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say I had a regression with

Y = dependent variable

X = independent variable

A = Control variable 1

B = Control variable 2

C = ( Potential ) Control variable 3.

I am wondering what the justification would be for including or excluding control variable 3 given that:

A is positively and significantly correlated with Y and X.

B is positively and significantly correlated with Y and X.

C is positively and significantly correlated with Y and X AND is negatively and significantly correlated with A AND is positively and significantly correlated with B.

Any help would be greatly appreciated!

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  • $\begingroup$ This is more-or-less the same question as your other one, right? $\endgroup$ – Adrian Keister Apr 21 at 19:01
  • $\begingroup$ Sort of, in my other question I say that "C" is not connected to the independent variable or dependent variable by either correlation or economic theory, whereas here I explicitly say it. Sorry if that's not the way to go about it on this forum, this is my first ever time using Stack Exchange $\endgroup$ – Spencer James Apr 21 at 19:25
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If you have prior reason to believe that X, A, and B all belong in the model (e.g. economic theory), then include them. Include a model with these three RHS variables as well as C. Then look at the magnitude of C's coefficient and its p-value. Remove C if it is not statistically significant and not economically significant (i.e. if the marginal effect of C on Y is negligible).

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  • $\begingroup$ Thanks dlnB. Perhaps, you may be able to help me with this slight extension too. Do you include a control variable if the only basis of doing so is that it is correlated significantly (negatively or positively) with other controls? What does this do in terms of explaining the variance of the dependent variable? $\endgroup$ – Spencer James Apr 21 at 16:40

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