What does the coefficient of determination (R^2) indicate?

The coefficient of determination, commonly denoted as R^2, is a statistical measure that offers insight into how well a regression model explains and predicts future outcomes. Specifically, R^2 quantifies the proportion of the variance in the dependent variable that can be attributed to the independent variables within the model. When R^2 is expressed as a percentage, it reflects the extent to which the model accounts for the variability observed in the data.

For example, an R^2 value of 0.85 would indicate that 85% of the variance in the dependent variable can be explained by the independent variables in the model, suggesting a strong relationship between them. Thus, R^2 serves as a key indicator of the model's explanatory power, allowing analysts to assess the effectiveness of the model in capturing the underlying patterns of the data.

The other options, while relevant to data analysis, do not accurately describe the specific purpose of R^2. The effectiveness of a model can depend on various other factors, such as model assumptions and validation metrics. The independence of variables relates more closely to multicollinearity concerns in regression analysis, and distribution of data refers to how data points are spread or clustered around a central value, which is not what R^2