Let e_i = Y_i - Y_i hat = Y_i - bo - b1*X_i, where bo and b1 are least-square estimators of β0 and β1.
(e_i is the "residual")
Consider simple linear regression.
Prove that Var(e_i) = σ^2 [1 -1/n - (X_i-X bar)^2 / ∑(X_i-X bar)^2].
Any help is appreciated!