What does a high R² value indicate in a regression model?

A high R² value in a regression model indicates that a significant proportion of the variance in the dependent variable is explained by the independent variables included in the model. This means that the model effectively captures the relationship between the predictors and the response variable.

When R² is close to 1, it signifies that most of the variability in the outcome can be accounted for by the variables in the model, suggesting that the model has a good explanatory power. This is particularly advantageous when evaluating the effectiveness of the predictors used in the analysis, as it implies that the model is a useful tool for understanding the dynamics at play and potentially making predictions based on the independent variables involved.

In contrast, while a high R² can sometimes raise concerns about overfitting, it is not a definitive indicator of that issue without further context about the model's complexity and performance on out-of-sample data. High predictive failures are usually associated with models that do not generalize well rather than with the R² value itself. Additionally, the systematic error in predictions is a separate concern not directly related to the R² value, as a model can have a high R² yet still make biased predictions.