Does it make sense to group variables together in a regression model? Would it make sense to use a variable that consists of two features when estimating the effect on a dependent variable?
For example, when estimating admission into a college - would having the variable "asian_female" make sense (1 indicates both Asian and female, 0 otherwise)? I'm examining a regression model that has both "asian_female" and "female" variables - do you see any issue with this?
Lastly, if the coefficient for "asian_female" was .203 and it was statistically significant, is it accurate to say - being both Asian and female increases the likelihood of being admitted compared to a female from another race?
Any guidance would be much appreciated.

Not an issue and actually this is a common practice. When you have a non linear relations in your data, a common practice is to move to higher polynomial degree, for example polynomial degree two. When moving to polynomial degree two, for the categorical variables we do carteIan products i.e we include all the possible pairs between the values of each category. If for example you have (man, women) and (asian, european) you will have 4 different features representing all the pairs. This is as an addition to the stand alone feature. And yes, the coefficient represents the specific pair of asian women.
