PROC QUANTREG question about estimated values, intercept and actual quantile

[plf515]

Hi and HNY

I am using SAS 9.4 TS 1M5 on Windows.

If I run

title;
proc quantreg ci=sparsity/iid algorithm=interior(tolerance=5.e-4)  data=sashelp.bweight order=internal plots = none;
   model Weight = MomWtGain/quantile = (0.25, .5, .75);
run;

then I get some slightly puzzling results.

For each quantile (25, 50, 75) we have

a. The actual quantiles which are 3062.0   3402.0  and 3720.0

b,  The predicted values at mean, which are 3068.02, 3394.93 and 3719.04

c. The intercepts which are  3062.0, 3389.46 and 3714.0

Sometimes they are exactly the same, sometimes slightly different. 

Why is that?

[PGStats]

I think the confusion comes from the fact that MomWtGain is roughly centered around zero (it has median=0). Thus the intercept roughly coincides with the mean of MonWtGain.