covariance concept
| Definition | The expectation of the product of two variables' deviations from their means, positive when they move together, the off-diagonal entry of the covariance matrix and the numerator of the correlation. Primer S, equation S.12. |
|---|---|
| Example | x = (1, 2, 3, 4, 5) and y = (2, 4, 5, 4, 5) have deviation products summing to 6, covariance 1.2 with n in the denominator. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id covariance, kind concept. |
| Status | no ledger row names this entry. Corrections: none recorded. |
| Defining equation | Book equation S.12. |
| Assumptions and scope | none |
| Prior art | none recorded |
| Evidence | none |
| Reviewed | semantic review 2026-09-09; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
Book equation S.12.
\[\operatorname{Cov}(X,Y)=\mathbb E\big[(X-\mu_X)(Y-\mu_Y)\big],\qquad r=\frac{\operatorname{Cov}(X,Y)}{\sigma_X\sigma_Y}.\]
Conditions
none
Ledger
none
First stated
Primer S section S.5 of Data Mining as Observation, added in draft 0.3 (2026-09-09) for the ECE 514 readers whose first courses are far behind. The idea is standard and TSK Appendix C covers it at length.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
none
Used in
Data Mining as Observation primers L and S, chapters 0, 1, 2, 3, 4, 9, 10, 11, 12.
Related
covariance matrix; correlation; variance; least-squares line.
See also
none
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.