In regression analysis, what statistic is described as the percentage of the variation in the dependent variable explained by the regression?

The statistic referred to as the percentage of the variation in the dependent variable explained by the regression is known as the coefficient of determination, often denoted as R². This measure is critical in regression analysis because it provides insight into how well the independent variables in the model predict the dependent variable.

When you calculate R², you are essentially assessing how much of the total variation in the dependent variable can be accounted for by the variability in the independent variables. An R² value close to 1 indicates that a significant proportion of the variance is explained by the model, while an R² value near 0 suggests that the model does not explain much of the variance. Thus, R² acts as a valuable gauge for the effectiveness of a regression model.

Understanding this concept is vital for interpreting the results of regression analyses and determining the predictive power of the model. It also allows analysts to communicate the strength of their findings in practical terms, which is essential for decision-making processes based on the regression results.