Comparison of Some Estimation Methods in Linear Regression

In this study, we are informed about some methods as alternatives to the classical least squares methods which are used for simple linear and multiple linear regression analysis. In short, linear regression model is shown via matrix as;Y=Xβ+ε where Y is the vector belonging to dependent variable, X is the design matrix of independent variables, β is the parameter vector, εis the vector belonging to error terms, so the least squares estimator of the linear regression is shown by hat{β}=(X^{´-1}X´Y) Alternative methods have emerged on the purpose of outliers existing in observations unlike the least squares estimation, data s not providing the regression assumptions or using of the previous information about parameters as well. In the study, we are informed about the least absolute deviations regression apart from the least squares method, artificial neural networks, M-regression, the nonparametric regression and Bayesian regression. On the purpose of comparison of the methods results, numerical results are derived by using the temperature variation data in Antalya and Fethiye regions for simple regression analysis and variables affecting the fuel percentage in crude oil for multiple regression analysis.