# Calculate the correlation coefficient from the coefficient of determination

The question is how to calculate $$r$$ from $$r^2$$. Now, I know that its just as simple as taking a square root but is it as simple as that?

• You won't get the sign of a bivariate correlation out of $R^2$: for that you need to look at the slope, or even the data. – Nick Cox Sep 27 '18 at 17:28

A Pearson correlation is really only defined for two variable problems. If you happen to run a regression to obtain $$R^2$$, yes the square root will just convert back to the correlation. In a multivariate context, however, the square root of $$R^2$$ really doesn’t tell you much.
• The square root of $R^2$ is the correlation between observed and predicted values and that's true for multiple regression too. So it has a fairly simple interpretation and as such it can be informative and useful. I'd go further and say that this interpretation can be as useful as, or more useful than, one based on various sums of squares or variances. Much depends on how familiar people are with regression. What is obvious to well trained people can be obscure to others, who may need all the interpretative hooks they can find. – Nick Cox Sep 27 '18 at 17:23