where τ A ð0; 1Þ is any quantile. The quantile βτ is the τth regression quantile. When τ
is equal to 0.5, it is median regression.
Using the point values in identifying the significance of vari- ables is also one of the
drawbacks of classical mean regression model. QR approach allows us to examine the behavior of
the response variable beyond the average of the Gaussian distribution. Therefore, QR can be used
to build prediction intervals (Mein- shausen, 2006). Investigating the behavior of the response
variable for different quantiles with respect to the independent variables may result in
different inferences in comparison with examining only the average of response variable (Benoit
and Van den Poel,