Consider the following simple linear regression model: Y₁ =ᵝ₁ + ᵝ₂X₁ + U₁ a. Derive an expression for the OLS estimator ᵝ₂. [8 Marks] b. Show that ᵝ₂ is a linear function of Y₁. [4 Marks] c. Show that ᵝ₂ is a linear function of u₁. [4 Marks] d. Show that ᵝ₂ is an unbiased estimator of ᵝ₂. [4 Marks] e. Show that ᵝ₂ has minimum variance.