Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 X bar term, whilst in the R2 term there is no such thing.

Can anyone provide a derivation as to why R2 = correlation coeff squared?

Thanks!

share|improve this question
2  
It might help if you define the terms in your question. What is the equation for $R^2$, in particular? –  Rahul May 10 '12 at 9:27
    
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 or this one for some ideas related to this. –  Dilip Sarwate Jan 4 '13 at 23:46
add comment

2 Answers

There are many forms of the computation available online (such as the Wikipedia page on the correlation coefficient http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient#Pearson.27s_correlation_and_least_squares_regression_analysis ) but note that this is a magical algebraic property of least squares linear regression, not linear regression in general.

share|improve this answer
    
hmm what I don't understand about that is why the correlation coeff equation doesn't have an X term any more? –  Scubadiver Apr 10 '12 at 5:49
    
Which equation does not have an X term? –  zyx Apr 10 '12 at 6:03
add comment

There are different forms to express R2: Some expressions have (X-Xbar) squared in the numerator, while others express it just with the square of predicted ys. All forms are equivalent.

References: Dougherty; Gujarati; Wooldridge

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.