# OLS with categorical variables [duplicate]

1) When we omit the intercept, aren't we forcing the regression line through the origin? Does that pose any problem because we assume that there is no variable that affects the outcome other than the independent variables we have in the model? 2) Is it okay for the intercept to be significant in a regression model with categorical/dummy variables?

# the first question has been answered in another query as pointed out by a user.

• Say your model is based off of category A (IE Y ~ A). And say that A has 4 categories. Your model should look like Y ~ B0 +(A==1)B1 + (A==2)B2 + (A==3)B3. Where B# is the respective beta. The case when A is equal to the forth category is handled by the intercept. Does this help clarify your questions wrt categorical regression? If not, you should post an example so that I can better help. – Eric Oct 8 '14 at 16:51
• @Eric thanks. the first question has been answered. I just need clarification on the second one with valid references. Thanks. – DjJinn Oct 9 '14 at 6:34
• [Why would you expect references on what's essentially a trivial question? It's not like someone's going to publish a paper on an obvious consequence of the model formulation.] Yes, the intercept can be significant in a regression with dummies; the intercept represents the mean with all dummies at 0. It's perfectly okay in general for that mean not to be zero, as Eric already explained. – Glen_b Oct 9 '14 at 7:32

Q1: If you omit the intercept in univariate regression, you not only assume that no other (included) independent variable has an impact on the dependent variable – you also assume that the dependent variable is zero if the independent variable is zero. If the intercept of the true model is non-zero, doing OLS without the intercept induces potentially huge bias. It is in general preferable to include the coefficient for the intercept and see if it is significant, unless you are sure the specification really does not include the intercept.

Q2: Dummy variable is pretty much similar to any other independent variable. So the intercept may be significant in the presence of dummies. The issue is if all the observations had the same value for the dummy as then you would have perfect multicollinearity with the intercept – but again, this is an issue for any independent variable.

• I couldn't understand your explanation for the second question. My prof tells me that if intercept is significant, there might be a problem with the model. But since the intercept talks for base categories also, will not the intercept be significant if some of the base variables are significant? – DjJinn Oct 9 '14 at 6:37