The Interpretation of Mallows's C p -Statistic

When selecting variables in multiple-regression studies, the model with the lowest value of Mallows's C p -statistic is often chosen. It is shown here that when the estimate of σ 2 comes from the full model an adjusted C p , V p , has the property that E(C p ) = p. It is suggested that a procedure be adopted which involves testing whether the model with minimum C p is really better than a simpler model. Tables approximating the null distribution of the test statistics are given.