I don't really understand why this occurs. Say you have a categorical variable with 5 levels. You are supposed to generate 4 dummies, k-1. If not, my understanding, you get perfect col-linearity and the model should fail. But I have accidentally done this many times and the model worked.

I have not noticed this, but I ran a test in SAS to see. I am not sure how the software would even know that the 71 dummies added as separate variables were related to a categorical variable. But that raises an interesting point. If I have a variable with 71 levels coded 1 or 0 and I add all 71 levels would the software realize this. And would including all 71 generate perfect collinearity.

I do not see an excluded level. And it estimated all the variables as far as I can tell. I am not sure what is occurring, maybe the fact that they make up all our units does not matter for the math here.

I have 71 units and I want to know their impact. I am not sure what that has to do with gender or any other variable?? This is specifically to see the impact of the 71 units controlling for other variables.