What If the Disturbances Have Nonzero Expectations or Different Variances?
What If the Disturbances Have Nonzero Expectations or Different Variances?
This chapter shows that the εi's must have the same expected value for regression to make any sense. However, we cannot tell if the εi's have a constant expected value that is different from zero, and it does not make any substantive difference. If the disturbances have different variances, ordinary least squares (OLS) estimates are still unbiased. However, they are no longer best linear unbiased (BLU). In addition, the true variances of b and a are different from those given by the OLS variance formulas. In order to conduct inference, either we can estimate their true variances, or we may be able to get BLU estimators by transforming the data so that the transformed disturbances share the same variance.
Keywords: regression analysis, variance, standard deviations, ordinary least squares, best linear unbiased estimators
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