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Consider a simple linear regression with an interaction term:

$Y=b_0 + b_1X +b_2Z+b_3XZ$

where $X$ is continuous and $Z$ is a dummy.

I want to find out whether $X$ has a significant impact on $Y$ when $Z=1$

$b_3$ is negative and significant but $b_1$ is positive and not significant.

The total effect of $X$ on $Y$ when $Z=1$ (i.e. $b_1$ + $b_3$) is negative. How can I determine whether this total effect is significant or not?

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  • $\begingroup$ One thing you could do is to "center" the $Z$ variable such that it has a value of 0 where there was 1 before, that way you will get effect of $X$ and $Y$ for when $Z$=0 (and 1 before transformation). $\endgroup$ – user2974951 Jan 7 at 11:39
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You should use an F-test for the linear hypothesis $H_0: b_1 + b_3 = 0$. You can implement that test on R by using the command linearHypothesis from the car package.

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  • $\begingroup$ Thanks! I believe this is what is also called a Wald test? $\endgroup$ – user6441253 Jan 7 at 11:52
  • $\begingroup$ Almost. The Wald is fairly similar to the F-test but uses different distributional assumptions that make it not as high-powered as the F-test. In other words, the Wald test is less likely to reject the null than the F-test. $\endgroup$ – Romain Ferrali Jan 10 at 14:43

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