An Application on Quantile Regression Analysis

Abstract

In general, when a research is desired to be conducted, the relationship between variables may be examined or prediction may be made with the help of a model. When it is desired to make predictions with the help of this model, the commonly used method is the standard regression analysis method. However, some assumptions must be fulfilled in order to use this regression analysis. Alternative methods are preferred when these assumptions are not fulfilled or when these assumptions are not met although transformations are made in some studies. One of these alternative methods is the quantile regression method. Quantile regression is very useful for heterogeneous data sets. It is a flexible method since it does not have any assumptions. In the study, 300 units of the Wine Quality data set and STATA 14 package program were used. Firstly, by taking 1 dependent (quality) and 5 independent variables from the wine quality data set, quantile regression analyses were performed according to 0,20, 0,25, 0,50 and 0,75 quantile values as well as standard linear regression at sample sizes of 100, 200 and 300. Then, the same procedures were repeated for 1 dependent (quality) and 11 independent variables. The results of linear and quantile regression analyses based on partial regression coefficient, standard error and confidence intervals were compared according to sample size and number of variables. As a result, it was observed that increasing the number of variables included in the model did not have much effect on the coefficients. In addition, it was determined that the effect of quantile values on the results is more important than the number of variables. Therefore, it is important to choose the appropriate quantile value to obtain low coefficient and narrow confidence interval.