relationship between RMSE and R^2
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First of all this is more like a theoretical question than a methodological one. I made a script to fit some time series data. I fitted many data series and calculated their goodness of fit statistics. When I analyzed the resulting data I found an inverse relationship between RMSE and R^2.
I´ve look around the web and my statistics books looking for a possible explanation but with no luck.
Is there anyone here who can give me some ideas ?
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Answers (2)
Tom Lane
on 24 Apr 2012
R^2 = 1 - SSE/SST = 1 - DFE*RMSE^2/SST
Here SSE is the error sum of squares, SST is the total sum of squares, and DFE is the degrees of freedom for error. So you would expect R^2 to go down as RMSE goes up. Is that what you meant by an inverse relationship?
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Samuel Fonseca
on 24 Apr 2012
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Tom Lane
on 25 Apr 2012
R^2 is sensitive to the x range. That's what some people dislike about it. RMSE should not be sensitive if the model is correct. However, usually a bigger range leads to large R^2 and no change in RMSE. You seem to be saying R^2 is smaller and RMSE is smaller. That is unexpected.
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