Home
Back
Adjusted R² Formula:
| From: | To: |
Adjusted R² (Coefficient of Determination) is a modified version of R² that has been adjusted for the number of predictors in the model. It increases only if the new term improves the model more than would be expected by chance and decreases when a predictor improves the model by less than expected.
The calculator uses the Adjusted R² formula:
Where:
Explanation: The formula penalizes the addition of unnecessary predictors to a model, preventing overfitting by accounting for the number of predictors relative to the sample size.
Details: Adjusted R² is crucial in regression analysis as it provides a more accurate measure of model fit than R² when comparing models with different numbers of predictors. It helps identify whether adding additional predictors improves the model sufficiently to justify their inclusion.
Tips: Enter R² value between 0 and 1, sample size (must be greater than 0), and number of predictors (must be non-negative). Ensure that n - k - 1 > 0 for valid calculation.
Q1: What's the difference between R² and Adjusted R²?
A: R² always increases when you add more predictors, while Adjusted R² increases only if the new predictor improves the model more than expected by chance.
Q2: Can Adjusted R² be negative?
A: Yes, Adjusted R² can be negative when the model fits worse than a horizontal line (when R² is very low relative to the number of predictors).
Q3: When should I use Adjusted R² instead of R²?
A: Use Adjusted R² when comparing models with different numbers of predictors or when you want to avoid overfitting your model.
Q4: What is a good Adjusted R² value?
A: There's no universal threshold, but higher values indicate better model fit. The value depends on your specific field of study and research context.
Q5: Are there limitations to Adjusted R²?
A: While useful, Adjusted R² shouldn't be the sole criterion for model selection. It's best used in conjunction with other metrics like AIC, BIC, and cross-validation.