# Reporting $R^2$

Following my question here, when is it appropriate (or inappropriate) to report r squared for a bivariate linear correlation.

As explained in the earlier question, r = 0.74 which results in r squared of 55%.

The size of r is an excellent outcome but when r squared is taken into account (especially when 45% of the variance in the dependent variable remains unexplained), it sort of dilutes the message.

As pointed out in the answer to the earlier question, I do understand that it is not readily possible for a single factor to explain all the variation.

I think all statistical textbooks that I have consulted (unless I am consulting the wrong books!) state that r squared is a better way of understanding r (or the effect size).

I do understand though that r of at least 0.71 is needed to get r squared of 50%.

Questions

1. Is reporting both r and r squared a good practice (in social science research)?
2. When can I not report r squared?

I have asked Q2 in order to to avoid a situation like the above, where my non statistical target audience may focus more on 45% of the unexplained variance, rather than on the 55% of the explained variance.

• Is it ever a good idea to report something when you have it? I realize there are different conventions for different sciences, but reporting $R^2$ is normal in economics. BTW, $R^2=.55$ is pretty good for a bivariate, non-time-series regression. Your biggest issue with a bivariate regression will be omitted-variable bias. Commented Nov 16, 2011 at 4:04

• Well, the sign of $r$ tells you the direction of the relationship, while $R^2$ does not. Commented Nov 16, 2011 at 1:25