We propose an efficient method for the high dimensional data regression. To this end, we use a least mean squares (LMS) filter followed by a recursive least squares (RLS) filter and combine them via boosting notion extensively used in machine learning literature. Moreover, we provide a novel approach where the RLS filter is updated randomly in order to reduce the computational complexity while not giving up more on the performance. In the proposed algorithm, after the LMS filter produces an estimate, depending on the error made on this step, the algorithm decides whether or not updating the RLS filter. Since we avoid updating the RLS filter for all data sequence, the computational complexity is significantly reduced. Error performance and the computation time of our algorithm is demonstrated for a highly realistic scenario.