if I run a regression without the dummies, then the coefficients of
the rest variables will be different.
What I need to do is using the coefficient of the independent
variables calculated while gender is included to estimated the
dependent variable while gender is exluded from the prediction
equation.
First off, you probably don't want to do that. You would be using
parameter estimates that no model has actually generated. I very strongly
suspect that what you propose doing is the wrong way to go but then you
know your work better than I do. (Students occasionally want to compute
predicted values based on some hypothetical set of values, and they ask me
whether the non-significant coefficients should just be treated as zero; I
say no, either leave them as is or re-estimate the model with those
variables dropped.)
