 Mallows proposed the statistic as a criterion for selecting among many alternative subset regressions.Under a model not suffering from appreciable lack of fit (bias), "Cp" has expectation nearly equal to "P"; otherwise the expectation is roughly "P" plus a positive bias term.Nevertheless, even though it has expectation greater than or equal to "P", there is nothing to prevent "Cp" < "P" or even "Cp" < 0 in extreme cases.