Which statement about the linear probability model is correct?

• A. It assumes a nonlinear relationship between probability of default and factors.
• B. It assumes a linear relationship between probability of default and factors.
• C. It assumes the probability of default follows a logistic distribution.
• D. It assumes the probability of default has a cumulative normal distribution.

Answer: (B)

In the linear probability model, the probability of the event (default) is assumed to change linearly with the explanatory factors. In practical terms, the model posits P(Y=1|X) ≈ Xβ, so each predictor contributes a constant amount, βj, to the predicted probability when it changes by one unit (holding others fixed). This makes the relationship between the factors and the probability linear, which is why ordinary least squares is often used for estimation.

That linear structure is what sets LPM apart from alternatives like logistic or probit models. Those models apply nonlinear transformations to link the factors with probability (logit uses the logistic function for p, probit uses the normal CDF), which ensures predictions stay within the 0–1 range and implies a nonlinear relationship between X and p. The linear probability model does not assume a logistic or normal distribution for the outcome; it simply uses a straight-line approximation of P(Y=1|X). Because of that, predicted probabilities can fall outside [0,1] and the error term is heteroskedastic, but it remains a straightforward and interpretable baseline approach.