Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 37 / 2 / a / Solution

The data do not cross every age with every gender: only age 21 has both genders, while age 30 has only women and age 40 only men. Thus a gender effect separate from age can be estimated under an additive model, but age-by-gender interactions cannot all be estimated or checked. There is only one observation in each recorded combination of age, gender, policy, and points, so there is no within-cell replication for separating pure error from lack of fit. No sampling method or additional risk characteristics are supplied, limiting comparisons between policyholder categories.

There is also a source discrepancy: the printed table gives $268$ for one comprehensive premium, whereas the R data vector gives $368$ at the corresponding position. The supplied regression output is treated as referring to the R data. This should be resolved against the original data before substantive use.