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Calculate an observable deviation
For each supplied pair, residual equals actual asset return minus its fitted return. In the original record, period four has asset return 2.5%, fitted return 3.3% and residual −0.8 percentage points.
State the population equation
A model equation Y=α+βX+ε uses population coefficients and an unobserved disturbance ε. Replacing the coefficients with estimates creates a residual, which is not automatically the same as that disturbance.
Keep fitted identities separate
| Object | Basis |
|---|---|
| Residual | Observed data and estimated line |
| Disturbance | Population model and its true coefficients |
| Zero residual sum | OLS identity with an intercept |
| Zero population error mean | A model assumption or property |
Avoid proving assumptions from an identity
Residuals summing to zero is built into this least-squares fit. It does not independently prove the disturbances are unbiased, independent, normal or have constant variance.