Homoscedasticity

Homoscedasticity refers to the assumption in statistics and regression analysis that the variance of the errors, or residuals, of the model are constant across all levels of the independent variables. This assumption is fundamental in linear regression models and is used to make statistical inferences about the parameters of the model.

Overview

In a statistical model, homoscedasticity implies that the variance of the error term, or the "noise" in the model, is constant across all levels of the independent variables. This is an important assumption in ordinary least squares (OLS) regression, as it ensures that the estimated coefficients of the regression model are the best linear unbiased estimators (BLUE).

If the variance of the errors is not constant across all levels of the independent variables, the model is said to exhibit heteroscedasticity. Heteroscedasticity can lead to inefficient parameter estimates and can invalidate statistical tests of significance.

Testing for Homoscedasticity

Several statistical tests exist for testing the assumption of homoscedasticity. These include the Breusch-Pagan test, the White test, and the Goldfeld-Quandt test. These tests generally involve regressing the squared residuals from the model on a set of explanatory variables and testing whether the explanatory variables are statistically significant.

Implications of Violating the Assumption

Violating the assumption of homoscedasticity does not cause bias in the coefficient estimates of a regression model, but it does make them inefficient. This means that the estimates are not the most precise estimates that could be obtained from the data. In addition, heteroscedasticity can lead to incorrect standard errors, which can in turn lead to incorrect conclusions about the statistical significance of the coefficients.

Remedies for Heteroscedasticity

If a model exhibits heteroscedasticity, several remedies are available. These include transforming the dependent variable (e.g., by taking its logarithm), using a different estimation method (e.g., weighted least squares), or using robust standard errors.

See Also

• Breusch-Pagan test
• White test
• Goldfeld-Quandt test
• Ordinary least squares
• Weighted least squares
• Heteroscedasticity