6. Consider a simple linear regression equation: Yi = 0 + 1Xi + ui . Suppose we have a sample with n observations: (X1,Y1),(X2,Y2),...,(Xn,Yn) and would like to use the sample to obtain estimates of 0 and 1 using Ordinary Least Squares (OLS). Derive the OLS estimators 0 and 1. Note: we have gone through (most of) the derivation of OLS estimators in class (see lecture slides on Moodle). Therefore there are two things I expect you to do for this problem: (a) Repeat the steps we have done, making sure you understand the process (b) Complete the last step, i.e. show that 1 = n i=1 XiYinXY n i=1 X 2 i nX 2 = n i=1 (XiX)(YiY) n i=1 (XiX) 2 Hint: Prove that: the numerators are equal, i.e. n i=1 XiYi nXY = n i=1 (Xi X)(Yi Y), and the denominators are equal, i.e. n i=1 X 2 i nX 2 = n i=1 (Xi X) 2 For both of these proofs, the easiest way to proceed is to start with the right hand sides and use algebra to arrive at the left hand sides.