= Solution
Let $h(q)=1$ for $q=0,3,6$ and $h(9)=2$. The new <normal linear model> allows an age-by-policy <interaction>:
$$
Y_{agpq}=\mu+\alpha_a+\delta_p+\kappa_{ap}+\gamma_g+\xi_{h(q)}+\varepsilon_{agpq},\qquad \varepsilon_{agpq}\overset{\mathrm{iid}}\sim N(0,\sigma^2).
$$
The <corner-point constraints> are $\alpha_{21}=\delta_{\mathrm{3rd}}=\gamma_F=\xi_1=0$ and $\kappa_{21,p}=\kappa_{a,\mathrm{3rd}}=0$. Compared with the six-parameter reduced additive model, there are two additional interaction coefficients. Its <F-test> gives
$$
\boxed{F=\frac{(22323-10028)/2}{10028/24}=14.7128,\qquad p\simeq6.75\times10^{-5}.}
$$
Thus the interaction model significantly improves the reduced additive model. Estimated premiums decrease with age. Men have an estimated premium $94.375$ higher than women at fixed other characteristics, and 9 points adds $41.708$ relative to 0, 3, or 6. Comprehensive cover costs more than third-party cover, but its increment depends on age: $175.375$ at 21, $148.500$ at 30, and $79.500$ at 40. These are model-based comparisons, including extrapolations into the unobserved age-gender combinations.
For a 40-year-old woman with comprehensive cover and 6 points, the gender and points contrasts vanish. The fitted premium is
$$
\boxed{269.760-207.812+175.375-95.875=141.448.}
$$
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