Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 5 / d / ii

Table of contents
- Solution ii

Solution

The second cross-product entry is

A_{12} = \sum_{i, j} X_{ij}

. Regressing earned on the ten person indicators without an intercept makes

(g_{x})_{i}

the mean of that person's ten earned values. Therefore

\sum_{i} (g_{x})_{i} = \frac{1}{10} \sum_{i, j} X_{ij} = 0.1 A_{12} .

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