申論題

7. Consider the simple linear regression model
Yᵢ = β₀ + β₁Xᵢ + εᵢ, Vᵢ = 1,2,...,n, and εᵢ's are i.i.d. N(0, σ²),
Show that the least squares estimators of parameters β₀ and β₁ satisfy
b₁ = ， and
b₀ =
whereare the sample means of the Xᵢ and Yᵢ observations,
respectively. (12%)