# [R] Odd r-squared

Simon Wotherspoon Simon.Wotherspoon at utas.edu.au
Mon Nov 3 07:53:25 CET 2003

```Hi,
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.

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,