In linear regression, if I have dependent variable Y and independent variables A and B, where B has a quadratic relationship with Y, and I'm looking for a possible interaction between A and B, I would need to include interaction terms as both AB and AB2, right?

So, Y=A+B+B2+AB+AB2 rather than just Y=A+B+B2+AB or just Y=A+B+B2+AB2 ?

But what if in Y=A+B+B2+AB+AB2, AB turns out to be not significant (barely), but AB2 is significant?

How can I interpret this? Can I still say there's an interaction?


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