Talk:Coefficient of determination
From Wikipedia, the free encyclopedia
Contents |
[edit] Adjusted R Square
There is a bit better explanation of this at: http://www.csus.edu/indiv/j/jensena/mgmt105/adjustr2.htm I think we can add to the definition: 1) the motivation for "Adjusted R Square". And 2) to note that it can be viewed as an Index when comparing regression models (like the standard Error).
Tal.
—The preceding unsigned comment was added by Talgalili (talk • contribs) 16:04, 21 February 2007 (UTC).
[edit] Causality
I thought that since R is based on the general linear model you could infer causality from the model?? You are really just doing an ANOVA with a continuous factor (X) as opposed to a categorical one
>> No. R^2 has nothing at all to do with causality. Causality can only be implied by imposition of specific assumptions on the process being modeled. -- Guest.
[edit] Range of R-squared
Who says R-squared should be greater than zero? For example if measured y-values are between 9 and 10, and model prediction is always zero, then R-squared is heavily negative.Kokkokanta 07:50, 28 January 2007 (UTC)
>> Go back and look at the definition. For one thing, all the sums are of squared differences. Moreover, SSE<=SST by construction. So R^2 is certainly non-negative. Adjusted R^2 *can* be negative, however. -- Guest.
[edit] Possible expansions
- Consider mention of the Nagelkerke criterion, an analogue
that you can use with generalized linear models, which are not fitted by ordinary least squares.
- We can't assume that R^2 is applicable with every kind of
least-squares regression. For example, it doesn't make sense with regression through the origen. There has been a discussion of limitiations, in American Statistician.
- Adjusted R^2 can be negative.
Dfarrar 14:04, 8 March 2007 (UTC)
Nagelkerke's pseudo-R^2 really doesn't belong in this article IMHO. It deserves a separate page, perhaps along with other pseudo-R^2 measures. The point is well-made about regression through the origin, but redefinition of R^2 is trivial in this context. Perhaps that should be mentioned.
---Guest
[edit] Causality
R^2 is only one measure of association. The causality issue applies to all of them. The issue has been addressed generically. See links inserted.
Dfarrar 14:29, 8 March 2007 (UTC)
[edit] Inflation of R-square
This has been a good day for additions to my watched pages. Regarding this new material, I think some terms could be explained to make the article more widely accessible, without doing much harm, e.g. "weakly smaller." Repeating a previoius point, I suggest inclussion of material on analogous statistics applicable with models other than Gaussian, e.g., with generalized linear models. Dfarrar 22:25, 20 March 2007 (UTC)
