# Is it legitimate to present results from univariate and multiple regressions?

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!

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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.

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I agree that legitimacy depends on whether the 'questions are reasonable and interesting' but it also depends on the sampling scheme, e.g. if Y was generated by fixing (or sampling with fixed proportions) X and observing (or randomly sampling) Z and then observing Y, then regressing Y on X makes sense but regressing Y on Z doesn't, in the sense that the parameter in the first case tracks an actual effect but in the second case tracks some sampling scheme-specific average that generally won't make sense outside the analysis. –  conjugateprior Apr 20 '12 at 11:26
I agree with this as well. –  Peter Flom Apr 20 '12 at 14:03
Thanks for these comments and the reference. My main concern was more about the fact that if multiple IVs have been found to explain the variation observed in the DV, then looking just at the relationship between one IV and the DV seems to me to be ignoring the important effects of the other IVs that were uncovered by the multiple regression. I imagine that I am misunderstanding something here. –  OliP Apr 23 '12 at 12:18
@Peter Flom I think that these references address my concerns quite well: (goo.gl/eVOZt) (ctspedia.org/wiki/pub/CTSpedia/EducationalMaterials044/…) The second reference implies to me that univariate regression is really only appropriate when a multiple regression is found to have no greater explanatory power. The points made in the first reference seem to me less to do with the appropriateness of the approach, and more about data and model checking. –  OliP Apr 23 '12 at 19:25
I've since realised that one reason I was unable to find much information on this issue was that I was searching for information on "univariate" versus multiple regressions, when I more properly should have called the one independent variable regression a "simple regression". I have since found the following paper (and a lot more besides) that answers my query: (circ.ahajournals.org/content/117/13/1732.full). Essentially, simple regressions can be very misleading if there are multiple IVs and they are even a little bit correlated. –  OliP May 1 '12 at 17:22
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