[R] Interpret R-squared and cor in R

[David Winsemius]

On Feb 15, 2013, at 9:26 PM, Janesh Devkota wrote:

> Hi I am trying to find the relationship between two variables.
>
> First I fitted a linear model between two variables and I found the
> following results:
> Residual standard error: 0.03253 on 2498 degrees of freedom
> Multiple R-squared: 0.5551, Adjusted R-squared: 0.5549
> F-statistic:  3116 on 1 and 2498 DF,  p-value: < 2.2e-16
>
> Then I used the cor function to see the correlation between two  
> variable
> I get the following result
> -0.7450344
>
> How can we interpret the result based on R-squared and correlation ?  
> From
> the p-value we can see that there is very strong relationship between
> variables as it is  way less that 0.001
>
> Can anyone kindly explain the difference between Multiple R squared,
> adjusted R-squared and correlation and how to report these values  
> while
> writing a report ?

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-- 

David Winsemius, MD
Alameda, CA, USA