Adjusted R-squared

Updated: Aug 20, 2021

A version of the ’coefficient of determination (R-squared) adjusted for the degrees of freedom. While R-squared will never decrease when adding a variable to regression, adjusted R-squared will rise or fall, depending on whether the contribution of the new variable to the fit of the regression more than offsets the correction for the loss of an additional degree of freedom. More specifically, it will rise if and only if the test statistic in the t-test for the individual significance of the added variable (or the test statistic in the F-test for the joint significance of the added group of variables) is greater than one. Adjusted R-squared can be negative if the model fit is extremely poor.

Reference: Oxford Press Dictonary of Economics, 5th edt.

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