Classical ML, validation, metrics, interpretation, debugging · insight-0173

Treat a funnel-shaped residual plot as a modelling decision, not cosmetic noise

Situation
Residuals versus fitted values widen as predictions grow, common for revenue, demand and claim size.
Action
Consider a log or variance-stabilizing transform, a loss and model suited to the variance pattern (for example Poisson or Tweedie for counts and amounts), and intervals that scale with the prediction.
Reason
Non-constant error variance violates the assumption behind ordinary least-squares inference and makes one interval width fit no one.
Boundary
Linear regression and other models whose uncertainty or inference matters.

Symptom or risk

Large-value segments dominate the loss; standard errors and constant-width intervals are wrong for small and large cases alike.

For point predictions evaluated by MAE alone, heteroscedasticity may be acceptable if errors by segment are tolerable.

Transforms help variance but complicate interpretation and back-transformation.

Judging the residual pattern on training data only; check held-out residuals too.

Non-constant error variance shows as a funnel shape in residual plots and can be addressed by transforming the response, such as log Y (ISL section 3.3.3).
An Introduction to Statistical Learning: with Applications in Python