In class we mentioned for a simple linear regression model, the corresponding σ 2 is estimated as ˆσ 2 = pn i=1(yi − yˆi) 2 n − 2 . show the estimator is unbiased by following the steps below. (a) show that cov(yi , yˆi) = σ 2 [ 1 n + (xi−x) 2 sxx ]. (b) show that var(yi − yˆi) = σ 2 [1 − 1 n − (xi−x) 2 sxx ]. (c) show that e( pn i=1(yi − yˆi) 2 ) = (n − 2)σ 2 . hint: cov(ax + by, cw + dv ) = accov(x, w) + adcov(x, v ) + bccov(y, w) + bdcov(y, v ), where a, b, c, d are constants and x, y, w, v are random variables.