Residual Plots & Non-linear Patterns – AP Statistics

The Math of Residuals

A residual is the vertical distance between an observed data point and the Least Squares Regression Line (LSRL).

$$ e = y - \hat{y} $$

Diagnosis via Residual Plots

Random Scatter: Linear model is appropriate.

U-Shape/Curve: Non-linear relationship (e.g. exponential or quadratic) present. LSRL is inappropriate!

Funnel/Fan-Shape: Non-constant variance (Heteroscedasticity).

Drag any cyan point on the top graph to magically pull the regression line and watch its red residual update real-time!