Please solve these problems.

Assume that the data y is generated according to the following model, it; = 31:81 + 52:82 + 6', where y, 5, 1:3- 6 {n and list E R forj = 1,2. Assume that E N N(0,21n) and 1 \"will\" = Ilwtllz = it {$1,932}: at, and n = 10. Suppose that we mistakenly pose and t the regression model 3; M 7:81. That is, we compute the LSE estiamte 3 = argmin Ily \"wall? 1-613 and form the ttedvalue vector ft = $321 and the residual vector e = y $31. Answer the following questions. Justify all your answers. (a) For each of the following vectors, determine whether 3 is guaranteed to be orthogonal to it or not: $1) $21 '3': 1:1 +11 (13] Is a unbiased for estimating 61? (c) Find the variance of i (d) Find the joint distribution of lll . e