$\frac{RSS+2d \hat{\sigma}}{n \hat{\sigma ^2}}$

The Akaike Information Criterion (AIC) metric describes the quality of the model with the data that is given. AIC is applicable in a broad range of modeling frameworks as it only requires large sample properties of the maximum likelihood estimator. It uses candidate models to manipulate the data but does not require the assumption that these models be true or correct. AIC is the trade-off between goodness of fit and complexity of the variables that are considered in the problem. R-Squared changes relative to the complexity of the system (variables) but AIC does not.

Note: AIC cannot be used to compare models with different datasets. For example, if one model involves transformations on the response variable (like log transformations) and another one does not, one cannot use AIC to compare the two models.