The purpose of a regression or curve-fitting net is, given the input signal variations, to model the corresponding target variations.
The average biased (e.g., divide by N) target variance is
MSE00 = mean(var(t'),1)
When adjusted (e.g., dividing by N-1) for the bias of using the estimate of the mean from the same data, the unbiased target variance is
MSE00a = mean(var(t'),0)
It is not difficult to show that MSE00 is the minimum mean-square-error resulting from a naïve constant output model. Of course, the minimum occurs when the constant is just the mean of the target. Consequently, the result is the variance.
When trying to model target variations, the constant output model is probably the most useful reference. This results in the scale-free entitities
NMSE = mse(t-y)/MSE00
R2 = 1- NMSE
Rsquare is interpreted as the fraction of target variance that is modelled by the net.
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