Homoskedastizität

Homoskedasticity refers to a statistical property where the variance of the errors or residuals in a regression model is constant across all levels of the independent variables. In simpler terms, the spread of the data points around the regression line is consistent throughout the entire range of the predictors. This is a crucial assumption in ordinary least squares (OLS) regression, as it ensures that the estimates of the regression coefficients are efficient and that the standard errors are unbiased.

The opposite of homoskedasticity is heteroskedasticity, where the variance of the errors is not constant. This often manifests as a funnel shape in residual plots, where the spread of residuals increases or decreases with the values of the independent variables. Heteroskedasticity does not bias the regression coefficients themselves, but it does lead to incorrect standard errors, which can affect hypothesis testing and confidence intervals.

To assess homoskedasticity, statistical tests like the Breusch-Pagan test or the White test can be employed. Visual inspection of residual plots is also a common method. If homoskedasticity is violated, methods such as weighted least squares (WLS) or robust standard errors can be used to address the issue and obtain reliable statistical inferences. Maintaining homoskedasticity is vital for the validity of many statistical analyses and the interpretation of their results.