DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Least-squares solution set

Definition

For integers $n, p \geq 1$ , a matrix $X \in R^{n \times p}$ , and a response vector $y \in R^{n}$ , define the least-squares solution set $B_{L S} (y) : = {arg min}_{b \in R^{p}} ∥ y - X b ∥_{2}^{2} .$ This is a set-valued definition; it does not select one coefficient vector. The next theorem proves that the set is nonempty and identifies the fitted vector and residual as unique, including when $X$ is rank-deficient.

Depends on

Used by

Dependency tree · two levels

16 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Statistics for Applications, Section 15: Multiple Linear Regression (standard reference, not scraped)
Statistics: Lecture Three — Linear Models (standard reference, not scraped)