In this paper, an algorithm for decentralized multi-agent estimation of parameters in linear discrete-time regression models is proposed in the form of a combination of local stochastic approximation algorithms and a global consensus strategy. An analysis of the asymptotic properties of the proposed algorithm is presented, taking into account both the multi-agent network structure and the probabilities of getting local measurements and implementing exchange of inter-agent messages. In the case of non-vanishing gains in the stochastic approximation algorithms, an asymptotic estimation error covariance matrix bound is defined as the solution of a Lyapunov-like matrix equation. In the case of asymptotically vanishing gains, the mean-square convergence is proved and the rate of convergence estimated. In the discussion, the problem of additive communication noise is treated in a methodologically consistent way. It is also demonstrated how the consensus scheme in the algorithm can contribute to the overall reduction of measurement noise influence. Some simulation results illustrate the obtained theoretical results.