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I am familiar with how to interpret the regression coefficients on dummy categorical variables when one chooses a reference category by dropping it. However, how does one interpret the regression coefficients on each categorical variable when all categories are included (i.e. one dummy variable for each category) and the intercept is dropped?

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This depends on what other terms are in the model, but the simplest interpretation is that each dummy variable coefficient is the intercept for that group. For example if you have dummy variables for "Male" and "Female" and the other term in the model is age, then the coefficient for "Male" is the estimated value for males age 0 (or at the mean age if you center age around its mean) and the coefficient for "Female" is the estimated value for the females at age 0.

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  • $\begingroup$ Thanks, this makes sense. Unrelated question, if I may, how would one know if the mean age is centered at 0 or at its mean? This seems to be quite important for the interpretation of the d.v. coefficients. $\endgroup$ – StatsScared Aug 23 '16 at 22:30
  • $\begingroup$ @StatsScared, Usually you would remember if you centered, but if the data comes from someone else, they may have centered it. One simple way is to look at the data. Generally there are no negative ages, so if you see any negative values then the variable has had something subtracted from it, if not, then it has not been centered. If there is a chance that your software centers the predictor variables then you can either read the documentation to find out when it centers, or create a dataset with known values and analyze it to see whether it centered or not. $\endgroup$ – Greg Snow Aug 24 '16 at 15:58

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