Regression Analysis
Regression analysis models how an outcome relates to explanatory variables and evaluates the uncertainty of that relationship. The skill includes choosing a functional form, interpreting parameters and checking assumptions. Prediction, association and causal estimation are different uses of regression and require different arguments beyond fitting the same numerical model.
What it is
A regression specifies a relationship between predictors and an outcome distribution or conditional summary. Linear regression models a conditional mean as a linear combination of terms; generalized models use links and outcome families for other target types. Interactions and transformations can express relationships beyond a straight line in the original variables. Regularization controls complexity, while robust or alternative estimators address particular distributional or loss assumptions. Parameter interpretation depends on coding, scale and the other included variables. Regression is a framework for estimation and prediction, but a coefficient is not automatically the effect of changing its predictor through an intervention.
What the work involves
State the outcome, target interpretation and available covariates before fitting. Examine functional form, correlated predictors, influential observations and residual behavior. Choose uncertainty calculations compatible with the sampling design and dependence. For prediction, validate on unseen relevant cases; for explanation, communicate what a coefficient means conditional on the specification. The deliverable should contain the model formula, parameter and uncertainty summaries, diagnostics and sensitivity to reasonable alternatives, enabling readers to distinguish a useful fitted relationship from an unsupported causal story.
Illustrative example
In an illustrative energy analysis, an analyst relates building consumption to temperature, occupied area and operating hours. They include a temperature transformation to capture heating and cooling behavior, then inspect residual patterns across seasons. A coefficient for operating hours is interpreted within that model and population. It does not establish the energy savings from shortening opening hours, because staffing, occupancy and equipment use may change together and require a separate causal analysis.
Limits and common mistakes
Misspecified functional form, measurement error and omitted variables can distort interpretation. Multicollinearity can make individual coefficients unstable even when predictions are adequate. Outliers and dependent observations affect fitting and uncertainty. Residual diagnostics do not establish that all confounding has been removed. Logistic regression belongs to the regression family but predicts class probabilities rather than a continuous mean through the same linear response. Distinguish predictive performance, parameter uncertainty and causal validity instead of using one as evidence for the others.
Prerequisites
Related skills
- → is subcategory of: Machine Learning
- → is subcategory of: Supervised Learning
- ← is subcategory of: Linear Regression
Sources and further reading
- scikit-learn: Linear Model
Linear, regularized and generalized predictive models.
- statsmodels: Time Series analysis and model documentation
Statistical modeling context and links to regression, generalized models and diagnostics.
Last updated: 2026-10-10