4-7 Adiusted R2 In order to get around these problems, a modification is often made which takes into account the loss of degrees of freedom associated with adding extra variables. This is known as r3, or adjusted R2 T-1 R2=1 (1-R) T-k So if we add an extra regressor k increases and unless r2 increases by a more than offsetting amount,R2 will actually fall ·R可用于决定某一变量是否应包括在模型中。 There are still problems with the criterion: 1.A“sof”'rule。如果只按这一标准选择模型,模型中会 包含很多边际显著或不显著的变量。 2. No distribution for r or r2。从而不能进行假设检验, 以比较一个模型的拟合优度是否显著高于另一个模型。4-7 Adjusted R2 • In order to get around these problems, a modification is often made which takes into account the loss of degrees of freedom associated with adding extra variables. This is known as , or adjusted R2: • So if we add an extra regressor, k increases and unless R2 increases by a more than offsetting amount, will actually fall. • 可用于决定某一变量是否应包括在模型中。 • There are still problems with the criterion: 1. A “soft” rule。如果只按这一标准选择模型，模型中会 包含很多边际显著或不显著的变量。 2. No distribution for or R2。从而不能进行假设检验， 以比较一个模型的拟合优度是否显著高于另一个模型。2 R       − − − = − (1 ) 1 1 2 2 R T k T R 2 R 2 R 2 R