Why is the adjusted R2 more informative than the R2?

Question

BlackTom AI · Accepted Answer

To evaluate why adjusted R2 is more informative than R2, let's examine what each metric does with new predictors.
Option A: 'Because the adjusted R Squared adjusts for potential outliers.' This is not accurate. Adjusted R2 does not specifically penalize for outliers; it adjusts for the number of predictors to account for overfitting. Outliers are not the central factor here, so this statement misattributes the purpose of adjusted R2.
Option B: 'Because the adjusted R Squared can never go down.' This is misleading about adjusted R2. In fact, adjusted R2 can decrease when adding a useless or irrelevant variable because the penalty for extra parameters may outweigh any slight improvement in fit. Therefore, this claim is incorrect.
Option C: 'Because the R Squared can't go down even when a useless variable is added.' This is a true property of R2: it does not decrease with the addition of new predictors, regardless of usefulness. However, this statement is describing R2, not adjusted R2, and it highlights why adjusted R2 provides more information: R2 can stay the same or increase, masking overfitting, while adjusted R2 can decrease to reflect unnecessary variables.
Option D: 'Because there is a penalty when a new, non-useful variable is added.' This captures the essence of adjusted R2: it introduces a penalty for adding extra predictors that do not improve the model fit, helping to guard against overfitting by potentially lowering the statistic when a useless variable is included.
In sum, A misidentifies the rationale (outliers aren't the central issue), B and C describe properties of R2 rather than adjusted R2, and D accurately describes the key mechanism that makes adjusted R2 more informative than R2 when comparing models with different numbers of predictors.

Why is the adjusted R2 more informative than the R2?

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