 Residual-versus-fitted plot

A residual-versus-fitted plot displays residuals vertically against predicted responses horizontally. Curvature suggests an incorrect conditional-mean model; a fan-shaped spread suggests heteroscedasticity, while isolated large residuals may indicate unusual observations. It does not alone measure leverage or influence: regression leverage records unusual predictor combinations, and Cook's distance combines leverage and residual size.

The figure in coefficient of determination shows why the plot is useful: subtracting the fitted linear trend makes a small curved component easy to see. A visible pattern supplies a reason to investigate the model, while the absence of a pattern in a small sample does not establish that all assumptions hold. Other views address other questions: regression residuals against observation order can reveal temporal dependence, and a normal probability plot examines distributional shape. NIST's statistical handbook develops this use of graphical residual analysis for model validation. ^[ref]