residualization instrument
| Definition | Removing from a column the least-squares multiple of another. The residual is orthogonal to the column removed. Chapter 8 section 8.6 and chapter 12 section 12.5. Also residual. |
|---|---|
| Example | Removing the least-squares multiple of (1, 1) from (3, 1) leaves (1, −1), which is orthogonal to (1, 1). |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id residualization, kind instrument. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | lean/DataMiningAsObservation/Residual.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- Removing from a column the least-squares multiple of another. The residual is orthogonal to the column removed, its squared length is the original less the squared dot product over the removed column’s squared length, a column orthogonal to the removed one is unchanged, and a column residualized on itself vanishes.
- Whether named categories survive residualization on the general valence channel is chapter 12’s test, and the book-length signal fell from 0.241 to a residual 0.093 at six and a half standard errors.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
none
First stated
Chapter 8 section 8.6 and chapter 12 section 12.5 of Data Mining
as Observation, with the bifactor readout in
xbse/docs/BIFACTOR_READOUT.md:14-100.
Measurements
| Where the book states it | Numbers, as the book’s sources table records them | Source |
|---|---|---|
| chapter 8 section 8.6 | books 0.241 at 17 sigma, residual 0.093, R2 0.009, z 6.5, p 5.7e-11, 85 percent, fiction 0.131 on 2250 | geometric-aesthetics/book/src/chapter-17-empirical-evidence-for-geometric-aesthetics.md:95-106 |
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Residual.lean,
theorems residual_orth, residual_sq,
residual_of_orth, residual_self, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
Used in
Data Mining as Observation primer L, chapters 8, 12, 14.
Related
correlation; orthogonal; confound; contraction; projection.
See also
Book equations stated beside the entry’s terms, not defining it: 0.1, 12.3, 14.2.
Ledger rows that cite the entry’s records without naming it: GO-B-legal (035→036).
Sources-table rows that share a record with the entry without naming it: chapter 8 section 8.6, chapter 12 section 12.5, chapter 14 section 14.8.
Status
Generated 2026-09-10 by encyclopedia/generate.py; book
at observation-data-mining f3914f0; the commit of every record is listed
in the encyclopedia’s provenance.