How to code and interpret a regression with 4-level categorical variable and continuous covariates I have a problem in which 4 groups of people are compared in their performance on a certain test. One way anova shows that they are in fact different. But I also know that my groups are different in some other covariate (e.g. age). I'd like to see that if those differences are still significant if I "adjust" for age etc. When I run a regression it shows me that one of the levels is "significant" but not 2 others (1 is a reference, I guess). Intercept is significant also, but it always is anyway. If I run the model withot the constant term, and with 3 dummy variables then all 3 are "significant". How do I interpret these results? Thanks.
 A: you should compare the performance of the total models based on e.g. F-test, adjusted R2, etc; e.g. with subset-selection-regresssion, not judge the "model fit" based on the significance of the individual components. i.e. - run a lm(y~.) on each model, and check the overall model performance - and then select the best model (running cross-validation recommended)
A: I agree with you re: the best-fit issue. You should include age in your model if you feel it might have an impact on your outcome variable (test score). It sounds like you do think this is a relevant variable, so you should leave it in the model.
I would interpret the result as follows:
-The significant intercept represents the expected score of a person who is 0 years old and in the reference group.
-The (significant, I assume) coefficient of age represents the expected unit increase in test score with each unit increase in age for a person in the reference group.
-The significant coefficient of one of your group variables represents the expected unit increase in test score holding age constant but moving from a person in your reference group to a person in the group this variable represents.
-The insignificant coefficients of your other group variables suggest that, for test-takers of a given age, there is no difference between members of the reference group and members of the group these variables represent.
Thus, I was saying that the group with the significant coefficient (in the full model including age) is significantly [better or worse] than the other groups when accounting for age. The other groups are not significantly different when accounting for age.
let me know if this helps 
