申論題

8. Given the following linear regression model: 
Υ₁ = β₁Χ₁+ εᵢ  where i = 1, 2, 3, ...., n

(1) Assume that the error terms εᵢ are independent N(0, σ²) and that σ² is known. State the likelihood function for the n sample observations on Y and obtain the maximum likelihood estimator of β₁. Is it the same as the least squares estimator of β₁? (10%)