median regression vs linear regression

Hello,

I have a continous independent variable Y, and would like to estimate
the difference in means between group A and B on the scores of this
variable. I use multiple linear regression:

Y (scores between 0-100) = X0+X1+X2+X3

X0=constant
X1=Group (A is coded as 0, B as 1)
X2= age (factor)
X3=sex

However, the distribution of the variable Y is highly skewed to the
left. Wouldn't it be better to use median regression in this instance,
and calculate what the difference in means would be at the median? Or
at several percentiles, like the 25th, 50th, and 75th? In my opinion,
this gives a better picture of reality. Thanks.

Raoul

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