Is it possible to obtain a positive correlation between a regressor and a response (+0,43) and, after that, obtain a negative coefficient in the fitted regression model for this regressor?

I'm not talking about changes in the sign of the regressor among some models. The coefficient sign always remains.

Could the remaining variables of the fitted model influence the changing of the sign?


2 Answers 2


Both @Henry, and @JDav are pointing you in the right direction (+1 to each). However, I'm very visual and it helps me if I can see how this works. In that respect, here's a quick plot in which the first variable is confounded with group membership. If the groups are ignored, the correlation coefficient is positive (as can be seen in the figure), but in a multiple regression, $\beta_{x1}=-1$, albeit with different intercepts for the three groups. enter image description here
As further food for thought, when all variables are categorical (instead of continuous as in this case) the phenomenon of reversing the apparent relationship upon inclusion of other variables is known as Simpson's paradox. Since it's ultimately quite similar, it may help to read about that as well. It is discussed on CV here.

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    $\begingroup$ FWIW, I have a fuller treatment of essentially the same issue here: Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression? $\endgroup$ Commented Feb 3, 2014 at 23:51
  • $\begingroup$ Could this same pattern occur in the context of causal inference? $\endgroup$ Commented Sep 28, 2022 at 16:57
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    $\begingroup$ @GuilhermeParreira, of course. $\endgroup$ Commented Sep 28, 2022 at 17:17
  • $\begingroup$ I see. Now I understand why this occurs. But it is still challenging to present it for a business area. Ex.: I have a variable X (satisfaction score ) positively correlated to Y (NPS score), which makes sense. When I run a Lasso model, the beta is negative (due to other covariates). In either 'causation' or 'correlation', how could I explain that increasing satisfaction score would decrease NPS? (net promoting score, which is likely you would recommend my business to someone else?) How could I communicate this? Tks!! $\endgroup$ Commented Sep 28, 2022 at 21:25
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    $\begingroup$ @GuilhermeParreira, comments are not the place to ask questions. 1st read the linked thread above to help better understand the phenomenon. You will also want to read some of our threads on causal inference with observational data. If you still have a question afterwards, you should ask a new question. $\endgroup$ Commented Sep 28, 2022 at 21:54

If the positively-correlated regressor is the only regressor in a linear model then its coefficient should be positive.

If there are several regressors and they are not independent then you can see the effect you are asking about. Read about confounding for some explanation


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