computing a global regression model from data available at the different peer-nodes using a traditional centralized algorithm for regression can be very costly and impractical because of the large number of data sources, the asynchronous nature of the peer-to-peer networks, and dynamic nature of the data/network. This paper proposes a two-step approach to deal with this problem. First, it offers an efficient local distributed algorithm that monitors the “quality ” of the current regression model. If the model is outdated, it uses this algorithm as a feedback mechanism for rebuilding the model. The local nature of the monitoring algorithm guarantees low monitoring cost. Experimental results presented in this paper strongly support the theoretical claims.