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>"Let's ignore the interaction term for the sake of simplicity. It doesn't change anything in what follows."

It changes the estimates if you don't assume the interaction coefficient = 0, how can you just ignore it? Actually, not assuming zero interaction changes everything: https://en.wikipedia.org/wiki/Principle_of_marginality



For the purpose of getting intuition about setting levels, it doesn't change anything. Obviously for what you actually fit, it matters.




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