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Say, i do a regression with one independent variable only even though there are more relevant variables that influence the dependent variable [omitted variable bias (ovb)].

It makes sense to me that a correlation might be detected which actually doesnt "exist" since it is caused by a third hidden variable.

Question:

Is it also possible that low/no correlation is indicated by the "OVB-regression" for the single independent variable, but there is actually a correlation which was not detected? --> So the "ovb" would decrease the (absolute) correlation.

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  • $\begingroup$ Your question is so vague I cannot tell what you are asking, except to guess it likely has some good answers already because we have a larger variety of threads concerning how regression coefficients and $R^2$ change as variables are added or dropped to the model. Could you clarify what you are looking for? $\endgroup$
    – whuber ♦
    Commented Oct 14, 2019 at 21:09
  • $\begingroup$ I am sry about that. I give it another try: Question is: I run a regression with ovb and the correlation between dependent and independent variable is close to zero. Could it be the case that the (absolute) correlation is actually way higher and biased close to zero due to the ovb? $\endgroup$
    – BigDataScientist
    Commented Oct 14, 2019 at 21:20
  • $\begingroup$ It's unclear what "correlation" means in this context, which hypothesizes several different regression models. Let me see whether I understand, by putting the situation a little differently: you run a regression of $Y$ against $X_1$ and obtain a small coefficient. Now you add another explanatory variable $X_2$ and regress $Y$ against $X_1$ and $X_2:$ are you asking whether the slope of $X_1$ can increase in size? $\endgroup$
    – whuber ♦
    Commented Oct 14, 2019 at 21:24
  • $\begingroup$ I didnt give it enough thought. I understand your question concerning correlation vs slope. "are you asking whether the slope of X1 can increase in size?" Yes, i think that would be the better question. $\endgroup$
    – BigDataScientist
    Commented Oct 14, 2019 at 21:39
  • $\begingroup$ Here's a search that might help you: stats.stackexchange.com/…. I posted an example of this phenomenon at stats.stackexchange.com/a/32237/919. $\endgroup$
    – whuber ♦
    Commented Oct 14, 2019 at 21:45

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