Regression Analysis Uses Quantile Method.

Abstract

Regression analysis is applied to analyze relation between response variable with one or more predictor variable, especially to construct a model that has not been known. In order to estimate the regression parameters, certain estimation method of regression coefficients are carried out. In this paper quantile regression method is applied to asymmetric data. This method divides data into two or more groups, where existence of different estimated values at different quantiles are suspected. In this regression analysis, the regression coefficients are estimated using quantiles regression approximation properties, i.e. weighted least square approximation with all predictor variables included and the suites approximation with partial regression decomposition for certain predictor variables. Quantile regression approximation property explains that the quantile regression coefficient vector can minimize the expected value of weighted mean square error, which will give the best fit. The quantile regression with suites approximation is used to omit predictor variables which do not have influence to the model. The approximation properties of quantile regression are illustrated with the salary data from the U.S. census at 1980, 1990, and 2000. Key word: quantiles regression, asymmetric data, weighted least square, partial regression.