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

The Akaike Information Criterion (AIC) is a metric that describes the relative quality of a statistical model for a given set of data. It is widely applicable because it only requires large-sample properties of the maximum likelihood estimator, and does not require the candidate models to be true or correct.

AIC estimates the test error by adjusting the training error to account for model complexity:

• $RSS$ is the Residual Sum of Squares.
• $d$ is the number of predictors.
• $n$ is the number of observations.
• $\hat{\sigma}^2$ is an estimate of the error variance.

While R-squared always increases as more variables are added, AIC balances goodness of fit and complexity by penalizing additional parameters to prevent overfitting.

Note: AIC cannot compare models fit on different datasets. For example, it cannot compare a model with a log-transformed response variable to one without a log transformation.