I have a regression of the following:
ax + bx + cx + Ax + Bx + Cx + intercept = y
where all x are dummy variables. This represents that I have 2 categorical variables each having 4 categories. So, if a=0, b=0, c=0 -> it means the fourth category of this is 1 automatically. In the same manner, if A=0, B=0, C=0 -> the other type of fourth category of this is 1 automatically.
If I want to simply get the effect of the fourth category from a, b, c can I simply set a=b=c=0 and get the intercept value as its fourth category value? If so, I am afraid that the fourth category variable of the other set when I do A=B=C=0 will give the same value as the intercept which I do not think making any sense.
May I get help on the interpretation?