Heteroscedasticity
A condition in statistics where the variance of the errors (residuals) is not constant across all levels of the independent variable.
What is Heteroscedasticity?
In regression analysis, heteroscedasticity occurs when the spread or dispersion of the residuals changes as the fitted values change. It violates the classical assumption of Ordinary Least Squares (OLS) regression known as homoscedasticity.
Why Heteroscedasticity Matters
If residuals are heteroscedastic, OLS estimators remain unbiased, but they are no longer the most efficient (minimum variance). More importantly, the standard errors become biased, which makes hypothesis tests (like t-tests and F-tests) and confidence intervals invalid.
How to Interpret
Usually detected using residual plots (looking for a funnel shape) or formal tests like the Breusch-Pagan or White test.
Example
Predicting household consumption based on income. Low-income households have very consistent (low variance) consumption because they must spend on necessities. High-income households have high variance in consumption—some save a lot, some spend a lot. The error variance increases with income.
Common Mistakes
- Ignoring heteroscedasticity and reporting standard OLS p-values, which might be artificially low or high.
- Confusing heteroscedasticity with autocorrelation.