I have two independent variables (both categorical) and one dependent (categorical) variable. I want to look at the predictive factor or significance of those two independent variables (either separately or combined) on the dependent variable. Is logistic regression the test I need to use? What if I run this same test on three different groups?
Logistic regression is meant for continuous independent variables. The textbook approach in your case is to use a chi-squared test of independence. To omit a variable, just add together the cell counts for cells that differ only in the omitted variable.