What does the coefficient of determination represent?

The coefficient of determination, commonly denoted as R², represents the proportion of variability in the dependent variable that can be explained by the independent variable(s) in a regression model. This value is calculated as the square of the correlation coefficient (R), which denotes the strength and direction of a linear relationship between two variables.

When the coefficient of determination is calculated, it provides insights into how well the regression model fits the data. An R² value of 1 indicates a perfect fit, meaning all variations in the dependent variable can be explained by the model, while an R² of 0 indicates that the model does not explain any of the variability.

Understanding the significance of R² is crucial in assessing the explanatory power of a regression model, helping analysts and investors determine how well predictions can be made based on the data available. In the context of this question, recognizing that the coefficient of determination is specifically the square of the correlation coefficient connects it to the underlying statistical concepts of correlation and regression analysis. This clarity on its definition reinforces the significance of R² in evaluating model performance.