Consider a problem of simple linear regression, and let ei = denote the residual of the observation

Question:

Consider a problem of simple linear regression, and let ei = denote the residual of the observation Yi (i = 1, . . . , n), as defined in Definition 11.3.2. Evaluate Var(ei) for given values of X1, . . . , Xn, and show that it is a decreasing function of the distance between xi and .