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

Table of contents
- i d
  - Solution i
- ii d
  - Solution ii

i

Solution

The first column of the model matrix is the all-ones intercept column. Hence

A_{11} = \sum_{i, j} 1 = 100

.

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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