Statistical Methods for Finding Outliers in Multivariate Data Using a Boxplot and Multiple Linear Regression

The objective of this study was to propose a method for detecting outliers in multivariate data. It is based on a boxplot and multiple linear regression. In our proposed method, the box plot was initially applied to filter the data across all variables to split the data set into two sets: normal data (belonging to the upper and lower fences of the boxplot) and data that could be outliers. The normal data was then used to construct a multiple linear regression model and find the maximum error of the residual to denote the cut-off point. For the performance evaluation of the proposed method, a simulation study for multivariate normal data with and without contaminated data was conducted at various levels. The previous methods were compared with the performance of the proposed methods, namely, the Mahalanobis distance and Mahalanobis distance with the robust estimators using the minimum volume ellipsoid method, the minimum covariance determinant method, and the minimum vector variance method. The results showed that the proposed method had the best performance over other methods that were compared for all the contaminated levels. It was also found that when the proposed method was used with real data, it was able to find outlier values that were in line with the real data.