Outlier Detection in Linear Regression

Outlier Detection in Linear Regression

A. A. M. Nurunnabi (University of Rajshahi, Bangladesh), A. H. M. Rahmatullah Imon (Ball State University, USA), A. B. M. Shawkat Ali (Central Queensland University, Australia) and Mohammed Nasser (University of Rajshahi, Bangladesh)
DOI: 10.4018/978-1-60960-551-3.ch020
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Regression analysis is one of the most important branches of multivariate statistical techniques. It is widely used in almost every field of research and application in multifactor data, which helps to investigate and to fit an unknown model for quantifying relations among observed variables. Nowadays, it has drawn a large attention to perform the tasks with neural networks, support vector machines, evolutionary algorithms, et cetera. Till today, least squares (LS) is the most popular parameter estimation technique to the practitioners, mainly because of its computational simplicity and underlying optimal properties. It is well-known by now that the method of least squares is a non-resistant fitting process; even a single outlier can spoil the whole estimation procedure. Data contamination by outlier is a practical problem which certainly cannot be avoided. It is very important to be able to detect these outliers. The authors are concerned about the effect outliers have on parameter estimates and on inferences about models and their suitability. In this chapter the authors have made a short discussion of the most well known and efficient outlier detection techniques with numerical demonstrations in linear regression. The chapter will help the people who are interested in exploring and investigating an effective mathematical model. The goal is to make the monograph self-contained maintaining its general accessibility.
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Regression Analysis And Least Squares Estimation

Regression analysis is a statistical technique, which helps us to investigate and to fit an unknown model, quantifies relations among observed variables in multifactor data. More specifically, regression analysis helps us understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables. Chatterjee and Hadi (2006) point out; it is appealing because it provides a conceptually simple method for investigating functional relationship among variables.

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