Homoscedasticity
An assumption in regression analysis that the variance of the residuals is constant across all levels of the independent variables.
What is Homoscedasticity?
Homoscedasticity means that the spread or scatter of the model's errors remains uniform regardless of the predicted value. If the variance of the errors systematically increases or decreases as the predictor changes, the data exhibits heteroscedasticity (e.g., the data forms a cone shape on a scatterplot).
Why Homoscedasticity Matters
If this assumption is violated, ordinary least squares estimators remain unbiased, but their standard errors become incorrect. This leads to invalid p-values and confidence intervals, increasing the risk of false positives or false negatives.
Example
An economist models household food expenditure based on income. If high-income households have much wider variation in their food spending than low-income households, the model's residuals will violate homoscedasticity.
Common Mistakes
- Ignoring visual inspections of residual plots to check for homoscedasticity.
- Failing to apply robust standard errors or data transformations when heteroscedasticity is severely present.