What is another name for the r-squared value in regression analysis?

The r-squared value, also known as the coefficient of determination, measures the proportion of variance in the dependent variable that can be explained by the independent variable(s) in a regression model. It provides insight into how well the independent variables explain the variation in the dependent variable.

When we say that a certain percentage of the variance is accounted for by the model (for example, an r-squared of 0.70 means 70% of the variance is explained), it establishes a direct correlation between the features of the model and the output. This makes the coefficient of determination a crucial metric for evaluating the effectiveness of regression models.

In contrast, the coefficient of variation relates to the ratio of the standard deviation to the mean and does not specifically measure explained variability in a regression context. The coefficient of correlation pertains to the linear relationship between two variables but does not denote the explained variance of a model. Lastly, the standard error of estimate provides an average distance that the observed values fall from the regression line, which is distinct from measuring explained variance directly. Thus, the designation of the r-squared value as the coefficient of determination precisely encapsulates its purpose and relevance in regression analysis.