Separate a model from its residuals

The idea

A straight-line model represents a relationship with an intercept and slope. Observations usually depart from that line. Those departures are not merely annoyances: their pattern can reveal omitted conditions, nonlinear relationships, or a poor description of the problem.

Worked example

A garden club models water use as 20 liters per day plus three liters for each additional planting bed. At ten beds the model predicts 50 liters. Actual use is 65 liters during a heat wave, leaving a residual of 15 liters. The club does not immediately declare the caretaker wasteful. It records temperature and soil conditions, then asks whether unusually hot days systematically produce positive residuals. The unexplained difference becomes a question for investigation.

Use it carefully

A useful prediction rule need not identify a causal effect. Adding one bed may also change staffing, crop mix, and watering equipment. Extending the line far beyond observed garden sizes may produce implausible forecasts. Record the range in which the model was assessed, inspect errors, and compare simple alternatives. Complexity should earn its place by improving decisions on new observations.

RETRIEVE. REASON. REMEMBER.

Knowledge check.

Choose one answer for each question, then check your reasoning.