# [R] Coefficient of determination when intercept is zero

endeitz endeitz at yahoo.com
Thu Jan 18 06:53:12 CET 2007

```Thanks for the guidance.  With the help of your explanation, I was able to
find this reference that provides a good explanation of why the definition
may be different in the "no intercept" or "regression through origin" case.
For future readers of this list, the reference is:

Joseph G. Eisenhauer (2003)
Regression through the Origin
Teaching Statistics 25 (3), 76–80.
doi:10.1111/1467-9639.00136

Cheers,

Ed.

Prof Brian Ripley wrote:
>
> 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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