Answer: The adjusted R² is always less than or equal to the R²

## Explanation The correct answer is **C**: The adjusted R² is always less than or equal to the R². ### Key Concepts: **R² (Coefficient of Determination):** - Measures how well the regression predictions approximate the real data points - An R² of 100% indicates that all changes in the dependent variable are completely explained by changes in the independent variable(s) - **Limitation**: Always increases as more independent variables are added to the model, even if those variables are only weakly associated with the response - This can lead to overfitting, where the model describes random error or noise instead of the underlying relationship **Adjusted R²:** - Accounts for the number of predictors in the model - Increases only if the new variable improves the model more than would be expected by chance - Can decrease if a variable improves the model less than expected by chance - **Always less than or equal to R²** because it penalizes for adding unnecessary variables ### Why Other Options Are Incorrect: **A**: The adjusted R² is not always greater than R² - in fact, it's usually less than or equal to R² **B**: While both metrics are non-negative and can take values between 0 and 1, they do not always have positive values - both can be zero if there's no linear relationship **D**: The adjusted R² does not always increase with more independent variables - unlike R², it only increases when new predictors genuinely enhance the model beyond what would occur by chance

Author: Tanishq Prabhu