Consider a model for whether a person has ever smoked. Let P=Pr(Y = 1) be the
probability that a person has ever smoked and assume the logit model is given by
log[P/(1-P)] = α(1-X) + βX
where 1-P is Pr(Y = 0) (never smoked) and X is a dummy variable that is 1 if the person
is female and zero if male.
(i) If your prior expectations are that males are more likely to smoke than females
and that both males and females have a less than 50% chance of ever smoking,
what would you expect about the values of α and β?
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