Prediction intervals in linear regression taking into account errors on both axes

This study reports the expressions for the variances in the prediction of the response and predictor variables calculated with the bivariate least squares (BLS) regression technique. This technique takes into account the errors on both axes. Our results are compared with those of a simulation process based on six different real data sets. The mean error in the results from the new expressions is between 4% and 5%. With weighted least squares, ordinary least squares, the constant variance ratio approach and orthogonal regression, on the other hand, mean errors can be as high as 85%, 277%, 637% and 1697% respectively. An important property of the prediction intervals calculated with BLS is that the results are not affected when the axes are switched. Copyright (C) 2001 John Wiley Sons, Ltd.