[R] Correlation question

[Jonathan Thayn]

Of course! Thank you, I knew I was missing something painfully obvious. Its seems, then, that this line

1-sum((cars$dist-fitted.wrong)^2)/sum((cars$dist-mean(cars$dist))^2)

is finding something other than the traditional correlation. I found this in a lecture introducing correlation, but , now, I'm not sure what it is. It does do a better job of showing that the fitted.wrong variable is not a good prediction of the distance. 



On Feb 21, 2015, at 4:36 PM, Kehl Dániel wrote:

> Hi,
> 
> try
> 
> cor(fitted.right,fitted.wrong)
> 
> should give 1 as both are a linear function of speed! Hence cor(cars$dist,fitted.right)^2 and cor(x=cars$dist,y=fitted.wrong)^2 must be the same.
> 
> HTH
> d
> ________________________________________
> Feladó: R-help [r-help-bounces at r-project.org] ; meghatalmazó: Jonathan Thayn [jthayn at ilstu.edu]
> Küldve: 2015. február 21. 22:42
> To: r-help at r-project.org
> Tárgy: [R] Correlation question
> 
> I recently compared two different approaches to calculating the correlation of two variables, and I cannot explain the different results:
> 
> data(cars)
> model <- lm(dist~speed,data=cars)
> coef(model)
> fitted.right <- model$fitted
> fitted.wrong <- -17+5*cars$speed
> 
> 
> When using the OLS fitted values, the lines below all return the same R2 value:
> 
> 1-sum((cars$dist-fitted.right)^2)/sum((cars$dist-mean(cars$dist))^2)
> cor(cars$dist,fitted.right)^2
> (sum((cars$dist-mean(cars$dist))*(fitted.right-mean(fitted.right)))/(49*sd(cars$dist)*sd(fitted.right)))^2
> 
> 
> However, when I use my estimated parameters to find the fitted values, "fitted.wrong", the first equation returns a much lower R2 value, which I would expect since the fit is worse, but the other lines return the same R2 that I get when using the OLS fitted values.
> 
> 1-sum((cars$dist-fitted.wrong)^2)/sum((cars$dist-mean(cars$dist))^2)
> cor(x=cars$dist,y=fitted.wrong)^2
> (sum((cars$dist-mean(cars$dist))*(fitted.wrong-mean(fitted.wrong)))/(49*sd(cars$dist)*sd(fitted.wrong)))^2
> 
> 
> I'm sure I'm missing something simple, but can someone explain the difference between these two methods of finding R2? Thanks.
> 
> Jon
>        [[alternative HTML version deleted]]
> 
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