What does the coefficient of determination (R²) indicate?

The coefficient of determination, denoted as R², is a crucial measure in regression analysis that indicates the proportion of the variance in the dependent variable that can be explained by the independent variables in the model.

When assessing the fit of a regression model, R² provides insights into how well the model captures the variability of the output data based on the input predictors. A higher R² value suggests that a greater proportion of the variance in the dependent variable is accounted for by the independent variables, which implies a better fit of the model to the data. Essentially, R² quantifies the degree of correlation between predicted values from the model and the actual values, providing a clear understanding of the model's explanatory power.

In contrast, the overall significance of the regression model relates to hypothesis testing of coefficients, while the average value of the dependent variable is a simple statistic without reference to the independent variables. Additionally, the total number of variables in a model does not inform the explanatory power of the model itself, but rather indicates its complexity. Thus, R² specifically addresses the relationship between the independent variables and the variance of the dependent variable, making it a vital statistic in evaluating regression models.