A summary fit number can conceal a curved relationship, changing error spread or time pattern.
Use the part the model did not explain
A residual is an observed value minus the model’s fitted value. Plotting residuals against predictors, fitted values and relevant sequence can expose structure left out of the fitted relationship. Systematic patterns call for investigation of the model and collection process. A large R-squared alone does not establish suitability for a particular prediction task.
A hypothetical straight-line shortcut
Imagine a straight line fitted to an illustrative trial response as an approved factor varies. The overall fit looks strong, but residuals are negative at both ends and positive in the middle. That pattern suggests the straight line misses curvature within the observed range; it does not identify the physical cause by itself.
If error spread grows at one end, also investigate whether the analysis assumptions and measurement behavior remain appropriate there. These are diagnostic questions, not directions to change an HM machine or claims that a different mathematical curve will make the process acceptable.
Retain the evidence needed to review the model
Provide the raw observations, factor units, tested range, run sequence, fitted equation and residual plots. Identify any excluded points and why they were excluded. Keep observations used to assess the model distinguishable from those used to construct it.
Before using the result in a quotation or trial conclusion, state where predictions will be used. A model fitted within one observed range has not automatically been checked outside it or for a different product. Ask for a confirmation strategy appropriate to the intended decision; preserve uncertainty information rather than presenting a fitted line as a deterministic machine specification.
Trial discussion worksheet
This blank worksheet is for your own project. It contains no H M machine trial result.
| Review question | Reference or observation to retain |
|---|---|
| Where are residuals plotted? | Factors, fitted response and sequence |
| What range was observed? | Actual tested conditions |
| What evidence assesses predictions? | Independent or identified confirmation observations |
Customer Questions
Does high R-squared prove good future predictions?
No. Review residuals, scope and confirmation evidence.
Does a curved residual plot diagnose a physical fault?
No. It indicates unexplained structure requiring investigation.
May a fitted equation be used beyond its tested range?
That extension needs a justified assessment and should not be presented as already verified.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
Discuss Your Machine Requirement
Share your product, container, required output and the evidence needed for your technical review.
Request a Technical Review