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True, False, or Uncertain. Please Provide Explanations!

(a) In a probit /logit model, the marginal effects of regressor j is defined as ΔP(Y=1|X)/ΔX_j . The marginal effect is dependent on X, and therefore, it is difficult to place a useful interpretation on Beta hat alone.

(b) As a simple diagnostic one can estimate OLS in data with a binary response variable, construct a histogram of the residuals, and compare their distribution to a normal or logistic to decide whether to use probit or logit.

(c) The major flaw of the linear probability model is that the actuals can only be 0 and 1, but the predicted are almost always different from that.

(d) The problem of whether being a female has an effect on earnings could be analyzed using probit and logit estimation (i.e. in a wage regression that includes a gender dummy, we use a probit model to analyze whether being a female has an effect on earnings).

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