Nested-model F-test

For nested Gaussian linear models differing by $r$ parameters, the statistichas an $F_{r,n-p_1}$ distribution under the reduced model.

For nested normal linear models, the decrease in residual sum of squares obtained by adding coefficients is their extra sum of squares. Dividing by the number of added coefficients and by the full-model residual mean square gives the partial F-test. A sequential analysis of variance attributes this decrease according to the specified order of entry; it need not equal the partial comparison when other terms are retained.