# How do I interpret a coefficient of a dummy variable in regards to several categorical variables?

Let's assume we have a regression model with variable age and two categorical variables: education and gender.

1st categorical variable

• woman
• man

2nd categorical variable

• no qualification

• higher intermediate

Income = age + woman + higher-intermediate + graduate-or-more

How to interpret the coefficient for women? Is it the income difference between a woman and a man both with no qualification or is it the income difference between the woman compared to the man regardless of their education, if 1) how do I measure the latter?

• How many categorical variables are there? You seem to be indicating just two. Commented Mar 31, 2017 at 14:30
• I simplified in the example keeping only 2, does it change the principle if there are more than 2 ? Commented Mar 31, 2017 at 14:41
• I have found that it is easier to interpret the effects of categorical values if you don't dummy code them but instead indicate in the software that they are categorical (leaving the coding to the software). Then, instead of interpreting coefficients, look at and possibly test differences among means. The adjusted means may be called least squares means or estimated marginal means depending on the software. Most software will let you do Tukey hsd tests on theses means (in your case the three levels of Categorical variable 2). Commented Mar 31, 2017 at 14:53