Interpretation of dummy variables Lets say that i have linear regression $Y= a +XB$, and in my $X$ matrix i have a dummy for the gender, lets call it $d_{g}$ which is 1 for male and 0 for female. The coefficient $b$ of $d_{g}$ shows the effect of being male relative to the effect for being female. How can i get the effect of being female ? Or the effect of being male, but not relative to the female.
 A: You can reconstruct what you want from your fit using the population fractions of male and female $f_M$ and $f_F = 1 - f_M$.
The expectation of $Y$ for males and females is given by:
$$ E[Y|M] = a + b \qquad E[Y|F] = a$$
so
$$ E[Y|M] - E[Y|F] = b$$
$b$ gives the expected change in $Y$ going from female to male, as you said in your post.
Given the male and female population fractions we can construct the unconditional expectation:
$$E[Y] = f_F E[Y|F] + f_M E[Y|M] = (1-f_M) a + f_M (a + b) = a + f_M b$$
and from that, we can get the expected change in $Y$ going from sex-unknown to male:
$$E[Y|M] - E[Y] = (1 - f_M) b$$
and, similarly, the expected change in $Y$ going from sex-unknown to female:
$$E[Y|F] - E[Y] = - f_M b$$
You should get the same results with this method as from the procedure suggested by Michael above, without having to re-run the regression.
A: This can simply be achieved by leaving out the constant (other wise you run in the so called dummy-trap) and using a model like
$$Y=d_{female} + d_{male} + X\beta + u, $$
where $d_{female}$ is one if female and $d_{male}$ is one if male.
Then you will have
$$E[Y|X,male]=d_{male} + E[X]\beta,$$
$$E[Y|X,female]=d_{female} + E[X]\beta$$
and $E[Y|X,male]-E[Y|X,female]=d_{male} -d_{female}$.
