Evaluation of outlier detection procedures in multiple linear regressions

Abstract

Regression analysis is conceptually the simplest method used for investigating the func
tional relationship between dependent and independents variables. In this paper, the 
problems of over and under detection of outliers in datasets are put to test by applying 
the various methods to the dataset without outlier injection at various sample sizes.
This study reviews methods of outlier detection in multiple linear regressions using DFFITS, 
Cook’s distance, DFBETAS, R-students, and Mahalanobis distance. It was seen from the 
result analyzed that the methods of outlier detection had different performances when 
detecting outliers in a dataset at various sample sizes. Data simulation was carried out 
without injection of outliers to independent and dependent variables.
The R-code simulation shows the performance of five outlier detection methods in mul
tiple linear regressions. From the five techniques compared, DFBETAS performed better 
than all the other methods for all the sample sizes except at sample size 10. The next best 
method was Cook’s distance, specifically for the higher sample sizes of 30, 50, and 100. 
Mahalanobis and DEFFITS were more liberal among the all other outlier procedures.