Mallows' $C_p$ is a metric used to estimate the bias introduced into predicted responses when using an underspecified regression model. It is defined as:

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

where $RSS$ is the Residual Sum of Squares, $d$ is the number of predictors in the model, $n$ is the number of observations, and $\hat{\sigma}^2$ is an estimate of the variance of the error associated with each response measurement (typically estimated using the full model containing all predictors). A smaller $C_p$ value indicates a better model with less bias.