What is heteroscedasticity?

Heteroscedasticity refers to a situation in regression analysis where the variance of the errors, or the residuals, is not constant across all levels of the independent variable. When the variance is unequal, it can lead to inefficiencies in the estimates, and potentially bias the results of hypothesis testing. This violates one of the assumptions of ordinary least squares (OLS) regression, which assumes that the residuals should have constant variance (homoscedasticity) regardless of the values of the independent variable.

The presence of heteroscedasticity can be detected through various methods, such as visual inspections using residual plots or statistical tests like the Breusch-Pagan test. Understanding and detecting heteroscedasticity is important as it can affect the reliability of regression coefficients and significance tests, which are foundational to making inferences in statistical modeling.