Assume the following population model

y_i = ₀ + ₁x_i + u_i ,

where i = 1, 2, ..., N. Further assume that you estimate the following model based on a sample i = 1, 2, ..., n:

i = ^₀ + ^1x_i + u_i ,

(a) State the estimators for ^0 and ^1 and explain how you would estimate them (you don't need to algebraically derive the estimators, but if you do so it must be complete).

(b) Explain why ^0 and ^1 are different from 0 and 1.

(c) What assumptions do you need to obtain unbiased estimators of the regression coefficients?

(d) How would you estimate the error variance of the model, ^ 2 ?

(e) Under which additional condition are the variances of the coefficient estimators unbiased?

Assmne the following population model ya = #30 + 3112+ \"to, where 2' = 1, 2, N. Further assume that you estimate the following model based on a sample 1' = 1,2, ...,n: A A is = n+1r+a (a) State the estimators for 30 and IE1 and explain how you would estimate them (you don't need to algebraically derive the estimators, but if you do so it must be complete). (b) Explain Wily 30 and .31 are different from .30 and 51. (c) 'What assumptions do you need to obtain unbiased estimators of the regression coefcients? (d) How would you estimate the error variance of the model, 32'? (e) Under which additional condition are the variances of the coefcient estimators unbiased