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In my regression one of the control variables has high statistical significance. But when I check the correlation coefficient between this variable and the dependent variable the correlation is almost zero. What is the conclusion that I can derive of this event?

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  • $\begingroup$ Is correlation analysis appropriate for your data, in the first place? $\endgroup$ – Ayalew A. Mar 29 '15 at 12:55
  • $\begingroup$ Often correlation is checked first and then the variables are entered in multiple regression to see their independent association. It may sometimes happen that there is no significant correlation on univariate analysis but on correction by other factors in multiple regression, a significant association is found. $\endgroup$ – rnso Mar 29 '15 at 13:21
  • $\begingroup$ Thank you for your answer, Basically, my analysis is cross-sectional $\endgroup$ – Antonis Mar 29 '15 at 14:05
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Are you dealing with big data? If you are dealing with big data you may found no (little) correlation between the covariate and the dependent variable, but the estimated coefficient may be statistically significant (however the effect should be very small).

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  • $\begingroup$ Thank you for your answer. My analysis is cross-sectional with 75 countries and 10 variables. $\endgroup$ – Antonis Mar 29 '15 at 14:06
  • $\begingroup$ @Antonis: Please add this relevant point to the original post. I am curious to learn in what way your data set can be considered a random sample (basic assumption of your hypothesis test) and on what population (or mechanism) your inferences refer to. $\endgroup$ – Michael M Mar 29 '15 at 19:01
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The meaning is that the variable is not significant -unless- other factors in your regression are controlled for.

In the regression: $Y=b_1 x_1+b_2 x_2$

It is possible (and often the case) that simply running $Y=b x_2$ will retrieve nothing of significance, even if $b_2$ is highly significant. This can happen if $x_1$ has a correlation with both $x_2$ and $Y$.

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