[R] Question about R2 in pls package

[David Winsemius]

On Sep 4, 2013, at 10:39 PM, Euna Jeong wrote:

> Hi,
>
> I have questions about R2 used in pls (or multivariate analysis).
>
> Is R2 same with the square of the PCC (Pearson Correlation  
> Coefficient)?
>
> I found the following description from wiki (Coefficient of  
> determination)
>
> ------------------------
> Similarly, in linear least squares regression with an estimated  
> intercept
> term, R2 equals the square of the Pearson correlation coefficient  
> between
> the observed and modeled (predicted) data values of the dependent  
> variable.
> -------------------------
>
> If so, Q2 (R2 of cross validation) should range between 0 and 1.
> But it doesn't. I got negative values of Q2 when running my dataset.
> Of course, from the definition of Q2, Q2 can be negative when my  
> model is
> not at all predictive.
>
> My question is what the relationship between R2 and pcc^2 is.
>

"Adjusted R-squareds" can become negative when the adjustment for the  
added number of predictors overwhelms the increased model fit on the  
scale of adjustment.

Do a search of the archives for negative r-squared. Here's just one of  
many:

http://r-project.markmail.org/search/?q=list%3Aorg.r-project.r-help%20%20negative%20r-squared#query 
:list%3Aorg.r-project.r-help%20%20negative%20r-squared+page:1+mid:rhiqm5bcm4maxnef+state:results

-- 

David Winsemius, MD
Alameda, CA, USA