What are the implications of using R-Squared vs. Adjusted R-Squared in a multiple regression model with many predictors?

  • R-Squared favors complex models; Adjusted R-Squared is more sensitive to noise
  • R-Squared favors more predictors without penalty; Adjusted R-Squared penalizes unnecessary predictors
  • R-Squared is better for small datasets; Adjusted R-Squared is only applicable to linear models
  • R-Squared provides better interpretability; Adjusted R-Squared favors simple models
In multiple regression models with many predictors, using R-Squared may favor the inclusion of more predictors without penalizing for their irrelevance, leading to potentially overfitted models. In contrast, Adjusted R-Squared includes a penalty term for unnecessary predictors, providing a more balanced assessment of the model's performance. It helps in avoiding the trap of increasing complexity without meaningful gains in explanatory power.
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