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I am having some strange results in a regression I am trying to run and I hope someone can help me to interpret them. Basically, first I regressed my dependent variable on a set of regressors which were all significant, then I added a control and some of them became not significant anymore. So far so good, I explained it with an omitted variable bias. The problem is that when I add an interaction between two of the regressors the coefficients become significant again, while the interaction coefficient is not significant at all. How could this be explained? thank a lot for the help!!

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After you add an interaction term between variables $x_1$ and $x_2$ the meaning of the effects of $x_1$ and $x_2$ (the "main effects") changes: The effect of $x_1$ is now the effect of $x_1$ when $x_2$ is zero. Similarly, the effect of $x_2$ is the effect of $x_2$ when $x_1$ is zero. So it is not surprising that the coefficients and their significance changes when interaction effects are added, even if these interaction effects are not significant, especially if the value zero is an extreme value for those variables.

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    $\begingroup$ To add to this. Before adding interaction variables, center the variables so that $0$ becomes a typical value, and better, a value with some special meaning in the context---so that the estimated coefficients become interpretable! $\endgroup$ – kjetil b halvorsen Jun 10 '14 at 16:06

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