Prove that Mallows’s Cp statistic can also be written where RSS j is the residual sum of squares for model M j ; s j is the number of parameters (including the constant) in model Mj; n is the number...

Prove that Mallows’s Cp statistic

can also be written

where RSS_j
is the residual sum of squares for model M_j; s_j
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 F_j
is the incremental F-statistic for testing the null hypothesis that the k + 1 - s_j
coefficients missing from model M_j
are 0.