A Note on Covariance in Propagation of Uncertainty

It is pointed out that whenever both the slope and the intercept are used in calculating a physical quantity from a linear regression, propagation of error must include the covariance as well as the variances. The point is illustrated with a calculation of the boiling point of water from the parameters of the lnP vs 1/T fit. If the covariance is omitted from the propagation of error, the estimate of uncertainty is unreasonably large.