Derive the least squares estimator of o for the regression model Y = Bo + . 2. Given the data (Xi) and (Y), we will

Derive the least squares estimator of ßo for the regression model Y₁ = Bo + ε₁. 2. Given the data (Xi) and (Y), we will assume that a regression model Y₁ = B₁X₁ + ₁ is appropriate with normally distributed independent error terms and variance ² 16. i X₁ Y₁ 1 7 128 2 12 3 4 25 30 213 446 540. 

(a) State the likelihood function for the four Y observations. 

(b) Evaluate the likelihood function for ₁ = 17 and ₁ = 19. For which of these is the likelihood function the largest? 

(c) Find the maximum likelihood estimates for ₁ and ßo and using Sxx, Sxy, and the means for Xi and Yi, respectively, as demonstrated in the instructional videos.