In my linear regression, I am trying to see if there's an interaction between a categorical variable with more than 2 levels (CatVar) and another independent continuous variable (ConVar) . The problem is that the continuous variable has a quadratic relationship with the dependent variable.


When I check for interaction by
regress Outcome i.CatVar##c.ConVar##c.ConVar
"testparm" reveals that neither quadratic interaction (CatVar#c.ConVar#c.ConVar) or linear interaction term (CatVar#c.ConVar) is significant.


However, when I put the interaction term as i.CatVar##c.ConVar##c.ConVar in the whole regression model together with other variables, "testparm" reveals that only the quadratic interaction term (CatVar#c.ConVar#c.ConVar) is significant, while the linear interaction term (CatVar#c.ConVar) is non-signficant.

How can I interpret this? Is there an interaction effect at all? Or do I conclude that there is no interaction?