Multiple regression RZ-SSRSST=1-SSE/SST ° Adjusted R2(R2) R2=1 SSE/n-p n-1 =1-(1-R2) SST/(n-1) n-p-1 where n is the number of observations and p is the number of independent variables The Adjusted r2 compensates for the number of independent variables in the model. It may rise or fall It will fall if the increase in r2 due to the inclusion of additional variables is not enough to offset the reduction in the degrees of freedom Slide 7Slide 7 Multiple Regression • R2=SSR/SST=1-SSE/SST • Adjusted R2 ( ) where n is the number of observations and p is the number of independent variables • The Adjusted R2 compensates for the number of independent variables in the model. It may rise or fall. • It will fall if the increase in R2 due to the inclusion of additional variables is not enough to offset the reduction in the degrees of freedom. 2 Ra 2 2 /( 1) 1 1 1 (1 ) /( 1) 1 a SSE n p n R R SST n n p − − − = − = − − − − −