'Prove that Mallowss Cp statistic, Cpj RSSj S2 E 2sj # n can also be...

'Prove that Mallows’s Cp statistic, Cpj ¼ RSSj S2 E

þ 2sj # n can also be written Cpj ¼ ðk þ 1 # sjÞðFj # 1Þ þ sj where RSSj is the residual sum of squares for model Mj; sj is the number of parameters (including the constant) in model Mj; n is the number of observations; S2 E is the usual estimate of error variance for the full model, which has k coefficients (excluding the constant); and Fj is the incremental F-statistic for testing the null hypothesis that the k þ 1 # sj coefficients missing from model Mj are 0.