A Comparative Study of Least Squares Method and Least Absolute Deviation Method for Parameters Estimation in Length-Weight Relationship for White Grouper (Ephinephelus aeneus)

Abstract

In fisheries science, by means of linear regression models, length-weight relationships are often estimated to determine weight and biomass when only length measurements are taken from fish. Least Squares method (LS) is commonly used to determinate the relationship between weight and length for fish, when the error term, e<inf>i</inf>, is assumed to be normally distributed. If it can be observed to degenerate the structure of data in the y-direction, LS method is not completely perform to estimate the regression parameters. And than LS method explains minimum levels to the total variation of the model. In this situation, one of the linear regression methods often recommended as robust or outlier-resistant alternatives to LS is Least Absolute Deviation (LAD). The aim of this study is to investigate for comparing the least squares method and the LAD method by means of drawing conclusions and to determine the model which is optimal for displaying the relationship between length and weight for Ephinephelus aeneus in the presence of outliers. Mean square error and R 2 are used to evaluate estimator performance. © 2006 Asian Network for Scientific Information.