Mallows' Cp

A statistic used as an aid in choosing between competing multiple regression models. Mallows' Cp compares the precision and bias of the full model to models with the best subsets of predictors. It helps you strike an important balance with the number of predictors in the model. A model with too many predictors can be relatively imprecise while one with too few can produce biased estimates. A Mallows' Cp value that is close to the number of predictors plus the constant indicates that the model is relatively precise and unbiased in estimating the true regression coefficients and predicting future responses.

For example, you work for a potato chip company that is looking at the factors which affect the number of crumbled potato chips per container (the response variable). Predictors include the percentage of potato, cooling rate, and cooking temperature.

Here are simplified results from Best Subsets Regression analysis:

The above table suggests that the model with the two terms "%Potato" and "Cooling rate" is relatively precise and unbiased because its Mallows' Cp (2.9) is closest to the number of predictors plus the constant (3). You should examine Mallows' Cp in conjunction with other statistics included in the Best Subsets output such as R2, Adjusted R2, and S.