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I'm really new to linear regression and am trying to teach myself.

In my textbook there's a problem that asks why $R^{2}$ in the regression of $Y$ on $X =$ the sample correlation between X and Y the whole squared.

I've been throwing my head against this for a while and I keep getting stuck because in the correlation coefficient there is a $X$ and $\bar{X}$ term, whilst in the $R^{2}$ term there is no such thing.

Can anyone provide a derivation as to why $R^{2}$ is the correlation coefficient squared?

Thanks!

  • 3
    It might help if you define the terms in your question. What is the equation for $R^2$, in particular?2012-05-10
  • 1
    If by $R^2$ you mean the "explained variance", then stats.SE might be a more suitable site for this question. See, for example, [this question](http://stats.stackexchange.com/q/28139/6633) or [this one](http://stats.stackexchange.com/q/20553/6633) for some ideas related to this.2013-01-04

4 Answers 4