# [R] explanation of lm's coefficients

Deepayan Sarkar deepayan at stat.wisc.edu
Sun Aug 24 01:33:11 CEST 2003

```lm() implicitly assumes the presence of the intercept term in the model, i.e.,

> lm(data ~ ftr)

is actually fitting

> lm(data ~ 1 + ftr)

You can override this by doing

> lm(data ~ ftr - 1)

You can always check the actual model being fitted by extracting the model
matrix:

> model.matrix(data ~ ftr)
> model.matrix(lm(data ~ ftr - 1))

etc.

HTH,
Deepayan

On Saturday 23 August 2003 17:44, Justin Fay wrote:
> I don't understand the coefficients returned from the lm function. I
> expected these to be the mean values for each factor in the model. Given
> this data and model:
>
> data<-c(rnorm(10,mean=0,sd=1),rnorm(10,mean=1,sd=1),rnorm(10,mean=-.5,sd=1)
>) ftr<-as.factor(rep(1:3,each=10))
> fit<-lm(data ~ ftr)
>
> the mean values of the three facotrs from the data:
>
> c(mean(data[1:10]), mean(data[11:20]), mean(data[21:30]))
>  -0.3589049  0.6034931 -0.7256897
>
> are not the same as the coefficients return from fit:
>
> fit\$coef
> (Intercept)        ftr2        ftr3
>  -0.3589049   0.9623980  -0.3667847
>
> ftr2 and ftr3 are offset by the value of the intercept.
>
> The fitted values are as I expected:
>
> fit\$fitted.values
>          1          2          3          4          5          6
> 7 -0.3589049 -0.3589049 -0.3589049 -0.3589049 -0.3589049 -0.3589049
> -0.3589049 8          9         10         11         12         13
> 14 -0.3589049 -0.3589049 -0.3589049  0.6034931  0.6034931  0.6034931
> 0.6034931 15         16         17         18         19         20
> 21 0.6034931  0.6034931  0.6034931  0.6034931  0.6034931  0.6034931
> -0.7256897 22         23         24         25         26         27
>  28 -0.7256897 -0.7256897 -0.7256897 -0.7256897 -0.7256897 -0.7256897
> -0.7256897 29         30
> -0.7256897 -0.7256897
>
> My goal is to get the mean values of the factors. Although easily done,
> I don't understand why the ftr2 and ftr3 are offset by the value of the
> intercept. Any explanations would be appreciated.
>
> Justin
>
> ________________________________________
> Justin Fay
> Assistant Professor of Genetics
> Washington University School of Medicine
> 4566 Scott Ave, St. Louis, MO 63110
> PH: 314.747.1808 Fax: 314.362.7855
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
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