I have two sets of data, $x$ and $y$, with poissonian distributions. I want to check if the relation between $x$ and $y$ is a proportionality $y = ax + b$, so I used some algorithms to do Bivariate Correlated Errors and intrinsic Scatter (BCES). It is the first time I use it.
These algorithms return the parameters values, their errors, and a $2\times2$ covariance matrix.
I am trying to read tons of numbers and definitions, often ambiguous and/or conflicting, and anyway not easy-to-understand.
My goal is to understand how good is the fit, that is if the line fits the data points. Something like the $\chi^2$ goodness-of-fit. Why the algorithms return the covariance matrix (instead of a goodness-of-fit value)? Is it possible to infer one from the other?