Coefficient of Determination

#1
Hi there,

I'm using non-linear regression (specially I'm using neural networks for time series prediction) and I'm a bit unsure about the calculation and interpretation of R^2. Reading the forum I gather that R^2 has a different interpretation for non-linear regression and reading Wikipedia I see that there are several ways to calculate R^2. I suspect that I can use the formula (take from Wikipedia): R^2 = 1 - SSerr/SStot where SSerr is the sum of squares of residuals and SStot is sum of all (observed values - sample mean)^2.

I'd really like to know if using the above formula is correct and how I can expect to interpret the R^2 value. I've read a few publications and mostly authors are quoting the mean absolute error and residual sum of squares... but quoting R^2 is important right (I hope at least that it's applicable and I haven't gone completely off target)?

Thank you for reading my post :)
 
#3
No, I was thinking R^2 is an important measure of the regressions performance? I'm predicting wind speed and it seems to exhibit cyclic behaviour (which I assumed makes it non-linear?)... also using a neural network seems to have worked for other researchers and so far seems to have the highest accuracy in my tests.

I'm not sure how one could use R^2 to determine if there is no linear relationship? At least in the definition I proposed, R^2 is calculated using the sum of squares of residuals which means it's calculated after some regression technique is used. So I guess if I tried a linear technique and R^2 was close to zero then there's some evidence that the relationship is non-linear (assuming the regression technique was modeled correctly).