Should an interaction without main effects be significant if the interaction term is significant in the model with main effects? I have continues variable and dummy variable that takes the value of 1 if the value in continues variable is above the threshold and 0 otherwise. I include the interaction between these two (corr is 0.5, VIF is less than 1.5) which is statistically significant. However, without main effects, the interaction term is not significant. Do I have a problem here?
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