A statistic indicating the proportion of the total variance in the dependent variable accounted for by the independent variable in a simple linear regression equation is known as?

The coefficient of determination is a key statistical metric in regression analysis, specifically in the context of simple linear regression. It quantifies the proportion of the total variance in the dependent variable that can be attributed to the independent variable. This statistic is commonly represented as ( R^2 ).

An ( R^2 ) value ranges from 0 to 1, where a value of 0 indicates that the independent variable does not explain any of the variance in the dependent variable, while a value of 1 indicates that all the variance in the dependent variable can be explained by the independent variable. This metric provides insight into how well the regression model fits the data. A higher ( R^2 ) value implies a better model fit, making this statistic valuable for assessing the effectiveness of the model.

The other terms mentioned, such as coefficient of dispersion, regression coefficient, and regression dispersion, do not specifically refer to the proportion of variance explained by the independent variable in the same way that the coefficient of determination does. Coefficient of dispersion typically relates to the relative spread of data, the regression coefficient describes the impact of the independent variable on the dependent variable, and regression dispersion is not a standard term used in regression analysis.