So let’s say i have a categorial variable with 3 different citys, n of dummys would be 3-1=2? How would we interpret that? Say citys is London, NY, Berlin, D1 = ? D2= ?
Take any city as refrence eg. London (0) then create 2 dummy variables dNY and dBerlin and insert values as NY(1) in which both London and Berlin (0) and when Berlin(1), London and NY (0) accordingly. Now run the regression using these 2 dummy variables. It would be interpreted impact of NY compared to London and impact of Berlin compared to London. The base or reference is of your choice. Basically you are comparing the dummy with the reference dummy.
Yes we need not interchange. At a time use d1 or d2. If you go for checking beta2 i.e.for d2 your d1 will be the reference variable or vice versa. You can check for individual variables effect that is d1 n d2
It may so happen that a dummy variable may be added twice for the very dummy variable you've already identified. Say for example when you talk about Gender(Male/Female) One may put 1-male/0-female again for the same variable one may put 1-female/0-male. Then this problem of d-trap comes up.
The number of dummy variables included in a regression model should always be one less than the total number of attributes you have. say for example you've 3 attributes (black/white/blue) then you've to include only 2 dummy variables i.e. (n - 1) where "n" is your total number of attributes.
