Editing Errors and residuals (section)

{{Short description|Statistics concept}}
{{more footnotes|date=September 2016}}
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In [[statistics]] and [[mathematical optimization|optimization]], '''errors''' and '''residuals''' are two closely related and easily confused measures of the [[deviation (statistics)|deviation]] of an [[observed value]] of an [[Elementary event|element]] of a [[Sample (statistics)|statistical sample]] from its "[[true value]]" (not necessarily observable). The '''error''' of an [[observation]] is the deviation of the observed value from the true value of a quantity of interest (for example, a [[population mean]]). The '''residual''' is the difference between the observed value and the ''[[Estimation|estimated]]'' value of the quantity of interest (for example, a [[sample mean]]). The distinction is most important in [[regression analysis]], where the concepts are sometimes called the '''regression errors''' and '''regression residuals''' and where they lead to the concept of [[studentized residual]]s.
In [[econometrics]], "errors" are also called '''disturbances'''.<ref name="Kennedy 2008 p. 576">{{cite book|last=Kennedy|first=P.|title=A Guide to Econometrics|publisher=Wiley|year=2008|isbn=978-1-4051-8257-7|url=https://books.google.com/books?id=69MDEAAAQBAJ&pg=PA576|access-date=2022-05-13|page=576}}</ref><ref name="Wooldridge 2019 p. 57">{{cite book|last=Wooldridge|first=J.M.|title=Introductory Econometrics: A Modern Approach|publisher=Cengage Learning|year=2019|isbn=978-1-337-67133-0|url=https://books.google.com/books?id=TONhEAAAQBAJ&pg=PA57|access-date=2022-05-13|page=57}}</ref><ref name="Das 2019 p. 7">{{cite book|last=Das|first=P.|title=Econometrics in Theory and Practice: Analysis of Cross Section, Time Series and Panel Data with Stata 15.1|publisher=Springer Singapore|year=2019|isbn=978-981-329-019-8|url=https://books.google.com/books?id=rK6tDwAAQBAJ&pg=PA7|access-date=2022-05-13|page=7}}</ref>