Quantile regression: A short story on how and why

Quantile regression quantifies the association of explanatory variables with a conditional quantile of a dependent variable without assuming any specific conditional distribution. It hence models the quantiles, instead of the mean as done in standard regression. In cases where either the requirements for mean regression, such as homoscedasticity, are violated or interest lies in the outer regions of the conditional distribution, quantile regression can explain dependencies more accurately than classical methods. However, many quantile regression papers are rather theoretical so the method has still not become a standard tool in applications. In this article, we explain quantile regression from an applied perspective. In particular, we illustrate the concept, advantages and disadvantages of quantile regression using two datasets as examples.