The researchers compared different methods for estimating weights in linear regression when the data has outliers, errors, and contaminations. They found that when the classical assumptions are met, Ordinary Least Squares Estimator is the best method. However, when these assumptions are violated, robust methods like Huber Maximum Likelihood Estimator, Least Trimmed Squares Estimator, S Estimator, and Modified Maximum Likelihood Estimator provide more reliable estimates.