Should we report R-squared or adjusted R-squared in non-linear regression? I am running a non-linear regression for a dose response with the equation:  
$$Y  = \frac{c}{1 + \big(\frac x g\big)^b}$$
When reporting my results for publication, do I report the R-squared or Adjusted R-squared, and why?
 A: You are fitting multiple parameters in your model.  (Usually, you fit one parameter for every variable, but your model is non-linear so that isn't the case, even though you have only one $X$ variable.)  With every additional parameter, your model has the opportunity to fit the data better, even if that parameter shouldn't be fitted (e.g., if $b$, or $g$ are actually $1$).  The adjusted $R^2$ statistic attempts to correct for that added flexibility.  
$R^2$ doesn't really mean too much on its own.  A low value may be appropriate (that's the amount of information that can legitimately be explained) or it may indicate a problem with lack of fit.  A high value may indicate a particularly informative model, or one that is badly overfit.  What constitutes a "low" or "high" $R^2$ will vary by subject matter.  Etc.  Thus, they are most useful in comparison.  I gather you will fit the same model to multiple $Y$ variables, but if the $X$ variable and the model's functional form are the same each time, it won't make any difference whether you used $R^2$ or $R^2_{\rm adj}$ as long as you used the same one each time.  As far as which should be reported in a paper, $R^2_{\rm adj}$ is probably ideal, but due to its comparative nature, whichever is more common in your field would be appropriate.  
A: You should use neither of those. This is because neither $R^2$ nor adjusted $R^2$ (for handling multiple explanatory variables) are well defined for non-linear regression. If the purpose is for reporting the accuracy of the models, I would suggest to use cross validation errors, MSE, on a hold out test set instead.
