What exactly does it mean when an effect for a variable is a linear combination of other effects? I understand that it's crucial to have an omitted reference dummy, but I don't understand why in a math sense. In a regression framework, an omitted reference is necessary so that comparisons can be made on the other dummies to that reference. But why would failing to have a reference group result in a "linear combination of other effects?" I guess I need some example or plain language here if possible.
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