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

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- Solution a

Solution

Model1 is the simple linear regression

Y_{ij} = α + β X_{ij} + ε_{ij}, ε_{ij} \sim iid N (0, τ^{2}) .

Model2 is a random-intercept linear mixed model

Y_{ij} = α + β X_{ij} + b_{i} + ε_{ij}, b_{i} \sim iid N (0, σ^{2}), ε_{ij} \sim iid N (0, τ^{2}),

with the random intercepts and errors mutually independent.

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