R- Squared and Adjusted R-Squared
Table Of Contents:
- What Is R-Squared Value?
- Formula For R-Squared Value.
- Interpretation Of R-Squared Value.
- Example Of R-Squared.
- Key Points To Note.
- Conclusion.
(1) What Is R-Squared Value?
- R-squared, also known as the coefficient of determination, is a statistical measure that shows how well the independent variable(s) in a regression model explain the variability of the dependent variable.
- It provides an indication of the model’s goodness of fit.
(2) Formula For R Squared Value
(3) Interpretation Of R-Squared
(4) Example Of R-Squared
(5) Key Points To Note
(6) Conclusion
(7) Adjusted R-Squared
- Adjusted R-squared is a modified version of the traditional R-squared that accounts for the number of independent variables (predictors) in a regression model.
- Unlike R2, which always increases as more predictors are added to the model, Adjusted R-squared penalizes the model for adding predictors that do not improve the model significantly.
(8) Formula For Adjusted R-Squared
(9) Why Use Adjusted R-Squared?
(10) Key Points Of Adjusted R-Squared?
Penalty for Extra Variables:
- Adjusted R2R^2 penalizes the inclusion of additional predictors unless they improve the model’s explanatory power significantly.
- If adding a predictor does not improve the model, Adjusted R2R^2 decreases.
Comparison with R- Squared:
- R2 increases or stays constant as predictors are added, even if those predictors are irrelevant.
- Adjusted R2 adjusts for the number of predictors, ensuring only meaningful improvements are rewarded.
Range:
- Adjusted R2 is always less than or equal to R2.
- It can be negative if the model performs worse than a simple mean-based model.
Usefulness:
- Adjusted R2 is particularly useful when comparing models with different numbers of predictors.
(11) Interpretation of Adjusted R-Squared:
(12) Example of Adjusted R-Squared:
(13) Key Takeaways of Adjusted R-Squared:
