A regression model predicting sales revenue from company size produces accurate, tightly clustered predictions for small companies and much more widely scattered, less accurate predictions for large companies — a pattern called heteroskedasticity, where a regression's prediction errors don't have consistent variance across the range of the data, violating one of the standard assumptions behind ordinary regression's statistical inference.
What the underlying assumption actually requires
Standard regression analysis assumes homoskedasticity — that the variance of prediction errors is roughly constant across the full range of predicted values, meaning the model should be about equally accurate (or equally inaccurate) regardless of where in the range of the independent variable a given prediction falls. Heteroskedasticity is the violation of this assumption: errors that are small and consistent in one part of the range and considerably larger and more variable in another part.
Why this doesn't necessarily bias the coefficients themselves
A specific, somewhat reassuring nuance: heteroskedasticity, on its own, doesn't generally bias the estimated coefficients in a standard regression — the estimated relationship between the independent and dependent variable can remain a reasonable, unbiased estimate of the true average relationship even when heteroskedasticity is present. What heteroskedasticity does damage is the standard errors calculated for those coefficients, and therefore any confidence intervals or statistical significance tests built on those standard errors, which can end up too small, too large, or simply unreliable depending on the specific pattern of unequal variance present.
Why this specifically matters for practical decision-making
A model with heteroskedasticity affecting large accounts specifically will tend to understate the genuine uncertainty in its predictions for those large accounts, if the standard, unadjusted confidence intervals are used and reported as though the homoskedasticity assumption held throughout — meaning decisions relying on those confidence intervals for large accounts specifically are working from an unreliable, likely overconfident sense of the model's actual precision in that part of the range.
How heteroskedasticity is actually detected
Plotting a regression's residuals (the differences between predicted and actual values) against the predicted values or against the independent variable directly is the most straightforward diagnostic check, since a genuine heteroskedasticity pattern typically shows up visually as a distinctive fan or cone shape, with the spread of residuals widening or narrowing systematically across the range, rather than remaining a consistent, even scatter throughout.
What actually corrects for this once detected
Robust standard errors — a family of statistical adjustments specifically designed to produce valid standard errors and confidence intervals even when heteroskedasticity is present, without requiring the underlying data to be transformed or the model to be fundamentally changed — are the standard, widely available practical fix, and are now routinely available as an option in most statistical software. Weighted least squares regression, which explicitly accounts for unequal error variance in how the model itself is estimated, is a more involved alternative used when the specific pattern of heteroskedasticity is well understood and can be modeled directly.
What this means for building and reporting regression results
- Check a residual plot for a fan or cone-shaped pattern before trusting standard confidence intervals and significance tests from a regression
- Use robust standard errors as a standard practice when heteroskedasticity is detected, or as a routine precaution generally, since the cost of applying them when not strictly needed is low
- Be specifically cautious of precise-looking confidence intervals for predictions in parts of the data range where errors appear to fan out wider in the residual plot
- Remember that heteroskedasticity primarily threatens inference (standard errors, confidence intervals, significance), not necessarily the coefficient estimates themselves
Heteroskedasticity is a common, usually manageable issue rather than a fatal flaw in a regression model — the risk lies specifically in reporting or trusting confidence intervals and significance tests calculated as though the assumption held, when a quick residual plot would have revealed it didn't.