2. Show that if 1,...,n are i.i.d. N(0, 2 ), then in straight-line regression the least-squares estimates

2. Show that if 1,...,n are i.i.d. N(0, σ2

), then in straight-line regression the least-squares estimates of β0 and β1 are also the maximum likelihood estimates.

Hint: This problem is similar to the example in Sect. 5.9. The only difference is that in that section, Y1,...,Yn are independent N(μ, σ2), while in this exercise Y1,...,Yn are independent N(β0 + β1Xi, σ2

).