Omitted Variables bias, comprehensive example and definitions
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Example, you want to understand the value of an NBA basketball player. You propose a model that considers three factors x=height, y=rebounding average per game, z=scoring average per game. You do a fit against all the players in the NBA and come up with best fit coefficients that go with these variables. Let’s presume you make no math mistakes.
Now someone asks you to do an omitted variable analysis where you just assess players according to only z. This could turn out to match your model’s coefficient for z pretty well, presuming that height and rebounding are independent from scoring.
But, if someone asks you to do that omitted variable analysis for x, you get a very different coefficient. That’s because height and rebounding are not unrelated, it turns out that tall players are significantly better rebounders than short players. This correlation means that your x analysis in biased incorrectly – and has produced the wrong coefficient.
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