It’s just a measure of how close the data is to the line—like the “inside view” uncertainty that the model has about the data. In fact, that’s more precisely what it is if this is the chi squared statistic (or square root thereof) that you minimized to fit the model. And it’s in nice convenient units that you can compare to other things.
It’s not quite right, because it uses an implicit prior about noise and models that doesn’t match your actual state of information. But it’s something that someone who’s currently reporting R^2 to us can do in 30 seconds in Excel.
I’d be curious why you think this is a good metric.
BTW, when you say “the difference between the data and the model”, I assume you’re referring to the residuals?
It’s just a measure of how close the data is to the line—like the “inside view” uncertainty that the model has about the data. In fact, that’s more precisely what it is if this is the chi squared statistic (or square root thereof) that you minimized to fit the model. And it’s in nice convenient units that you can compare to other things.
It’s not quite right, because it uses an implicit prior about noise and models that doesn’t match your actual state of information. But it’s something that someone who’s currently reporting R^2 to us can do in 30 seconds in Excel.