Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 1 / 13J / i

Kilometres is an ordinal categorical variable: its five levels have a meaningful order. Treating it as an ordinary factor would use four indicator variables and hence four unrelated regression coefficients. Converting the levels to numerical scores instead imposes a single linear trend across successive mileage bands. This is more parsimonious and gives greater precision when that trend is a reasonable approximation, although it also assumes that adjacent levels are equally spaced in their effect.