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| In [[statistics]], the '''White test''' is a [[statistical test]] that establishes whether the [[errors and residuals in statistics|residual]] [[variance]] of a variable in a [[regression model]] is constant: that is for [[homoscedasticity]].
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| This test, and an estimator for [[heteroscedasticity-consistent standard errors]], were proposed by [[Halbert White]] in 1980.<ref>{{cite journal
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| |last=White |first=H. |authorlink=Halbert White
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| |year=1980
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| |title=A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity
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| |journal=[[Econometrica]]
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| |volume=48 |issue=4 |pages=817–838
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| |mr=575027 | jstor = 1912934
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| }}</ref> These methods have become extremely widely used, making this paper one of the most cited articles in economics.<ref>{{cite journal
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| |title=What Has Mattered to Economics since 1970
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| |journal=Journal of Economic Perspectives
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| |volume=20 |number=4 |year=2006 |pages=189–202
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| |last1=Kim |first1=E.H.
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| |last2=Morse |first2=A.
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| |last3=Zingales |first3=L.
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| |doi=10.1257/jep.20.4.189
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| |url=http://faculty.chicagogsb.edu/finance/papers/What%20Has%20Mattered%20to%20Economics%20Since%201970.pdf
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| }}</ref>
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| ==Testing constant variance== | |
| To test for constant variance one undertakes an auxiliary regression analysis: this regresses the squared residuals from the original regression model onto a set of [[regressor]]s that contain the original [[regressor]]s, the cross-products of the regressors and the squared regressors. One then inspects the <math>R^{2}</math>. The [[Lagrange multiplier test|Lagrange multiplier (LM) test]] statistic is the product of the ''R''<sup>2</sup> value and sample size:
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| :<math>\ LM = n \cdot R^2 .</math> | |
| This follows a [[chi-squared distribution]], with degrees of freedom equal to the number of estimated parameters (in the auxiliary regression).
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| An alternative to the White test is the [[Breusch–Pagan test]].
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| If homoscedasticity is rejected one can use [[heteroscedasticity-consistent standard errors]].
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| ==See also==
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| *[[Heteroscedasticity]]
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| ==References==
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| {{reflist}}
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| [[Category:Statistical tests]]
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| [[Category:Regression diagnostics]]
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| {{statistics-stub}}
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