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I have several regressions in my bachelor's thesis about macro economics. In the first regression one particular coefficient was significant on the 5% level. Let's call the significant coefficient C1, with ic being the intercept.

$$ Y_t = ic_t + βC1_1 + ε_t $$ This significance went away as I added another term with a dummy variable in front of the same variable. $d$ is the dummy variable, and it is only equal to $1$ in $15$% of the observations.

$$ Y_t = ic_t + βC1_t + θd_t*C1_t + ε_t $$

How do I interpret that? I thought it should be interpreted as a type I error, but my supervisor said that it shouldn't be interpreted that way, and also said I shouldn't be talking about type I/II errors, without any further explanations as to why not. I had no opportunity to ask why not either.

So how is this loss of significance supposed to be interpreted?

Edit: I was referred to another topic below, however that topic deals with introducing a completely new variable. In my case I don't see how the interpretation can still be that "holding this constant..." etc, as I am introducing a term that is essentially the same variable just in different circumstances, when d is equal to 1.

Edit2: Again, the second topic I have been referred to and had this topic marked as identical to, does not answer this question.

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  • $\begingroup$ It is not a good idea to include an interaction without also including all the main effects (here you have left out $d$) unless you are sure you know what that model means. $\endgroup$
    – mdewey
    Commented Jan 3, 2018 at 13:34
  • $\begingroup$ Do you mean that I left out d in the first regression? $\endgroup$
    – Chisq
    Commented Jan 3, 2018 at 14:07
  • $\begingroup$ You should find the information you need in the linked threads. Please read them. If they aren't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know, don't just say they don't answer your question. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. Your question is very sparse. It's possible it is unclear & only looks the same as previous questions. Nonetheless, the answer to what your Q appears to be is in the linked threads. $\endgroup$
    – gung - Reinstate Monica
    Commented Jan 3, 2018 at 19:35
  • $\begingroup$ I have read them and explained why they are not the same. My question is about when adding a second term that is essentially the same variable but only calculated from 15% of observations. The first of those questions regards two completely different variables. The other question regards two different variables that in two simple LRM:s are significant but when put together in a multiple LRM are not significant anymore. $\endgroup$
    – Chisq
    Commented Jan 3, 2018 at 19:47
  • $\begingroup$ Whether the model is logistic regression or linear regression is irrelevant. The answer is the same. Whether the variable is a continuous / "completely different" variable or "essentially the same variable but only calculated from 15% of observations" is irrelevant. The answer is the same. $\endgroup$
    – gung - Reinstate Monica
    Commented Jan 3, 2018 at 21:35

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