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      Question

      The logit model specifies P(Y=1|X) = ╬Ы(X╬▓). OLS is

      inappropriate for two fundamental reasons. Which correctly states BOTH?
      A OLS requires normality of errors and a linear functional form; both violated since logit errors follow a logistic distribution and the link is non-linear Correct Answer Incorrect Answer
      B OLS is inconsistent for logit because: (1) binary Y produces heteroskedastic errors [Var(╬╡|X) = P(X)(1тИТP(X))], violating Gauss-Markov; AND (2) OLS predictions are not constrained to [0,1], making them theoretically incoherent as probabilities Correct Answer Incorrect Answer
      C OLS cannot estimate logit because the log-likelihood has no closed-form solution Correct Answer Incorrect Answer
      D OLS gives biased estimates because the logistic CDF is asymmetric while OLS assumes symmetric residuals Correct Answer Incorrect Answer

      Solution

      Two core failures of OLS for binary outcomes: (1) Heteroskedasticity: Var(╬╡|X) = P(X)(1тИТP(X)) тАФ varies with X тЖТ violates homoskedasticity assumption. (2) Unbounded predictions: OLS can give predicted тАЬprobabilitiesтАЭ below 0 or above 1, which is theoretically invalid. MLE with the logistic link function resolves both: it respects the [0,1] constraint by construction and handles non-constant variance via the likelihood function.

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