Explanation
Adjusted R² is a modified version of R² that penalizes for adding unnecessary variables to the model.
Key properties:
- Can be negative: When the model performs worse than using the mean as predictor, adjusted R² can be negative (option A is correct)
- Penalizes overfitting: It adjusts for the number of predictors, unlike regular R² which always increases with more variables
- Not for bias detection: It doesn't indicate whether predictions are biased (option B is incorrect)
- Not a significance test: F-test or t-tests are used for significance testing, not adjusted R² (option C is incorrect)
Formula: Adjusted R2=1−[n−k−1(1−R2)(n−1)]
Where n = sample size, k = number of predictors
When the model is very poor, this formula can yield negative values.
