Answer: can take on a negative value.

## 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**: $\text{Adjusted } R^2 = 1 - \left[\frac{(1-R^2)(n-1)}{n-k-1}\right]$ Where n = sample size, k = number of predictors When the model is very poor, this formula can yield negative values.

Author: LeetQuiz Editorial Team