I recently saw a paper that presented the results of a multiple regression, and then proceeded to also present the results from univariate regressions for the independent variables in which they were most interested.
The multiple regression already showed 4 significant independent variables (interactions were not considered), is it then legitimate to present, and interpret, results from univariate regressions for these variables?
I would particularly appreciate references to books or published articles that discuss this issue.
Thanks!
Best Answer
The wonderful book "Statistics as Principled Argument" by Robert Abelson doesn't discuss this particular question, but it does suggest the approach I take below. (I reviewed the book)
I would say "Sure!" The multiple and simple regressions answer different questions. The key is whether the questions are reasonable. Multiple regression asks about the relationship of several variables to a dependent variable, controlling for each other. Simple regression asks about the relationship between one IV and one DV.
Whether these questions are legitimate depends, in my view, not on whether some p is less than .05 but on whether the questions are reasonable and interesting.
The presence of interactions is a different matter, but even there, it doesn't depend on whether the interaction is significant but whether it is big.