We consider the problem of finding the best subset of sensors in wireless sensor networks where linear Bayesian parameter estimation is conducted from the selected measurements corrupted by correlated noise. We aim to directly minimize the estimation error which is manipulated by using the QR and LU factorizations. We derive an analytic result which expedites the sensor selection in a greedy manner. We also provide the complexity of the proposed algorithm in comparison with previous selection methods. We evaluate the performance through numerical experiments using random measurements under correlated noise and demonstrate a competitive estimation accuracy of the proposed algorithm with a reasonable increase in complexity as compared with the previous selection methods.