Consider the Linear Regression Model

1. For any X = x, let Y = x + U, where R ^k .
2. X is exogenous
3. The probability model is {f(u; )is a distribution on R : E_f [U] = 0, Var_f [U] = 2 , > 0} .
4. Sampling model: {Yi} ⁿ _i=1 is an independent sample,where the U_i are a IID(0, ² ).

Let X be the n x k matrix of regressors, and let Y be the n x 1 vector of the dependent variable. 1. Compute BLs by minimizing (Y - XB) (Y - XB) , where B ERk. 2. Prove that BLS P B, V( B. ( ) ERk x R