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Ability, quality of education, or quality of experience are assumed not to make any systematic difference to the predictions of the model. The story about the error term—that the ’s are independent and identically distributed from person to person in the data set—turns out to be critical for computing statistical significance. Discrimination cannot be proved by regression modeling unless statistical significance can be established, and statistical significance cannot be established unless conventional presuppositions are made about unobservable error terms.

You have to choose an act: That is the decision problem. Informally, if you choose the act f , and the state of nature happens to be s, you enjoy (or suffer) the consequence f (s). For example, if you bet on those horses, the payoff depends on the order in which they finish: The bet is an act, and the consequence depends on the state of nature. The set of possible states of nature, the set of possible consequences, and the set of possible acts are all viewed as fixed and known. You are supposed to have a transitive preference ordering on the acts, not just the consequences.

Handwaving is inadequate. We doubt the case could be made for the shelter example or any similar illustration. Nevertheless, reliance on imaginary populations is widespread. Indeed, regression models are commonly used to analyze convenience samples: As we show later, such analyses are often predicated on random sampling from imaginary populations. The rhetoric of imaginary populations is seductive precisely because it seems to free the investigator from the necessity of understanding how data were generated.

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