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In my model I want to include two dummies ($d_1$,$d_2$) and also the interaction effects of these two dummies with another independent variable, $x_1$. The interaction terms are $x_1\cdot d_1$,$x_1 \cdot d_2$. The model also includes six other independent variables.

I run the model with all variables. Could I consider the interaction terms ($x_1 \cdot d_1$ and $x_1 \cdot d_2$) reliable if I find each of $x_1$, $d_1$, $d_2$ variables statistically significant but their interaction terms $x_1 \cdot d_1$, $x_1 \cdot d_2$ not statistically significant? In addition, if I find these results should I remove the interaction terms from the model? Since there is no reason to use them.

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    $\begingroup$ Why do you say there is no reason to use them? Is it because they are not statistically significant? Since why would you have included them in the first place if there was no reason to use them? In general, removing insignificant regressors is not a trivial question. See e.g. here. $\endgroup$ Mar 7, 2015 at 14:37
  • $\begingroup$ Thank you for your answer.Yes, because they are no significant. I understand what you mean but since they are not significant i can't see any reason to keep them in my model and affecting also the other results. Any idea about the other part of my questio? $\endgroup$
    – Ant
    Mar 7, 2015 at 15:43
  • $\begingroup$ Other part of the question -- whether the interaction terms are reliable? If they are not statistically significant, that means you do not have enough evidence that the effect is not equal to zero. If you had a larger sample, perhaps they would have turned statistically significant, but you cannot tell that now given the current sample. Meanwhile, is the coefficient economically significant? Is it large? If so, you may still care even though statistical significance cannot be established in this sample. Think about effect size. $\endgroup$ Mar 7, 2015 at 15:58
  • $\begingroup$ Thank you again, now it is clear. Only one point makes me confused. It is about the interaction term. The interaction term is the product of one dummy variable and one independent variable. Let's suppose that both are statistical insignificant but the interaction term (their product) it is statistical significant. Is it matter or not? Because you say that I have only to see whether or not the interaction term is statistical significant or not. $\endgroup$
    – Ant
    Mar 7, 2015 at 17:07
  • $\begingroup$ You should distinguish two stages. In the first stage, you create your variables (you already have simple variables so you only have to add the interaction terms). You could name them by different letters to hide that they are related by construction. From now on you have a regular multiple regression (forget how the variables were constructed). In the second stage, you estimate your model. Does it confuse you from the statistical perspective that variable $A$ is insignificant while variable is $B$ is significant? Normally, no. No recall how those variables were constructed. $\endgroup$ Mar 7, 2015 at 17:26

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