Consider the linear regression model with deterministic regr

Consider the linear regression model (with deterministic regressors) y_i=beta_1+beta_2x_i+ ~(0,alpha^2) i.i.d., i=1,...,n. Let be he OLS estimator of beta=(beta_1,beta_2)\', and be another estimator of beta_1 Is the estimator unbiased? Which of the estimators would you prefer for estimating beta?

Solution

i)

yes it is unbiased because B1 is the slope of the regresssion and expected value of \"Y\"

ii)

I would prefer B1 with ^ because it the best estimator for the estimating Betha