R help - Jul 2012 - Understanding the intercept value in a multiple linear regression with categorical values

Hi!

I'm failing to understand the value of the intercept value in a
multiple linear regression with categorical values. Taking the
"warpbreaks" data set as an example, when I do:
> lm(breaks ~ wool, data=warpbreaks)
Call:
lm(formula = breaks ~ wool, data = warpbreaks)

Coefficients:
(Intercept)        woolB
     31.037       -5.778

I'm able to understand that the value of intercept is the mean value
of breaks when wool equals "A", and that adding up the
"woolB"
coefficient to the intercept value I get the mean value of breaks when
wool equals "B". However, if I also consider the tension variable in
the model, I'm unable to figure out the meaning of the intercept
value:
> lm(breaks ~ wool + tension, data=warpbreaks)
Call:
lm(formula = breaks ~ wool + tension, data = warpbreaks)

Coefficients:
(Intercept)        woolB     tensionM     tensionH
     39.278       -5.778      -10.000      -14.722

I thought it would be the mean value of breaks when either wool equals
"A" or tension equals "L", but that isn't true for this
dataset.

Any clues on interpreting the value of intercept?

Thanks!

--
Joao.

Joao,

There's a very thorough explanation at
http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm

Jean


Joao Azevedo <joao.c.azevedo@gmail.com> wrote on 07/27/2012 06:32:31
AM:
> 
> Hi!
> 
> I'm failing to understand the value of the intercept value in a
> multiple linear regression with categorical values. Taking the
> "warpbreaks" data set as an example, when I do:
> 
> > lm(breaks ~ wool, data=warpbreaks)
> 
> Call:
> lm(formula = breaks ~ wool, data = warpbreaks)
> 
> Coefficients:
> (Intercept)        woolB
>      31.037       -5.778
> 
> I'm able to understand that the value of intercept is the mean value
> of breaks when wool equals "A", and that adding up the
"woolB"
> coefficient to the intercept value I get the mean value of breaks when
> wool equals "B". However, if I also consider the tension variable
in
> the model, I'm unable to figure out the meaning of the intercept
> value:
> 
> > lm(breaks ~ wool + tension, data=warpbreaks)
> 
> Call:
> lm(formula = breaks ~ wool + tension, data = warpbreaks)
> 
> Coefficients:
> (Intercept)        woolB     tensionM     tensionH
>      39.278       -5.778      -10.000      -14.722
> 
> I thought it would be the mean value of breaks when either wool equals
> "A" or tension equals "L", but that isn't true for
this dataset.
> 
> Any clues on interpreting the value of intercept?
> 
> Thanks!
> 
> --
> Joao.
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