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Regression: estimate relationships with assumptions

Regression estimates how an outcome relates to one or more predictors under a specified model.

Statistical and evaluation practice; ADM HR worked application · 2026 teaching guide · Original editorial explanation
Regression: estimate relationships with assumptions — simplified model sketchDefine outcome · Specify variables · Check model · Interpret uncertainty. Editorial interpretation, after Statistical and evaluation practice; ADM HR worked application (2026 teaching guide).Defineoutcome01Specifyvariables02Check model03Interpretuncertainty04ADM HR · ORIGINAL INTERPRETATIONStatistical and evaluation practice; ADM HR worked application · 2026 teaching guide
Original simplified sketch after Statistical and evaluation practice; ADM HR worked application (2026 teaching guide). Read the explanation for assumptions and limitations. Download SVG ↗

The core idea

Regression estimates how an outcome relates to one or more predictors under a specified model. Linear regression is often used for continuous outcomes; other outcome types may need other models. Including variables can account for measured differences, but it does not automatically remove confounding or establish causation. The meaning of a coefficient depends on units, coding, functional form and which other variables are included.

Source and attribution [1]

Using it in practice

Define the question and plausible relationships before selecting variables. Inspect data quality and missingness. Check residual patterns, influential observations and whether the model is suitable for the outcome. Separate predictive validation from causal interpretation. In repeated or clustered workforce data, account for the dependence structure rather than treating every record as an unrelated observation.

An example, not a reported case

Worked example · illustrative

A fictional analysis estimates an association of two additional training hours with one fewer recorded error per team-month after including recorded workload and team size. That is not proof that assigning two hours will prevent an error. More capable teams may receive different training, and measurement may vary. HR uses the model to refine questions and designs a pilot to investigate the proposed mechanism.

What to watch for

Adding more variables can create new problems, including overfitting and inappropriate adjustment for variables affected by the intervention. Unmeasured factors remain possible. Coefficients can be unstable when predictors overlap strongly. Model output needs competent review; a low p-value does not establish a useful or fair employment decision.

Explain the estimate

Report the outcome unit, predictor unit, population and uncertainty interval. Make clear whether the result is an association or a causal estimate supported by a particular design. Avoid translating a coefficient into a guaranteed individual result.

Check use on new data

For prediction, reserve suitable data that was not used to tune the model, preferably reflecting future deployment. Compare with a simple baseline and monitor later drift. For causal questions, focus on identification assumptions as well as statistical fit.

Take it into your next conversation

Three useful questions.

  1. What question can this method answer, and what can it not establish?
  2. Are the comparison, observation period and assumptions defensible?
  3. What decision follows, and how will its consequences be reviewed?

Related terms

Go to the evidence

Sources & attribution

[1] NIST: Linear least squares regression ↗

The core idea is an original summary of the cited work. Application notes, examples and sketches are our interpretations, not quotations or reproductions of the authors’ figures. Publisher records may require access to read the full original work.

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Published 2026-09-20 · Reviewed 2026-09-20. Editorial approach

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