Basic Concepts
A key assumption in ordinary least squares (OLS) linear regression is the homogeneity of the variances (aka homoskedasticity). Suppose the variances of the residuals εi of an OLS regression are σi, i.e. var(εi) = σi2. When the homoskedasticity assumption is met, then there is a constant σ such that σi2 = σ for all i from 1 to n where n = the sample size. Heteroskedasticity is the absence of homoskedasticity.
The homoskedasticity assumption may be violated for a variety of reasons. E.g. if we are regressing non-essential spending for a family based on income, then we might expect more variability for richer families compared to poorer families.
Also, misspecification can cause heteroskedasticity. E.g. using a regression model that includes independent variables x1 and x2 but excludes x12 or x1 ⋅ x2 when one of these is relevant.
The following topics show how to test for heteroskedasticity.
Testing for Heteroskedasticity
Dealing with Heteroskedasticity
References
Wooldridge, J. M. (2013) Introductory econometrics, a modern approach (fifth edition). Cengage Learning
https://faculty.cengage.com/works/9781337558860
Williams, R. (2020) Heteroskedasticity
No longer available online
Statistical (2024) Introduction to heteroscedasticity
https://timeseriesreasoning.com/contents/introduction-to-heteroscedasticity