,[1][2] named for Colin Lingwood Mallows, is used to assess the fit of a regression model that has been estimated using ordinary least squares.
Mallows's Cp has been shown to be equivalent to Akaike information criterion in the special case of Gaussian linear regression.
Instead, the Cp statistic calculated on a sample of data estimates the sum squared prediction error (SSPE) as its population target where
The mean squared prediction error (MSPE) will not automatically get smaller as more variables are added.
Mallows proposed the statistic as a criterion for selecting among many alternative subset regressions.