Monte Carlo simulation has been used to test the robustness of three methods of regression in the comparison of analytical accuracy. The methods used were simple linear regression, weighted linear regression and a new method based on maximum likelihood estimation. The new method is capable of unbiased estimation with different heteroscedastic variance of both the y-values and the x-values, and is the most generally useful. However, even simple linear regression can estimate linear biases accurately as long as elementary safeguards are applied. The simulations realistically covered a wide range of circumstances likely to be encountered in analytical practice.