# Re: [R] Coefficient of determination when intercept is zero

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Thu 18 Jan 2007 - 04:18:10 GMT

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
>  0.6257541
>> cor(predict(mod0),test\$Div)^2
>  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
>  0.9099358
>> cor(predict(mod1),test\$Div)^2
>  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@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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