How can I interpret the categorical variables in quantile regression? Suppose I fit a quantile regression model with BMI as a response and gender as a predictor.  Now, How can I interpret the estimated coefficient for gender.
Note that :gender 1=male , 0=female.
 A: The coefficient is the amount by which men are expected to outweigh women for the quantile you have selected in the quantile regression. 
A: First, let's streamline the complexity.  Quantilte regression is no different from linear regression, except that it centers it on the Median instead of the Mean.  In other words, quantile regression is a nifty type of regression that reduces the impact of outliers on the regression coefficients. 
So, how would you interpret the coefficient for male in your regression.  Let's say your regression equation looks like this: 
BMI = 25 + 1(Gender with Male = 1 and Female = 0)
We could rewrite this regression as follows: 
BMI = 25 + 1 if Gender is Male. 
As depicted, just writing the regression equation out perfectly explains the interpretation of the Gender coefficient.  In this case, if Gender is Male the estimated BMI will be greater by one unit than if it is not Male.  
Note that this coefficient does not necessarily have to be positive.  This will very much depend on your actual sample.  
Dr. Halls, a source on the Internet posted this relevant information: Are men heavier than women? Normally, Yes. What about their Body Mass Index (BMI)?
Usually, BMI values of girls are slightly higher than boys (from age 7 to 16). As long as men and women are not overweight, BMI values of men are also slightly higher than for women( after age 18).
