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To my understend in a clasical linear regression the asumption of
normality is in the distribution of the error term, but in glm the
asumption defined by the family selection is on the distribution of
the dependent variable. Isnt that a huge cost for using glm instead
of a clasical linear regression model?
You are laboring under a misunderstanding. To say that the
distribution of Y conditional on X is Normal with mean XB and
variance sigma^2 is the same as saying that the distribution of the
errors (i.e., Y - XB) is Normal with mean 0 and variance sigma^2.
And to emphasize the GLM approach, what is most important (if you're
fitting a linear regression) is that the mean is XB and the variance
is constant (i.e., that your assumptions about the first and second
moments are correct).
It just occurred to me (and I should have thought of this initially,
given that your data are on housing rents) that you may be coming from
an econometrics background rather than statistics. If so, you may
have seen linear regression developed without taking X to be fixed but
rather in terms of assumptions regarding the error term (e.g.,
conditional on X, the errors have mean zero and constant variance).
This is a different approach from that normally taken in basic
statistics texts, where the covariates are treated as fixed and the
assumption that the errors are uncorrelated with the covariates is
treated as definitional rather than scrutinized (note, however, that
these two approaches lead to many of the same basic results).
Generalized linear models are normally presented from the perspective
of the latter approach (e.g., as in the book Generalized Linear Models
by McCullagh and Nelder, or in [R] glm).
I only mention this in case it may have been partly responsible for