Originally Posted by

**kingwinner** "Suppose that in a MULTIPLE linear regression analysis, it is of interest to compare a model with 3 independent variables to a model with the same response varaible and these same 3 independent variables plus 2 additional independent variables.

As more predictors are added to the model, the coefficient of *multiple* determination (R^2) will increase, so the model with 5 predicator variables will have a higher R^2.

**The ***partial* F-test for the coefficients of the 2 additional predictor variables (H_o: β_4=β_5=0) is equivalent to testing that the increase in R^2 is statistically signifcant."

I don't understand the bolded sentence. Why are they equivalent?

Thanks for explaining!

[also under discussion in Talk Stats forum]