Trouble about the interpretation of intercept in lm models

Actually, notice that you are averaging identical values, so the "mean"
in the tapply is slightly misleading.

Notice also that the intercept may be defined even when _no_
observations have zero entries in the design matrix. This is the usual
case in linear regression, for instance, but it can happen in factorial
designs (unbalanced, or using other than treatment contrasts) as well.

Thanks for the answers.
Still I am not totally convinced about the interpretation of intercept 
as a mean of fitted values for group belonging to first level of each 
factor (those having 0 in all columuns in matrix.models, except the 
first column) because the reasoning seems to me a little cirucular.
Being the intercept value the expected value for that group and, as 
Peter point out, being the same value for all observations in the group 
it seem clear that it intercept it is the mean of these value.

It is not completeley clear to me why (in some cases, not always) the 
intercept is not equal to the mean of the first group of raw data.

Sorry if I am annoying with this issue... but I found in several books 
about R and also in this same mailing list that intercept *should* be 
equal to the mean of the first group.

Thanks
Stefano

======================================================================
  Stefano Leonardi
  Dipartimento di Scienze Ambientali
  Universita` di Parma                E-mail: stefano.leonardi at unipr.it
  Viale Usberti 11/A                            Phone : +39-0521-905659
  43100 PARMA  (Italy)                          Fax   : +39-0521-905402