Abstract: In this paper, by applying multivariate linear regression theory to multiple coherence analysis, a simplified way to compute multiple coherence function, paritial coherence function, partial multiple coherence function, as well as all types of coherent output spectra is presented. The vague concept of ‘residual cross spectrum’ has been avoided the formulas for computing are simple and easy to be programed. The problems in noise source identification by partial coherence function are discussed. The results for noise source identification in a simulated model are given.