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Interpreting dummy variables and the dummy-variable trap

You have a categorical regressor, sector, with four levels (Tech, Energy, Financials, Healthcare), and you encode it with 0/10/1 dummy variables in a regression with an intercept.

How do you interpret each dummy's coefficient, and why can you not include a dummy for every level alongside the intercept?

Show a hint

If you add up all four "one per level" dummies, what do you get for every single row?

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

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