I want to perform a simply regression of a variable y on several independent variables (x1, x2, x3) and additionally on dummy variable(s) for each of 10 categories.
I read about dummy variables, so I created one for each of the 10 categories, whereby one of them is the base, i.e. consists of only zeros. Next I performed the regression including all 10 dummy variables but there was an error: Coefficients: (1 not defined because of singularities). I think this is because of perfect multicollinearity of a dummy variable with the intercept.
So from what I read, I can fix this error by removing the base dummy; this will be covered by the intercept instead.
First question: Is this correct? If so, it is ok, but when I look at the output I'd prefer to have sthg there which is not labelled as 'intercept', but rather as the base dummy which it refers to.
So here is my main question: Could I also drop the intercept and include the base dummy instead? I have tested this, but it does not seem to work. I believe if I dropped the intercept I would have to include a new dummy for the base category which also includes ones and not only zeros. Is this the right way?
Thanks for any hints. The sources on the internet were not really clear about this.