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COMPARING R-SQUARES

For nested regression models, in which one model contains all the variables in another, plus a few, we can test whether adding those additional variables results in a significantly better r-square.

The test statistic is calculated as follows, where R2L is the r-squared from the regression with more variables, and R2S is the r-squared from the regression with fewer variables. The quantity dfL-dfS is simply the difference in the number of variables between the two models

We then look up the F statistic in an F table, with degrees of freedom corresponding to the two denominators in the equation. If the F statistic is larger than the critical value in the table, the difference is significant.