What does a residual plot tell you?

A residual plot shows how a regression model's prediction errors behave across its predictions. It helps reveal systematic mistakes that a single metric such as MAE or RMSE may hide.

How to read the plot

In a typical residual-versus-fitted plot:

• Horizontal axis: the model's predicted values (ŷ).
• Vertical axis: residuals (actual − predicted).
• Zero line: observations the model predicted exactly.

A point above zero means the model underpredicted. A point below zero means it overpredicted.

Example: If a model predicts 80 but the actual value is 95, the residual is +15. That point appears at predicted value 80, above the zero line.

What the pattern tells you

• Random scatter around zero: no obvious systematic pattern; generally encouraging.
• Curved or U-shaped pattern: the model may be missing a nonlinear relationship.
• Funnel-shaped spread: error variability changes with predicted value, suggesting heteroscedasticity.
• Mostly positive or negative residuals in one region: consistent underprediction or overprediction there.
• Isolated extreme points: observations worth checking for data issues, unusual cases, or poor model fit.

What a residual plot cannot prove

A random-looking plot does not guarantee the model is correct or that all regression assumptions hold. Error independence, distributional assumptions, and performance on unseen data may require separate checks.

In short, a residual plot helps you see *where and how* a regression model makes errors. Ideally, residuals fluctuate around zero without a clear pattern or systematic change in spread.