Building statistically significant robust regression models in empirical software engineering

Outliers have been a constant source of problems in the analysis of Empirical Software Engineering data. In some cases, outliers are due to corrupted data, while they may be the result of highly unlikely circumstances in others. In either case, outliers may unduly greatly bias data analysis, as is the case with Ordinary Least Squares (OLS) regression. Robust data analysis techniques have been proposed to address this problem. In this paper, we describe an existing robust linear regression technique based on the Least Median of Squares (LMS) and provide a statistical significance test for the associations obtained with it. We also apply LMS and OLS regression to real-life, publicly available Empirical Software Engineering data sets, to compare the results obtained and investigate commonalities and differences between LMS and OLS from a practical point of view.