EC2020 Econometrics I: Christmas ProjectThis is the project for this module that counts 60%. All questions carry the same weight.The submission deadline is 3:00pm, Tuesday 12th of January 2021. Collusion and plagiarism will not betolerated, and punished ruthlessly according to the strict University regulations on academic integrity.1. Consider the following model:yi=α+βxi+i;i= 1,2,···,n(1)wherexiis fixed in repeated sampling, and the random disturbance termisatisfies the usualassumptions ofE(i) = 0∀iE(2i) =σ2∀iE(ij) = 0∀i6=jLet ˆαandˆβdenote the ordinary least squares (OLS) estimators ofαandβ, respectively. Thereis no need to derive the least squares estimators for this question. Also, let ˆyidenote the fittedvalue ofyiobtained by the least squares estimation.a) Show thatn∑i=1ˆyi=n∑i=1yi.(2)[30%]b) Show thatE[(ˆβ−β)] = 0where=1nn∑i=1i.(3)[30%]c) Find the covariance between ˆαandˆβ