The real question is "Does adding Indept_var2 into the model alter the relationship between Dept_var and Indept_var1?" I kind of separated this into two Parts (1) does it change the slope of Indept_var1? (2) Does it change the significant of Indept_var1? That is what I could come up to approach the "real question". Maybe there is a different (better) way to look at this. Thanks for your help. ... View more

Thanks PaigeMiler. It looks like the "Extra Sum of Squares Principle" compares the two models, not exact what I was asking. In My question, first I have a simple regression model Dep_var = Indept_var1 I can model this with glm and get the slope of Indept_var1, and a p value Then I can do another model with glm Dep_var = Indept_var1 + Indept_var2 I get the slope and p values of Indept_var1. Of course, I also solve that for Indept_var2 too, but that's not quite the concern here. I want to know if there is a statistical test to see if the slope and p values for Indept_var1 are different between the two models.   Thanks. ... View more