I am running two models: one ANOVA-like model where I use dummy-coded variables for three of the four categories used, and the other an ANCOVA-like model where I add a continuous covariate in addition to these dummy-coded predictors. I am getting means for the various groups by adding the coefficient for a given group to the intercept term. This works well for the model without the covariate, but in the model with the covariate I am getting adjusted means that are outside the range of possible scores for the dependent variable. Am I doing something wrong, or is this what should be happening?
Using your example, I assume you have 4 groups and the 3 group variables that you mention are 0/1 dummy scored where only one of them has a value 1 while the others are 0, and when all 3 are zero this refers to the 4th group. I also assume that test_age is continuous. Then what I meant was that the mean of heightav for group j (j=1 or 2 or 3) is
where betaj is the slope for heightav ON groupj and beta is the slope for heightav ON test_age.