Regression Diagnostics & Linear Models

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Abstractions about fitting and diagnosing linear statistical models, covering estimation methods (generalized least squares, best linear unbiased prediction, stepwise regression), diagnostic tools for model fit (DFFITS, partial residual plot, portmanteau test), and variance or sensitivity concepts (homoscedasticity, variance-based sensitivity analysis, smearing retransformation).

11 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Best linear unbiased prediction — The minimum-mean-square-error predictor among estimators linear in observations and unbiased for a target random effect under a specified linear mixed model.
• DFFITS — A regression influence diagnostic measuring the studentized change in an observation's fitted value when that observation is omitted from model estimation.
• Generalized least squares — A linear-model estimator that minimizes residuals in the inverse-covariance metric when errors have known nonconstant variance or correlation.
• Homoscedasticity and heteroscedasticity — Distinguish statistical models whose disturbance variance is constant across the conditioning space from models whose variance changes with predictors, fitted values, time, or another declared index.
• Partial residual plot — A regression diagnostic plotting a predictor against residuals augmented by that predictor's fitted contribution to reveal its adjusted functional relationship with the response.
• Portmanteau test — An omnibus hypothesis test designed to detect a broad family of departures from a well-specified null model rather than optimize power for one narrowly specified alternative.
• Regression analysis — A family of statistical methods for estimating conditional relationships between an outcome and one or more predictors, supporting explanation, adjustment and prediction under explicit model assumptions.
• Smearing retransformation — A nonparametric regression correction that converts predictions from a log-transformed outcome back to the original scale by averaging exponentiated residuals.
• Stepwise regression — An automated regression-model selection procedure that iteratively adds, removes or exchanges predictors according to a prespecified statistical criterion.
• Variance-based sensitivity analysis — A global sensitivity method decomposing model-output variance into first-order and interaction contributions from uncertain inputs, commonly summarized by Sobol' indices.
• Working–Hotelling procedure — A simultaneous-inference procedure giving a confidence band for the entire mean-response line in linear regression rather than separate pointwise intervals.