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I am sorry if my title is not very clear, here I will try to be specific about what I meant. My response variable in the regression model 'y' is a z-score calculated following some gold standard that is adjusted for age (so 'y' is not just a z-score but a z-score that accounts the age of the subjects as well). My question is when I run the regression to see the relationship between 'y' and an exposure (say 'x'), do I need to include age as a covariate in the model to adjust for? Would it be necessary? Any suggestion is highly appreciated! Thank you in advance!

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    $\begingroup$ In an answer at stats.stackexchange.com/a/46508/919, I perform precisely this operation and carefully analyze it algebraically and graphically. You might find a close study of the figures to be rewarding. $\endgroup$ – whuber Jan 18 '17 at 17:10
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    $\begingroup$ @whuber Thank you for referring to the thread. I will read it a few more times to have a better understanding. The explanation is very interesting and helped me to gain some understanding :)\ $\endgroup$ – curiousmind Jan 19 '17 at 16:23
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If your response (score y) is properly adjusted for age and you include age as predictor, you will find that age parameters are not significant in your model. If they were significant, it would mean that there are effects of age that have not been accounted for when adjusting y.

Therefore, what I would do is:

  • Adjusting a regression model with age as predictor (covariate).
  • Checking for significance of age parameters and interactions. That could be done comparing a model with age and a model without age in an F-test.
  • If age parameters aren't significant, discard them and adjust the model without age.
  • If age parameters are significant, rethink if y has actually been properly adjusted for age and decide if age should keep being included in the model.
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  • $\begingroup$ @Pete Thanks, Pete. I think this way of looking at the analysis makes sense. Thank you very much for your well-thought response! $\endgroup$ – curiousmind Jan 23 '17 at 15:42

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