When one runs an OLS regression, one often prefers to look at $R^2$ rather than the mean squared error, though both measure goodness of fit. $R^2$ is dimensionless and has some advantageous properties: for example, it's related to other important quantities such as correlation, and it behaves nicely if you scale or translate your data.
When I run an LAD regression, I can look at the sum of absolute errors or the mean absolute error or something. But is there a different statistic, something like $R^2$, that people tend to look at instead?
