LO Page view A" Read aloud Question 3 (10 marks) Consider the simple linear regression model yi = Bo+ Birite i=1,...,n. 3 MA Uni Question 3 (10 marks) a) (2 marks). Using the fact that the maximum likelihood estimator (MLE) of regression model the normal equation: 3 = ( XT X)-1xTy. show that MLE in this case is given by the following equations, which may be familiar fro statistics classes: B1 = Li(di -x) (yi -y) _ Digi - nay Ex - nx2 Bo = y - BIZ. b) (1 marks). Consider we fit the model y = Bo + Bix using least squares. Unfortunately we not original data, (2;, y:), but we do have the following functions (statistics) of the data: y() = yi i= 1 II Cri - x)(yi - y), (yi - 1)2 n n i=1 n i=1 li=1 What are the minimal set of statistics that we need to estimate B1 ? c) (1 mark). What are the minimal set of statistics that we need to estimate Do