Table 1.

A comparison of goodness-of-fit statistics for the characterization or comparison of nonlinear regression models. Care should be taken to choose the appropriate statistic(s) for the intended use case.

Statistic	Formulation	What is described	Unit independent	Range of possible values	Direction of better fits	Appropriate use cases
R2	$1.0-\frac{{\mathit{\text{SS}}}_{\mathit{\text{residual}}}}{{\mathit{\text{SS}}}_{\mathit{\text{total}}}}$	The SSresidual expressed as a proportion of SStotal.	Yes	−∞ ↔ 1.0	Closer to 1.0	Describing how much of the variability in a dataset is accounted for by a model
RMSE	$\sqrt{\frac{{\mathit{\text{SS}}}_{\mathit{\text{residual}}}}{n-1}}$	The square root of the mean SSresidual	No	0 ↔ ∞	Closer to 0.0	Describing the fit of the model in the units of the dependent variable without considering total data variability
AIC	$n\times \text{ln}\left(\frac{{\mathit{\text{SS}}}_{\mathit{\text{residual}}}}{n}\right)+2k$	The mean SSresidual with an additional penalty for the complexity of the model	No	−∞ ↔ ∞	Lower values	Determine which of a set of models is the most parsimonious after accounting for model complexity

Note: SS = sum of squares; n = number of data points; k = number of fitted parameters in the regression model.