[R] Odd r-squared
Prof Brian Ripley
ripley at stats.ox.ac.uk
Mon Nov 3 09:02:25 CET 2003
On Mon, 3 Nov 2003, Simon Wotherspoon wrote:
> I would consider the calculation of r-squared in the following to be a
> bug, but then, I've been wrong before. It seems that R looks to see if the
> model contains an intercept term, and if it does not, computes r-squared in
> a way I don't understand. To my mind, the following are two alternative
> parametrizations of the same model, and should yield the same r-squared.
But the minimal model contains a overall mean in the first case and not in
the second. Your models are 1+g+x+g:x and 0+g+g:x. So whereas they are
alternative parametrizations of the same full model, R^2 compares two
models, not just one.
You will find this explained on ?summary.lm (RTFM!) and several times in
the archives. One solution is to ignore the R^2 lines (as I do and tell
my students to do). But we might consider labelling the printed output as
say
Multiple R-Squared (no int): 0.8061, Adjusted R-squared: 0.6769
to remind people.
>
> Any insight much appreciated
>
> Simon.
>
>
>
> > set.seed(10,kind=NULL)
> > x <- runif(10)
> > g <- gl(2,5)
> > y <- runif(10)
> >
> > summary(lm(y ~ g*x))
>
> Call:
> lm(formula = y ~ g * x)
>
> Residuals:
> Min 1Q Median 3Q Max
> -0.35205 -0.14021 0.02486 0.13958 0.39671
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 0.3138 0.2749 1.141 0.297
> g2 -0.1568 0.4339 -0.361 0.730
> x 0.3556 0.6082 0.585 0.580
> g2:x 0.3018 1.0522 0.287 0.784
>
> Residual standard error: 0.276 on 6 degrees of freedom
> Multiple R-Squared: 0.1491, Adjusted R-squared: -0.2763
> F-statistic: 0.3505 on 3 and 6 DF, p-value: 0.7907
>
> > summary(lm(y ~ g/x-1))
>
> Call:
> lm(formula = y ~ g/x - 1)
>
> Residuals:
> Min 1Q Median 3Q Max
> -0.35205 -0.14021 0.02486 0.13958 0.39671
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> g1 0.3138 0.2749 1.141 0.297
> g2 0.1570 0.3357 0.468 0.657
> g1:x 0.3556 0.6082 0.585 0.580
> g2:x 0.6574 0.8586 0.766 0.473
>
> Residual standard error: 0.276 on 6 degrees of freedom
> Multiple R-Squared: 0.8061, Adjusted R-squared: 0.6769
> F-statistic: 6.237 on 4 and 6 DF, p-value: 0.02491
>
>
>
> --please do not edit the information below--
>
> Version:
> platform = i386-pc-mingw32
> arch = i386
> os = mingw32
> system = i386, mingw32
> status =
> major = 1
> minor = 8.0
> year = 2003
> month = 10
> day = 08
> language = R
>
> Windows ME 4.90 (build 3000)
>
> Search Path:
> .GlobalEnv, package:methods, package:ctest, package:mva, package:modreg,
> package:nls, package:ts, Autoloads, package:base
> ---
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help
>
>
--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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