Review Residuals Before Using a PCB Process Regression for Decisions

A fitted line can have a high reported fit statistic and still predict poorly in the region that matters to production. Before using a regression to adjust a process or estimate a board characteristic, inspect the errors it leaves behind. Those residuals can reveal structure that the fitted equation missed.

NIST’s model-validation guidance emphasizes residual analysis and explains why a high R-squared value alone does not establish an adequate model. A residual is the observed response minus the model’s prediction at that observation’s conditions.

Keep each residual attached to its context

Retain the original response, predicted response, input values, board identity, run order, and relevant production groups. A residual column without these fields is difficult to investigate. Verify that predictions were calculated using the same units and transformations as the fitted model.

Separate data used to fit the model from independent confirmation data where available. Good performance on the fitting records can overstate performance on a later production run, particularly when the model was repeatedly adjusted after examining those same records.

Inspect several relationships

Use the plots to generate questions rather than declaring a cause from appearance alone. A pattern may reflect measurement configuration, an omitted variable, or an unsuitable model form. Check the underlying records and process history before adding terms mechanically. Record which observations drove the proposed revision and whether the revised explanation predicts a new, independently testable change under specified process conditions.

Revise with a defined purpose

1. Identify the practical prediction problem.
2. Review residual patterns and influential observations.
3. Investigate plausible engineering explanations.
4. Fit an appropriate revised model if justified.
5. Check performance on relevant confirmation conditions.

Do not delete an inconvenient observation merely to improve R-squared. If a record is erroneous, preserve its correction history. If it represents a real process condition, decide whether the model must account for that condition or whether the intended domain should be explicitly restricted.

State the range of inputs and production conditions supported by the evidence. Extrapolating beyond those conditions adds assumptions that a tidy residual plot within the observed range cannot validate. The final recommendation should connect model performance to the decision tolerance, including uncertainty where a small prediction error would change the engineering action.