When both coordinates of the data have errors, LinearFit by default uses an "effective variance" technique. When ReturnEffectiveVariance is set to True, the final values of the effective variances are returned by LinearFit in a separate window.
Information on the effective variance may be found here.
This help document is Copyright © 1999 David M. Harrison. This is version 1.1 of the help document, date (m/d/y) 11/25/99.