The linear probability model in credit scoring assumes which relationship between the probability of default and the input factors?

• A. It assumes a nonlinear relationship between the probability of default and factors.
• B. It assumes a linear relationship between the probability of default and factors.
• C. It assumes the probability of default follows a normal distribution.
• D. It assumes the probability of default is independent of input factors.

Answer: (B)

In a linear probability model, the probability of default given the predictors is expressed as a straight-line combination of those factors. Specifically, P(D=1|X) = β0 + β1 X1 + … + βk Xk. This means each input factor has a constant, additive effect on the probability: a one-unit change in a predictor changes the predicted probability by its coefficient, holding other factors fixed.

This setup makes estimation straightforward and the coefficients easy to interpret as percentage-point changes in default probability. But it also has drawbacks: predicted probabilities can fall below 0 or above 1, and the error variance is not constant because the outcome is binary. These issues are why logistic or probit models are often preferred, as they constrain predictions to the 0–1 range while modeling the relationship in a nonlinear way.