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Analysis & synthesisControl variablesPredictionConfounding controlQuantitative analysisCausal inference

Regression Analysis

Regression Analysis
Also known as: Multiple regression、Logistic regression、Multivariate analysis

Models relationships between outcome and explanatory variables. Distinguish prediction, description of associations and effect estimation, and check models and assumptions suited to the outcome type. [2] [1]

Regression model design and implementation checklist — openReferences and checked sections
Difficulty
Intermediate
Cost
Low
Duration
Planning example, not a universal standard duration: 1–2 weeks, including data preparation, modeling and interpretation
Content updated: 2026-10-07Source checked: 2026-09-13 (includes AI cross-checking)No documented human reviewIncludes fictional examples

How it works at a glance

Linear regression expresses the mean outcome as a function of explanatory variables. Consider other models, such as logistic regression, for binary outcomes or counts. [2] [1]

Coefficient interpretation depends on the model, units and adjusted variables. Diagnose residuals, outliers and error dependence, and state that unobserved confounding remains possible despite observational regression adjustment. [2] [1]

  1. Define the research question and model purpose
  2. Prepare variables and clean data
  3. Check basic correlations and associations
  4. Build and specify the regression model
  5. Assess model fit and diagnostics
  6. Interpret coefficients and report
Sequence of implementation steps. See “Implementation steps” for details of each stage.

When to use it and when it is unsuitable

When to use it

  • When estimating how a program variable affects outcomes while controlling several background factors
  • When identifying factors influencing outcomes to decide where intervention would have greater effects
  • When exploring predictors of binary outcomes such as service reach, dropout or target achievement through logistic regression
  • When analyzing program cost and effect patterns using large administrative or statistical survey datasets

When it is unsuitable

  • When model complexity exceeds data quantity and variation, preventing stable estimation or validation. Required counts cannot be determined solely by explanatory variable counts.
  • When claiming causal effects merely by adding regression variables. Design must address questions, assignment, confounding and measurement; method names alone do not determine causal strength.
  • When nonlinearities or interactions exist but only a simple linear model omitting them is used. Regression can itself be extended to nonlinear designs.

Participants, roles, and deliverables

Participants and roles

1–2 evaluators with statistical and data analysis knowledge and skills in R, Python, SPSS or other statistical software

Main deliverables

  • Regression coefficient table: unstandardized and standardized coefficients, p-values and 95% confidence intervals
  • Diagnostic plots: residual distributions and Q–Q plots
  • Interpretation report: effect sizes, substantive meaning and limitations

Implementation steps

  1. Define the research question and model purpose
    Clarify prediction versus effect estimation. For effect estimation, theoretically identify confounders first; a directed acyclic graph (DAG) is recommended.
  2. Prepare variables and clean data
    Identify dependent, independent and control variables; address missing data and outliers. Dummy-code categorical variables with reference categories specified, and examine continuous distributions.
  3. Check basic correlations and associations
    Examine distributions and interrelationships. Pairwise correlations cannot capture all multicollinearity; diagnose the design matrix and coefficient instability as well.
  4. Build and specify the regression model
    Enter independent variables based on theory using the Enter method. Stepwise addition and removal can become data-driven; do not add theoretically unjustified controls.
  5. Assess model fit and diagnostics
    Assess fit and predictive performance according to purpose and model. For linear regression, check residual shape, variance, dependence and influential observations. Do not impose identical residual-normality or R² requirements on logistic regression. Do not select variables solely by fixed VIF thresholds.
  6. Interpret coefficients and report
    Show coefficient units, conditioning variables and estimation uncertainty. Do not confuse logistic odds ratios with risk ratios or interpret standardized coefficient size as causal importance.

Strengths and limitations

Strengths

  • Models conditional associations and predictions. Causal interpretation requires separate design and assumptions.
  • Available in Excel, R, Python, SPSS and other tools, with many policy and practice applications.
  • Examines variable–outcome relationships, but coefficient size alone should not determine intervention priorities.
  • Logistic regression has an established record in risk-factor analysis and targeting in health and social policy.

Limitations

  • Observational data cannot rule out endogeneity, correlation between independent variables and errors, so causal interpretation always requires qualification.
  • With unmeasured confounders, estimates remain descriptions of associations.
  • Model misspecification, such as wrong variable selection or linear approximation of nonlinear relationships, distorts results.
  • Exploratory testing of many variables creates false-positive problems.

Common pitfalls

  • Inferring program causation from statistical significance. In observational regression, describe associations and always state design limitations for causal interpretation.
  • Overfitting: too many variables relative to sample size fit the observed data excessively and reduce generalization.
  • Ignoring collinearity destabilizes coefficients. Consider diagnostics, domain knowledge and the estimation question together when responding.

Conditions of use and evidence

  • Check assumptions about errors and functional form, and distinguish predictive fit from causal evidence. [1]
Fictional example; not actual results

Predict waiting times from preceding consultation counts

A fictional illustrative linear model: predicted waiting time = 5 + 2 × preceding consultation count.

Preceding consultation countPredicted valueMeaning
2 cases9 minutes5+2×2
5 cases15 minutes5+2×5

Common errors in judgment

Common mistake

Treating a significant coefficient as a cause

How to revise

Examine identification design and unobserved confounding.

ReasonStatistical associations differ from causal effects.

Common mistake

Assuming high R² guarantees prediction at a new site

How to revise

Check prediction errors in other data or periods.

ReasonTraining-data fit does not guarantee generalization.

Organize your thinking by writing

Regression model design and implementation checklist

A practical template is available to fill in and print on A4 paper.

Open worksheet

Related methods

Descriptive Statistics and Cross-tabulationSurvey / QuestionnaireRandomized Controlled TrialDifference-in-DifferencesPropensity Score MatchingMeta-Analysis and Systematic ReviewSecondary Data Analysis

References and checked sections

  1. NIST/SEMATECH e-Handbook: What are the typical underlying assumptions in process modeling?
    NIST
    Section consulted
    Underlying assumptions
    How it relates to the text
    Check assumptions about errors and functional form, and distinguish predictive fit from causal evidence.
    Source checked: (includes AI cross-checking)
  2. NIST/SEMATECH e-Handbook: Linear Least Squares Regression
    NIST／SEMATECH
    Section consulted
    Definition of a Linear Least Squares Model / Disadvantages of Linear Least Squares
    How it relates to the text
    Regression models and linear least squares; limitations of outliers and extrapolation
    Source checked: (includes AI cross-checking)

Editorial and checking information

Content updated: Source checked: (includes AI cross-checking)No documented human reviewIncludes fictional examplesEditorial policy and scope of checkingCite this pageReport a correction

How to cite this page

EvalCompass Editorial Team. “Regression Analysis”. EvalCompass, updated 2026-10-07. https://evalcompass.jun-nakatani.com/en/methods/regression-analysis/
Add the date you accessed the page. Text created by this site is available under CC BY 4.0. Quotations, external materials, and bundled fonts have their own terms of use. When reusing content, credit the source, link to the license, and indicate any changes.

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Change history
  • — Checked sources for definitions and applicability conditions, and added fictional examples, reasons for judgments and examples for every worksheet field. Revised unverified claims about history and adoption. Also reviewed existing procedures and cautions, and adjusted fixed participant counts and thresholds and generalizations about institutions. Preserved field positions, types and counts while revising fixed conditions and thresholds in the forms.
  • — Correction based on independent content review (content-check-causal). Revised table headings and explanations to prevent reading VIF as a variable-pair measure. Preserved field positions and counts.