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I recently implemented and uploaded a Mathematica package for computing regression quantiles using Mathematica’s function LinearProgramming - see the package QuantileRegression.m provided by the MathematicaForPrediction project at GitHub. Roger Koenker, Gilbert Bassett Jr., “Regression Quantiles”, Econometrica, Vol. (See this Wikipedia entry.)įor a complete, interesting, and colorful introduction and justification to quantile regression I refer to this article: To compute quantiles other than the median the so called “tilted” function is used. Further, QRP is re-formulated as a linear programming problem, which allows for efficient computation. The Quantile Regression Problem (QRP) is formulated as a minimization of the sum of absolute differences.

With quantile regression we obtain curves - “regression quantiles” - that together with the least squares regression curve would give a more complete picture of the distribution values (the Y’s) corresponding to a set of X’s. Similarly, quantile regression corresponds to finding quantiles of a single distribution. We can say that least squares linear regression corresponds to finding the mean of a single distribution.