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The Scientific World Journal
Volume 2014, Article ID 821623, 12 pages
Research Article

Outlier Detection Method in Linear Regression Based on Sum of Arithmetic Progression

1Group Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, Germany
2Institut für Landtechnik und Tierhaltung, Vöttinger Straße 36, 85354 Freising, Germany
3Computer Unit, Faculty of Agriculture, University of Ruhuna, Mapalana, 81100 Kamburupitiya, Sri Lanka

Received 25 March 2014; Revised 23 May 2014; Accepted 26 May 2014; Published 10 July 2014

Academic Editor: Zengyou He

Copyright © 2014 K. K. L. B. Adikaram et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with elements, the ratio ( ) of the sum of the minimum and the maximum elements and the sum of all elements is always . always implies the existence of outliers. Usually, implies that the minimum is an outlier, and implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of to from the correct value.