In ordinary regression you are concerned with E[y|x] that is how the mean of the response variable relates to the explanatory variable(s). This is sensible in many applications, but sometimes one may be interested in how someother part of the distribution of y relates to x. Say for instance that y is a maths' test result for students and x is say the weekly number of hours with maths tutoring. Maybe the rationale for the tutoring is to raise primarily the weakest students math ability. In that case it is less interesting to know how the mean result relates to x. One would rather want to know, say, how the weakest 10% perform as a function of x. So one would model q10[y|x] i.e. the 10th percentile of the distribution of y as a function of x. Thus the need for quantile regression.

I can strongly recommend paper by Zietz, Zietz & Sirmans (2007). Step by step, they explain how to employ quantile regression (see pages 320-322) and (what is more important) interpret results of the method. Please, notice the table 12 (page 331), in which the authors explain relationship between independent variables and dependent one, as shown by the quantile regression. Moreover, the authors clearly compare the results of OLS and quantile regression.

Article Determinants of House Prices: A Quantile Regression Approach

Assalamu 'aleykum, Bro Buerhan,

Steps for running quantile regression using R:

1. To install the package (for the first time), run code: install.packages(“quantreg”)

2. To turn on the package, run code: library(quantreg)

3. Import data and run: attach(YOURDATA)

4. Define independent variables: X=cbind(variable1, variable2, variable3)

5. To run quantile regression and read summary, for example for 0.25, run:

rq25=rq(variableY ~ X, data=YOURDATA, tau=0.25)

summary(rq25)

6. To run 0.25 and 0.75 and read summary, you can run as following:

rq2575=rq(variableY ~ X, data=YOURDATA, tau=c(0.25, 0.75))

summary(rq2575)

7. To plot the quantile regression:

rq0595=rq(variableY ~ X, data=YOURDATA, seq(0.05, 0.95, by =0.05))

rq0595sum=summary(rq0595)

plot(rq0595sum)

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As for Stata, there is a package called 'grqreg'.

To install it you can run:

ssc install grqreg

Here is the manual with codes and examples: http://www.stata.com/manuals13/rqreg.pdf

Best regards,

Ibn_Abdullah

Waalaikum Assalam Brother Adam, 

Thanks for your kind explanation and help.  When I run this code under R programming the system saying that I do not have such package, if I do not have for the first time, where I can get this package ? 

Thanks and wassalam. 

To install the package (for the first time), run code in R and it will install:

install.packages(“quantreg”)

Quantile regression is a type of regression analysis used in statistics and econometrics. It estimates the conditional median (or other quantiles) of the response variable across values of the predictor variables. Here are some steps to run this technique using R 1: