Adjusted R-squared Value

#interview #statistics #evaluation

Adjusted R-squared value is the modification of R-squared Value. In R-squared Value value, it always increases with adding a parameter in the Linear Regression. But it doesn't always mean that it has added a lot of value to the prediction. On the other hand, adjusted R-squared value increases only when the parameter is significant.

Adjusted R-Squred value

$Adjusted R^{2} = 1 - \frac{(1 - R^{2}) (N - 1)}{N - p - 1}$

Here, $N$ = number of instances, $p$ = number of predictors

Adjusted R-squared value helps to balance between accuracy and model's complexity as it penalizes predictor with high complexity.
It decreases overfitting by penalizing very complex models
A good metric to compare multiple predictors, as R-squared Value will always increase with the complexity of the model. So a very complex model with always get higher R-squared Value than a less complex but more accurate and robust model.

References

Related Notes

ROC Curve
Mean Squared Logarithmic Error (MSLE)
Confusion Matrix
Root Mean Squared Error (RMSE)
R-squared Value