# [R] Coefficient of determination when intercept is zero

Prof Brian Ripley ripley at stats.ox.ac.uk
Thu Jan 18 05:18:10 CET 2007

```This is documented on ?summary.lm.

It is not that 'intercept is zero' or 'zero intercept', it is that there
is no intercept term in the model.

On Wed, 17 Jan 2007, endeitz wrote:

>
> I am curious as to the "lm" calculation of R2 (multiple coefficient of
> determination, I assume) when intercept is zero.  I have 18 data points, two
> independent variables:
>
> First, a model with an intercept:
>
>> mod0=lm(Div~Rain+Evap,data=test)
>> summary(mod0)\$r.squared
> [1] 0.6257541
>> cor(predict(mod0),test\$Div)^2
> [1] 0.6257541
>
> The \$r.squared and the result from "cor" are the same, as I would expect.
>
> Now we try a model with zero intercept:
>
>> mod1=lm(Div~0+Rain+Evap,data=test)
>> summary(mod1)\$r.squared
> [1] 0.9099358
>> cor(predict(mod1),test\$Div)^2
> [1] 0.5813659
>
> Why has the \$r.squared value increased to 0.9?  And now the result from
> "cor" is not the same?  Is there a special way to calculate the coefficient
> of determination when the intercept is zero?
>
> Cheers,
>
> Ed.
>
>

--
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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