 Thus, if we aim to select the model giving the smallest residual sum of squares, the model including all variables would always be selected.Instead, the "Cp" statistic calculated on a sample of data estimates the mean squared prediction error (MSPE) as its population target

where formula_2 is the fitted value from the regression model for the "j"th case, "E"("Y""j" | "X""j") is the expected value for the "j"th case, and σ2 is the error variance (assumed constant across the cases).The MSPE will not automatically get smaller as more variables are added.