# What is the relationship between R-Squared and the correlation coefficient of a model?

##### 1 Answer

#### Answer:

See this . Credit to Gaurav Bansal.

#### Explanation:

I was trying to think of the best way to explain this and I stumbled across a page that does a really nice job. I would rather give this guy the credit for the explanation. In case the link doesn't work for some I have included some information below.

Simply stated: the

The **correlation coefficient ( #R# )** of a model (say with variables

- If
#x# and#y# are in perfect unison, then this value will be positive#1# - If
#x# increases while#y# decreases in exactly the opposite manner, then this value will be#-1# #0# would be a situation where there is no correlation between#x# and#y#

However, this

This is where the ** #R^2#** value comes into play. It is simply the square of the correlation coefficient. It takes values between

**is much more useful as it can be used to describe multivariate models as well.**#R^2#

If you would like a discussion on some of the mathematical notions involved with relating the two values, see this .