A Comparative Study of Some Estimation Methods in Simple Linear Regression Model for Different Sample Sizes in Presence of Outliers

Abstract

The aim of this study was to compare some estimation methods (LS, M, S, LTS and MM) for estimating the parameters of simple linear regression model in the presence of outlier and different sample size (10, 20, 30, 50 and 100). To compare methods, the effect of chest girth on body weights of Karayaka lambs at weaning period was examined. Chest girth of lambs was used as independent variable and body weight at weaning period was used as dependent variable in the study. Also, it was taken consideration that there were 10-20% outliers of data set for different sample sizes. Mean square error (MSE) and coefficient of determination (R2) values were used as criteria to evaluate the estimator performance. Research findings showed that LTS estimator is the best models with minimum MSE and maximum R2 values for different size of sample in the presence of outliers. Thereby, LTS method can be proposed, to predict best-fitted model for relationship between chest girth and body weights of Karayaka lambs at weaning period, to the researches who are studying on small ruminants as an alternative way to estimate the regression parameters in the presence of outliers for different sample size.