(See attached file for full problem description)
a. When the variance of the error term is constant you will have Vj(ε)=σ^2 for all j. For this problem, you can see that heteroskedasiticity exists because of the additional X3i term. In the presence of heteroskedasiticity OLS estimates of β are still unbiased and consistent, but are inefficient i.e., they are no longer the best linear unbiased estimators. In addition the usual estimators for the standard errors of least squares are biased, so the usual confidence intervals and test statistics are incorrect, and may lead to incorrect conclusions. Recall that OLS is designed to minimize Σei^2. It therefore gives more weight to the data points with potentially the largest error terms. For example, suppose you have two cases, where Y = 100 for the first case and Y = ...
Determining the existence of and overcoming possible problems of associated with heteroskedasticity