Take the 2-minute tour ×
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's 100% free, no registration required.

In linear regression, we often get multiple R and R squared. What are the differences between them?

share|improve this question
add comment

1 Answer 1

Capital $R^2$ (as opposed to $r^2$) should generally be the multiple $R^2$ in a multiple regression model. In bivariate linear regression, there is no multiple $R$, and $R^2=r^2$. So one difference is applicability: "multiple $R$" implies multiple regressors, whereas "$R^2$" doesn't necessarily.

Another simple difference is interpretation. In multiple regression, the multiple $R$ is the coefficient of multiple correlation, whereas its square is the coefficient of determination. $R$ can be interpreted somewhat like a bivariate correlation coefficient, the main difference being that the multiple correlation is between the dependent variable and a linear combination of the predictors, not just any one of them, and not just the average of those bivariate correlations. $R^2$ can be interpreted as the percentage of variance in the dependent variable that can be explained by the predictors; as above, this is also true if there is only one predictor.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.