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Q113Section III (Statistics)113 of 145

Reading "se(β^,γ^)\mathrm{se}(\hat\beta,\hat\gamma)" as the s.e. of β^γ^\hat\beta\hat\gamma (delta method)

Consider log⁡yi=α+βxi+γzi+εi\log y_i=\alpha+\beta x_i+\gamma z_i+\varepsilon_i with β^=1.5\hat\beta=1.5, se(β^)=0.75\mathrm{se}(\hat\beta)=0.75, γ^=4\hat\gamma=4, se(γ^)=0.75\mathrm{se}(\hat\gamma)=0.75 and Cov⁡(β^,γ^)=0.2\operatorname{Cov}(\hat\beta,\hat\gamma)=0.2. What will be se(β^,γ^)\mathrm{se}(\hat\beta,\hat\gamma)?

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