In applications of Web of Things or Web of Events, a massive volume of multi-dimensional streaming data are automatically and continuously generated from different sources, such as GPS, sensors, and other measurement devices, which are essentially imprecise (inaccurate and/or uncertain). It is challenging to monitor and get insights over imprecise and low-level streaming data, in order to capture potentially important data changing trends and to initiate prompt responses. In this work, we investigate solutions for conducting multi-dimensional and multi-granularity probabilistic regression for the imprecise streaming data. The probabilistic nature of streaming data poses big computational challenges to the regression and its aggregation. In this paper, we study a series of techniques on multi-dimensional probabilistic regression, including aggregation, sketching, popular path materialization, and exception-driven querying. Extensive experiments on real and synthetic datasets demonstrate the efficiency and scalability of our proposals.