# Interpretation of dummies (several variables and categories!)

I am trying to figure out how to interpret the coefficients when using several qualitative independent variables of which some have more than two categories. I found this short article that touches upon that issue (the one page preview is enough to understand what I mean but I will explain here too). The article says that the interpretation is messed up in this case. Let me use the example variables of the article to make it clear what I mean. Wage is my dependent variable. The independent variables are all dummies that can be grouped in:

educational attainment

E2 = bachelor (value 1 if bachelor's degree, 0 otherwise)

E3 = high school (value 1 if high school, 0 otherwise)

marital status

R1 = married/in relationship (value 1 if married, 0 otherwise)

R2 = divorced (value 1 if divorced, 0 otherwise)

R3 = single (value 1 if single, 0 otherwise)

sex

M = male (value 1 if male, 0 otherwise)

F = female (value 1 if female, 0 otherwise)

Now, to avoid the dummy trap I delete E3, R3 and F. My regression equation would then look like this:

wage = b0 + b1*E1 + b2*E2 + b3*R1 + b4*R2 + b5*M

The article states that the baseline to compare against would thus be a single female that went to high school and that would mess up interpreting the individual dummy coefficients. My questions:

1. Do I understand it correctly that it is indeed using several qualitative variables that have more than 2 categories (in this case educational attainment and marital status have each 3) that messes up the interpretation? I get that if I for example only used the marital status dummies (again excluding R3 to not face the dummy trap), I could easily state that married people (R1) earn more or less compared to single people (R3). But is this no longer possible as soon as I include the educational attainment dummies in my regression as well?
2. Are dummy variables that only have 2 categories and therefore are represented in the regression equation with 1 dummy only (e.g. my sex variable -> M in the equation) affected by this at all or could I still state that men earn more or less compared to females, despite having educational attainment and marital status in my equation?
• Velcome to the site! Commented May 19, 2014 at 12:03

One note- although you didn't ask about it, models for wage or income often use log(wage) for two reasons: 1) Models on wage often have non-normal residuals and 2) Changes in wage are often better conceptualized as multiplicative rather than additive. E.g. Going from a wage of \$10,000/year to \$20,000/year is not like going from \$100,000/year to \$110,000/year; it's more like going from \$100,000/year to \$200,000/year.