Mathematically, what are the drawbacks of R-squared in evaluation a regression model?

Asked Feb 21 '19 at 00:09

Active Feb 21 '19 at 00:09

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I kept seeing articles about the drawbacks of R-squared (and that's why we need to have adjusted R-squared).

One drawback is that: "Every time you add a predictor to a model, the R-squared increases, even if due to chance alone. It never decreases. Consequently, a model with more terms may appear to have a better fit simply because it has more terms." (link).

Mathematically, why does this happen? And mathematically, why adjusted R-squared can solve this problem?

asked Feb 21 '19 at 00:09

RockTheStar

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Check this and this. – Lucas Farias Feb 21 '19 at 00:52
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For further analysis on the problems with R-Squared – Kunio Feb 21 '19 at 01:33
Perfect @LucasFarias Will them out. – RockTheStar Feb 21 '19 at 17:55
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Also relevant: https://stats.stackexchange.com/questions/414349/is-my-model-any-good-based-on-the-diagnostic-metric-r2-auc-accuracy-e/414350#414350 – mkt Jun 25 '19 at 08:34

Mathematically, what are the drawbacks of R-squared in evaluation a regression model?

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