Data Analysis Papers
An Introduction to Quantile Regression and the QUANTREG Procedure
Colin (Lin) Chen, SAS Institute, 2005
Abstract
Ordinary least-squares regression models the relationship between one or more covariates X and the conditional mean of a response variable Y given X = x. In contrast, quantile regression models the relationship between X and the conditional quantiles of Y given X = x, so it is especially useful in applications where extremes are important, such as environmental studies where upper quantiles of pollution levels are critical from a public health perspective. Quantile regression also provides a more complete picture of the conditional distribution of Y given X = x when both lower and upper or all quantiles are of interest, as in the analysis of body mass index where both lower (underweight) and upper (overweight) quantiles are closely watched health standards. This paper describes the new QUANTREG procedure in SAS 9.1, which computes estimates and related quantities for quantile regression by solving a modification of the least-squares criterion.
Statistics and Operations
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