abs value for correlation = square root of R2?

I found this in the readings, but I am confused on why this is so. The book did not go much into explanations.


I don’t think there is a proof for this, but assuming you understand the definition of both R^2 and correlation. It should be clear that the higher the correlation the higher your R^2. If you are given one you should know how to compute the other… If you can so this you will be perfectly fine on exam day. Take it from somebody who is not taking the level 2 exam for the first time… :slight_smile:

R^2 is the squared value of correlation only in simple linear regression

A squared number is always POSITIVE.

But if you take the square root of the number - you can get either the negative or the positive square root.

Correlation is the (Absolute) value of the square root - which means you take the positive square root only.

The sign of the correlation gives you whether the two variables you are looking at are positively, negatively or not correlated. (+, -, 0 being the sign of the correlation).

This is an important point-- it’s pretty much useless to take the square root of R-squared in a multivariable regression (more than one independent variable). It is a real thing, but it doesn’t really do much for us (it’s the correlation between the actual and predicted y-values).

To the other post: I’m not sure what you meant about a proof, but there is definitely a proof to show that the positive square root R-squared is equivalent to the absolute value of the correlation between x and y in a simple linear regression (and I’m sure there is one showing that the negative or positive square root of R-squared is chosen based on the directionality of the estimated coefficient on that x variable).

Don’t forget that they’re referring to the Pearson correlation, which is a measure of a linear relationship. The Pe a rson correlation can be zero, but there can be a very strong non-linear relationship (think of a parabola). This is why saying “no relationship” or “no correlation” isn’t always accurate.

Edited to correct spelling

You have it backwards: the absolute value of the correlation is the square root of R². The correlation is not necessarily positive, so it’s not necessarily the absolute value of anything.