# Collinearity or not?

In a multiple regression analysis, if you have, in addition to host of other varibales, a dummy i.e. (0,1) coded gender variable with 0=male 1= female, and another dummy variable, say an occupational dummy for a nan engineer, and for all engineer=1 gender=male. Not all males are engineers but all engineers are male. An issue in terms of BLUE / OLS?

## 1 Answer

You only have an insurmountable problem with collinearity if the values of one predictor can be expressed as a linear combination of other predictors. So it depends on the rest of the data.

If all engineers are men and also all men are engineers, then you have a problem. One could imagine more complicated scenarios that similarly lead to exact linear dependency among the predictors.

Otherwise the correlation between gender and engineer status would do what less-than-perfect collinearity tends to do: make the standard errors of regression coefficient estimates higher than they might be otherwise. The point estimates of the coefficients will still be best linear unbiased estimates provided the standard assumptions hold.