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

Let $Y_{agpq}$ be the premium at age $a\in \{21,30,40\}$, gender $g\in \{F,M\}$, policy $p\in \{3rd,\mathrm{comp}\}$, and points $q\in \{0,3,6,9\}$, for the combinations actually observed. The additive normal linear model isIts corner-point constraints are ${\alpha }_{21}={\gamma }_F={\delta }_{3rd}={\eta }_0=0$. Thus $\mu$ is the reference-category mean; the other coefficients are additive contrasts. The model assumes a common variance and excludes all interactions. It has $1+2+1+1+3=8$ estimable mean parameters and $32-8=24$ residual degrees of freedom. The variance estimate is