Assumption of Homogeneity of variance

Question

Why is assumption of Homogeneity of variance required. What are the problems if they are not satisfied

duplicates: https://stats.stackexchange.com/questions/81914/why-is-homogeneity-of-variance-so-important?rq=1 https://stats.stackexchange.com/questions/349619/how-is-homogeneity-of-variances-in-residuals-a-requirement-for-anova-when-anova?rq=1 https://stats.stackexchange.com/questions/8955/advice-on-explaining-heterogeneity-heteroscedasticty https://stats.stackexchange.com/questions/97098/practically-speaking-how-do-people-handle-anova-when-the-data-doesnt-quite-mee — kjetil b halvorsen, Nov 12 '20 at 14:53

score 0 · Answer 1 · answered Nov 12 '20 at 14:10

To answer your question, I quote an educational source:

Heteroskedasticity has serious consequences for the OLS estimator. Although the OLS estimator remains unbiased, the estimated SE is wrong. Because of this, confidence intervals and hypotheses tests cannot be relied on. In addition, the OLS estimator is no longer BLUE. If the form of the heteroskedasticity is known, it can be corrected (via appropriate transformation of the data) and the resulting estimator, generalized least squares (GLS), can be shown to be BLUE. This chapter is devoted to explaining these points.

So in summary, heteroskedasticity can result in loss of precision in variance estimation (and associated test based thereon), and while the ordinary Least-Squares point estimates remain unbiased, they are no longer considered to belong to the class of best linear unbiased estimates.

Assumption of Homogeneity of variance

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