Here I compare the quantile regression and the least square regression.

I show the general trend least square regression as compared with the 50 % quantile ("the most likely value"). 

I also compare the 0.5 % quantile as a method to identify the support line.

The equivalent using least square is using a 60 % deviation from the trend. 

I have done graphs before where I used several regression methods. They all show a power law behavior.

That is the fundamental message. The slope and y intercept can differ a bit mostly because there is not a perfect method to deal with the bubbles. 

Different methods give slightly different angles that also need proper interpretation. 

That is the major issue but in general the the power law behavior is revealed no matter what.