Question

If increasing the number of independent variables increases R², why isn't it advised to simply increase the number of independent variables in a model to explain the variability in the dependent variable?

Answer 1

Ans:

All data contain a natural amount of variability that is un-explainable. Unfortunately, R-squared doesn’t respect this natural ceiling. Chasing a high R-squared value can push us to include too many predictors in an attempt to explain the unexplainable.

In these cases, you can achieve a higher R-squared value, but at the cost of misleading results, reduced precision, and a lessened ability to make predictions.

Both adjusted R-squared and predicted R-square provide information that helps you assess the number of predictors in your model:

• Use the adjusted R-square to compare models with different numbers of predictors
• Use the predicted R-square to determine how well the model predicts new observations and whether the model is too complicated