The effects of serially correlated residuals on the accuracy of linear regression are considered, and remedies are suggested. The Cochrane-Orcutt method specifically remedies the effects of serially correlated residuals and yields more accurate regression coefficients than does ordinary least squares. We illustrate the effects of serially correlated residuals, explain the application of the CO method, and evaluate the gains to be achieved in its use. We apply the method to an example from climate reconstruction, and we show that the effects of serial correlation in residuals are present and show the significantly improved result.