On a log-log plot of surface gravity to planet mass, what is the meaning of the y-intercept? I am playing around with data from exoplanets.org, and am interested in the plot of surface gravity to planet mass. I reproduced this plot  after downloading their data and performed a non-linear regression model to fit the curve. Unfortunately,the covariance matrix of my fit has infinite values, so I am now trying out a linear fit on a log-log plot, shown below.  My fit, for $y=ax+b$, is $a=0.9511$, $b=0.8631$. 

I am now thinking about what I am plotting. I suspect there may not be anything interesting in $\log \frac{GM}{R^2}$ vs. $\log M$, but, regardless, I am trying to understand if there is any meaning in the y-intercept. 

What are possible explanations for the value $b$?
For planets of constant mean density you have:
$$
M=\rho \times 4\pi r^3
$$
and the surface value of $g$ is:
$$
g(r)=\frac{GM}{r^2}=G \times \rho\times 4 \pi \times r
$$
So for bodies of constant density the surface gravity is proportional to the radius, and the slope as $r \to 0$ tells you the density. So for bodies of equal density $\log(g(r)) \to -\infty$ as $r \to 0$

In terms of mass:
$$
g(M)={G(4\pi \rho)^{2/3}M^{1/3}}
$$ 
So as $M\to 0$ we have $g(M)\to 0$ and again $\log(g(M))\to -\infty$ and the intercept of the $\log-\log$ plot as $M$ goes to zero alows you to calculate the mean density.