This is nearly the same headline as my previous question, but it turned out I was asking about multiple issues. I still have not understood the more basic issues, which have to do with the interpretation of the intercept and the role of the reference category.
Let's say I do a regression (in this case, a logistic regression) with a single predictor, "color", a dummy coded categorical variable having three categories ("red", "blue", and "green"). The regression and results have two predictor variables, let's say "red" and "blue" with "green" as the omitted reference category.
In the results, the intercept is the log odds when "red" and "blue" are zero. But in that case, it's also the log odds when "green"=1.
The results have an intercept and a test of its significance. If the intercept is significant but the coefficients for "red" and "blue" are not, what does this say about:
the value "green" as a predictor of the outcome?
the categorical variable "color" as a predictor of the outcome?
(I have an inkling that the answers may depend on how perfectly "color" predicts the outcome, but I don't know how to talk about this.)
Thanks for your help with these elementary questions.