Answer-The logit model specifies P(Y=1|X) = Λ(Xβ). OLS is inappropriate for two fundamental reasons. Which...

Two core failures of OLS for binary outcomes 1 Heteroskedasticity VarX PX1PX varies with X violates homoskedasticity assumption. 2 Unbounded predictions OLS can give predicted probabilities 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.

Question

The logit model specifies P(Y=1|

X = Λ(Xβ). 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

B OLS is inconsistent for logit because: (1) binary Y produces heteroskedastic errors [Var(ε|X) = P(X)(1−P(X))], violating Gauss-Markov; AND (2) OLS predictions are not constrained to [0,1], making them theoretically incoherent as probabilities

C OLS cannot estimate logit because the log-likelihood has no closed-form solution

D OLS gives biased estimates because the logistic CDF is asymmetric while OLS assumes symmetric residuals

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