Homoscedasticity

In statistics, a sequence or a vector of random variables is homoscedastic /ˌhoʊmoʊskəˈdæstɪk/ if all random variables in the sequence or vector have the same finite variance. This is also known as homogeneity of variance. The complementary notion is called heteroscedasticity. The spellings homoskedasticity and heteroskedasticity are also frequently used.

The assumption of homoscedasticity simplifies mathematical and computational treatment. Serious violations in homoscedasticity (assuming a distribution of data is homoscedastic when in reality it is heteroscedastic /ˌhɛtəroʊskəˈdæstɪk/) may result in overestimating the goodness of fit as measured by the Pearson coefficient.

As used in describing simple linear regression analysis, one assumption of the fitted model (to ensure that the least-squares estimators are each a best linear unbiased estimator of the respective population parameters, by the Gauss–Markov theorem) is that the standard deviations of the error terms are constant and do not depend on the x-value. Consequently, each probability distribution for y (response variable) has the same standard deviation regardless of the x-value (predictor). In short, this assumption is homoscedasticity. Homoscedasticity is not required for the estimates to be unbiased, consistent, and asymptotically normal.

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