Stepwise regression¶

An automated regression-model selection procedure that iteratively adds, removes or exchanges predictors according to a prespecified statistical criterion.

Version: v1 · 2026-09-08 · History
Domain-specific #: 6912
Origin domain: statistics
Subdomain: variable selection

Core Idea¶

Stepwise regression searches a nested or locally connected sequence of predictor subsets using repeated data-dependent decisions. At each step the procedure scores eligible additions or deletions and changes the active set when an improvement crosses its rule, stopping at a local criterion optimum. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

The load-bearing residual is not the broad topic of statistics. It is greedy sequential variable selection embedded in regression fitting. That residual remains recognizable when examples, notation, scale, or implementation change, but it disappears if the carrier is mistyped, the condition that candidate set, direction, criterion and stopping rule are fixed in advance and inference acknowledges that the final model was selected from the same data fails, a neighboring object is substituted, or notation and topical resemblance replace the constitutive test.

Scope of Application¶

Stepwise regression belongs to statistics and is useful where the analyst can specify a response and candidate predictor set, regression model family, forward, backward or bidirectional search, entry and removal criterion, fitted candidate models, stopping rule, selected model, uncertainty and validation data, then evaluate candidate set, direction, criterion and stopping rule are fixed in advance and inference acknowledges that the final model was selected from the same data. The scope is broad within that domain but bounded by the need for candidate set, direction, criterion and stopping rule are fixed in advance and inference acknowledges that the final model was selected from the same data.

Clarity¶

The abstraction clarifies a crowded vocabulary by making candidate set, direction, criterion and stopping rule are fixed in advance and inference acknowledges that the final model was selected from the same data the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Stepwise regression can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Stepwise regression. Stepwise regression compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: a response and candidate predictor set, regression model family, forward, backward or bidirectional search, entry and removal criterion, fitted candidate models, stopping rule, selected model, uncertainty and validation data. Reject examples whose alleged carrier belongs to a different problem. 2.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of statistics because they reuse a response and candidate predictor set, regression model family, forward, backward or bidirectional search, entry and removal criterion, fitted candidate models, stopping rule, selected model, uncertainty and validation data, At each step the procedure scores eligible additions or deletions and changes the active set when an improvement crosses its rule, stopping at a local criterion optimum., and type the carrier, state every parameter and convention in the definition, test that candidate set, direction, criterion and stopping rule are fixed in advance and inference acknowledges that the final model was selected from the same data, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Stepwise regression Domain-specific

Parents (1) — more general patterns this builds on

Stepwise regression is a kind of Selection Prime

The proposed strict upward parent is prime:selection.

Hierarchy path (1) — routes to 1 parentless root

Stepwise regression → Selection

Neighborhood in Abstraction Space¶

Stepwise regression sits in a crowded region of the domain-specific corpus (38^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Regression Diagnostics & Model Fit (9 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08