Homoscedasticity and heteroscedasticity

Uncommon card · No. 131424

In statistics, a sequence of random variables is homoscedastic () if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The term originates from the Ancient Greek σκεδάννυμι skedánnymi, 'to scatter'. Assuming a variable is homoscedastic when in reality it is heteroscedastic () results in unbiased but inefficient point estimates and in biased estimates of standard errors, and may result in overestimating the goodness of fit as measured by the Pearson coefficient. The existence of heteroscedasticity is a major concern in regression analysis and the analysis of variance, as it invalidates statistical tests of significance which assume that the modelling errors all have the same variance. While the ordinary least squares (OLS) estimator is still unbiased in the presence of heteroscedasticity, it is inefficient and inference based on the assumption...

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