Using summation notation, derive the expression for the variance of the OLS estimator

when the error is heteroskedastic (VAR( u i ) = ?i^2 ), but all other SLR assumptions hold.

Explain each step of the derivation, and cite each necessary assumption. Will this

variance term necessarily be larger than that for a homoscedastic error OLS model?

Explain.

all other SLR assumptions:

Assumption SLR. 1 Linear in Parameters In the population model, the dependent variable, y, is related to the independent variable, x, and the error (or disturbance), u, as y = Bot Bux+ U. [2.47] where Bo and B, are the population intercept and slope parameters, respectively.Assumption SLR.2 Random Sampling We have a random sample of size n, { (; );): / = 1, 2, .... n}, following the population model in equation (2.47).Assumption SLR.3 Sample Variation in the Explanatory Variable The sample outcomes on x, namely, {x; / = 1, .. ., n}, are not all the same value.Assumption SLR.4 Zero Conditional Mean The error u has an expected value of zero given any value of the explanatory variable. In other words, E(ulx) = 0