| name | statistical-modeling |
| description | Regression analysis, ANOVA, generalized linear models, Bayesian methods, and model selection. Covers the full modeling workflow from problem formulation through diagnostics -- linear regression, logistic regression, Poisson regression, mixed-effects models, prior specification, posterior inference, AIC/BIC comparison, cross-validation for model selection, and assumption checking. Use when fitting models, testing hypotheses, or selecting among competing statistical explanations. |
| type | skill |
| category | data-science |
| status | stable |
| origin | tibsfox |
| modified | false |
| first_seen | "2026-04-12T00:00:00.000Z" |
| first_path | examples/skills/data-science/statistical-modeling/SKILL.md |
| superseded_by | null |
Statistical Modeling
Statistical modeling is the practice of fitting mathematical structures to data in order to quantify relationships, test hypotheses, and make predictions. Unlike machine learning, which optimizes prediction, statistical modeling privileges interpretability and inference -- understanding why variables relate, not just that they do. Leo Breiman's "two cultures" paper (2001) crystallized this distinction. This skill covers the inferential tradition while acknowledging where the two cultures overlap.
Agent affinity: tukey (EDA and diagnostics), fisher (experimental design and ANOVA), breiman (model comparison)
Concept IDs: data-hypothesis-testing, data-confidence-intervals, data-correlation, data-normal-distribution
The Modeling Workflow
| Stage | Goal | Key operations |
|---|
| 1. Formulation | Define the question as a model | Specify response variable, predictors, functional form |
| 2. Exploration | Understand data structure | Scatterplots, correlation matrices, distribution checks |
| 3. Fitting | Estimate parameters | OLS, MLE, MCMC, IRLS depending on model class |
| 4. Diagnostics | Check assumptions | Residual plots, Q-Q plots, leverage, VIF |
| 5. Inference | Draw conclusions | Confidence intervals, hypothesis tests, effect sizes |
| 6. Selection | Compare models | AIC, BIC, cross-validation, likelihood ratio tests |
| 7. Communication | Report results | Effect estimates with uncertainty, not just p-values |
Linear Regression
The Model
y = beta_0 + beta_1 * x_1 + beta_2 * x_2 + ... + beta_p * x_p + epsilon
where epsilon ~ N(0, sigma^2) independently. The betas are estimated by ordinary least squares (OLS), minimizing the sum of squared residuals.
Assumptions (LINE)
| Assumption | Check | Violation consequence |
|---|
| Linearity | Residual vs. fitted plot -- no pattern | Biased estimates, meaningless coefficients |
| Independence | Study design, Durbin-Watson test | Underestimated standard errors, inflated significance |
