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As $R^2$ increases, $R^2_{adj}$ increases too.

Is that statement true?

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  • $\begingroup$ Is that probably a self-study question? Consider tagging it as such. Regarding the question, open up any econometrics textbook, and you will find the answer. $\endgroup$ Feb 28, 2020 at 10:35

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Note that $R_{\text{adj}}^2 = 1-(1-R^2){n-1 \over n-p-1}$

So, if you fix $n$ and $p$, but move your data points about to increase $R^2$, then yes, adjusted $R^2$ must increase.

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