Question: Prove that in the model y 1 = X 1 1 + 1 , y 2 = X 2 2 +

Prove that in the model

y₁ = X₁β₁ + ε₁,

y₂ = X₂β₂ + ε₂,

generalized least squares is equivalent to equation-by-equation ordinary least squares if X₁ = X₂. Does your result hold if it is also known that β₁ = β₂?

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