The subsets of {1,2} are Φ, {1}, {2} and {1,2}. So there are four possible potential models when deciding on a regression with a choice of inputs from a dataset containing two potential input variables. Your friend tells you this is nonsense and there are three possible models because the empty set Φ is just an imaginary concept concocted by some mathematician. What should you say to your friend? You should explain that the empty set corresponds to the model y = β + ε, where β is some constant and ε is a residual term. In this model, the output predictions are always equal to the output's sample average. You should explain that the empty set corresponds to the model y = ε, where ε is a residual term. In this model, the output predictions are totally random. You should indeed agree. Your friend is spot on and one cannot have a regression with no input variables. You should partially agree. Your friend is spot on that there are three models and not 4. We add Φ only because we need to follow what set theory says.
The subsets of {1,2} are Φ, {1}, {2} and {1,2}. So there are four possible potential models when deciding on a regression with a choice of inputs from a dataset containing two potential input variables. Your friend tells you this is nonsense and there are three possible models because the empty set Φ is just an imaginary concept concocted by some mathematician. What should you say to your friend?
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You should explain that the empty set corresponds to the model y = β + ε, where β is some constant and ε is a residual term. In this model, the output predictions are always equal to the output's sample average. |
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You should explain that the empty set corresponds to the model y = ε, where ε is a residual term. In this model, the output predictions are totally random. |
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You should indeed agree. Your friend is spot on and one cannot have a regression with no input variables. |
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You should partially agree. Your friend is spot on that there are three models and not 4. We add Φ only because we need to follow what set theory says. |
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