Editing Observational error (section)

==Effect on regression analysis==
If the [[dependent variable]] in a regression is measured with error, regression analysis and associated hypothesis testing are unaffected, except that the [[coefficient of determination|R<sup>2</sup>]] will be lower than it would be with perfect measurement.

However, if one or more [[independent variable]]s is measured with error, then the regression coefficients and standard [[hypothesis test]]s are invalid.<ref>{{cite book
  | last = Hayashi | first = Fumio
  | title = Econometrics
  | year = 2000
  | publisher = Princeton University Press
  | isbn = 978-0-691-01018-2
  | page = 187
  }}</ref> This is known as [[Regression dilution|attenuation bias]].<ref>{{Cite book|last1=Angrist|first1=Joshua David | url=https://www.worldcat.org/oclc/877846199|title=Mastering 'metrics : the path from cause to effect| last2=Pischke|first2=Jörn-Steffen | year=2015|isbn=978-0-691-15283-7| publisher=Princeton University Press|location=Princeton, New Jersey | pages=221 | oclc=877846199 | quote=The bias generated by this sort of measurement error in regressors is called attenuation bias.}}</ref>