By definition, R^2 is the fraction of the total squared error that can be explained by the model (baseline, linear regression, and random error). Simply speaking, R^2 is a measure of "goodness of fit", and the values of R^2 approaching one would be desirable: A higher R^2 indicates a better fit.

However, R^2 is a relative measure in the sense that there is no consensus for what would be high enough. Moreover, the caveat is that, for some models, as you add more explanatory variables (e.g., the higher order of polynomial for baseline, or more regressors, etc.), R^2 would always increase. This would make the model appear as if the model is getting better even if the explanatory variables are just some nonsense addition. Plus, estimating the coefficients of more insignificant variables would cost more degree of freedom, which leads to other estimates less reliable.

Based on the above consideration, although R^2 does provide some sense of the coefficient of determination (the success of the regression equation in explaining the variation in the data), it can be deceptive and has to be used in precaution. I would suggestion that F or t statistic is used for thesholding while keeping some percent signal change or constrast as your intensity.

Gang

Edward J. Butterworth wrote:

> When 3dDeconvolve is used, the result is presented with the
> R^2 correlation coefficient as the intensity, with the F-test
> used to threshold the data. Some people in my lab have
> suggested that it should be the other way around, with the
> F-value as intensity and using the R^2 coefficient as
> threshold. Not being a statistician, I'm not sure how to
> answer them. Any comments?