A practical computing technique is presented for the joint estimation of regression coefficients and the error spectrum in regression problems with stationary errors. In problems where unweighted least squares is not efficient, the procedure gives an estimate approaching the minimum variance linear unbiased estimate. Whether unweighted least squares is nearly efficient or not efficient, the procedure, in general, gives a much closer estimate of the covariance matrix of the estimated regression coefficients. The proposed approach, which involves the finite Fourier transformation of the observations and regression vectors, gives a useful intuitive understanding of the effects of correlated errors on regression.