title: Biases in summary statistics of slopes and intercepts in linear regression with errors in both variables.
abstract: Monte Carlo simulations are employed to investigate the bias in linear regression parameters for cases in which both variables are subject to normally distributed errors. Both homoscedastic and heteroscedastic errors are treated. The results show that, in general, the arithmetic mean, geometric mean, and angle mean (tangent of the mean of the arctangents) of the slopes are biased and non-normally distributed. The arithmetic and geometric means of the intercepts are generally biased and non-normally distributed as well. However, for all the cases considered, the medians of the slopes and of the intercepts are found to be unbiased. In view of the non-normal distributions of the slopes and intercepts, a nonparametric method is used to determine confidence intervals for the slopes and intercepts.
authors.affiliation: Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada.
authors.forename: A H
authors.initials: AH
authors.lastname: Kalantar
authors.forename: R I
authors.initials: RI
authors.lastname: Gelb
authors.forename: J S
authors.initials: JS
authors.lastname: Alper