What is the term that describes the proportion of variability in the dependent variable explained by the regression equation?

The term that describes the proportion of variability in the dependent variable explained by the regression equation is the multiple coefficient of determination, commonly referred to as R-squared (R²). This statistic provides a measure of how well the independent variables in the regression model explain the variability of the dependent variable.

A high R² value indicates that a large proportion of the variance in the dependent variable is accounted for by the independent variables, which suggests a good fit of the model to the data. Conversely, a lower R² value signifies that the independent variables do not explain much of the variability, indicating either a poor fit or that additional independent variables may need to be included.

The other options represent different concepts. Standard deviation is a measure of the amount of variation or dispersion in a set of values but does not specifically indicate how much variability in the dependent variable is explained by the model. The variance ratio is not a well-defined term in this context. Error variance pertains to the variability in the dependent variable that is not explained by the independent variables in the regression model. Instead of capturing the explained variability, it focuses on what remains unexplained.