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Extending my previous question ( Multiple regression with correlated variables ), can I do multiple regression with height, weight, waist, BMI (body mass index) and BSA (body surface area) as predictor variables on a health variable (yvar) in a large data set (N=about 7000)? Obviously, BMI and BSA are derived from height and weight, but I want to find out if correlation is greater for BMI or BSA (so that they may be better to use for prediction) than for height and weight. Will the results be valid or is there some major limitation?

Edit: The regression runs without any error and shows that height, weight and BSA are significant predictors of yvar but waist and BMI are not significant predictors.

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  • $\begingroup$ Have you tried to run it? Unless I'm missing something, it sounds like you'll get an error saying that BMI is a (perfect) linear combination of other predictors included in your model (I don't know what BSA is) $\endgroup$ – Patrick Coulombe Jan 30 '15 at 17:41
  • $\begingroup$ BSA is body surface area (also derived from height and weight). The regression runs without any error and shows that height, weight and BSA are significant predictors of yvar but BMI is not a significant predictor. $\endgroup$ – rnso Jan 30 '15 at 17:49
  • $\begingroup$ Right, @AK12's comment about the BMI term being something of an interaction term is a nice way to phrase it, I was mistaken in thinking it wouldn't run. $\endgroup$ – Patrick Coulombe Jan 30 '15 at 18:56
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Assuming multicollinearity is not an issue (from the answer to your previous question), BMI and/or BSA will effectively serve as an interaction(s) between height and weight in your model, because they both incorporate height and weight into their calculations. So, does the effect of height on your health variable depend on weight (or vice-versa)? If BMI and/or BSA are significant predictors, then the answer yes.

I would still be concerned about multicollinearity in your model if you include both BMI and BSA at the same time, but as the answer to your previous question mentions, you may have enough data to make this a non-issue.

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