# interpretation on the regression with categorical variables

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?

• The coefficients in this model represent estimated mean differences from the baseline (i.e. fourth) category. The estimated mean difference of the fourth category from itself is 0. Jul 22, 2017 at 3:48

Here, $y$ is equal to the intercept when you have the fourth category in both variables.

Hence, there isn't a problem. Note that one thing is we think of "intercepts" as "y-intercept for a line," but that is for numerical predictors. Since here you only have two categorical variables, there are only 16 possible values for $y$.

• Thank you. Then if I want to report the effect of the fourth variable only for the first categorical variable out of two, may I know what it should be..?
– Eric
Jul 22, 2017 at 6:29
• The effect of the fourth variable, reiative to the other variables, is given by the $a$, $b$, and $c$ coefficients - if you'd like to predict $y$, you would need to know the mean value attained by the second categorical variable (or have some sort of idea what value to put in; perhaps it could be a mode instead). Jul 22, 2017 at 15:35