en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q2229066

2013-03-14T18:59:51Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q2229066

← Older revision		Revision as of 20:59, 14 March 2013
Line 1:		Line 1:
	~~Greetings~~. ~~The author'~~s ~~title~~ is ~~Phebe~~ and ~~she feels comfy when people use~~ the ~~full title~~. ~~South Dakota~~ is ~~her birth location but she needs~~ to ~~move because~~ of ~~her family~~. ~~Bookkeeping~~ is ~~what I do~~. ~~To do aerobics~~ is a ~~thing~~ that ~~I'm completely addicted~~ to.<br><br>~~Here~~ is ~~my website;~~ [~~http~~://~~www~~.~~associazioneitalianafotografi~~.it/~~community~~/~~gruppi~~/~~points~~-to-~~know~~-~~when~~-~~confronted~~-~~with-candidiasis/~~ http://~~www~~.~~associazioneitalianafotografi~~.it]		In [[statistics]], the '''Breusch–Pagan test''' (named after [[Trevor Breusch]] and [[Adrian Pagan]]) is used to test for [[heteroscedasticity]] in a [[linear regression]] model. It tests whether the estimated [[variance]] of the [[errors and residuals in statistics\|residual]]s from a regression are dependent on the values of the independent variables.

			Suppose that we estimate the regression model

			:<math>
			y = \beta_0 + \beta_1 x + u, \,
			</math>

			and obtain from this fitted model a set of values for <math>\hat{u}</math>, the residuals. [[Ordinary least squares]] constrains these so that their mean is 0 and so, given the assumption that their variance does not depend on the [[dependent and independent variables\|independent variables]], an estimate of this variance can be obtained from the average of the squared values. If the assumption is not held to be true, a simple model might be that the variance is linearly related to independent variables. Such a model can be examined by regressing the squared residuals on the independent variables, using a regression equation of the form
			:<math>
			\hat{u}^2 = \gamma_0 + \gamma_1 x + v.\,
			</math>

			This is the basis of the Breusch–Pagan test. If an [[F-test]] confirms that the independent variables are jointly significant then the null hypothesis of homoscedasticity can be rejected.

			The Breusch–Pagan test tests for conditional heteroscedasticity.{{citation needed\|date=June 2012}} It is a [[chi-squared test]]:{{clarify\|reason=justy said its an F-test\|date=June 2012}} the test statistic is [[chi-squared distribution\|''n''χ<sup>2</sup>]] with ''k'' degrees of freedom. If the Breusch–Pagan test shows that there is conditional heteroscedasticity, it{{clarify\|reason=what can be corrected?\|date=June 2012}} can be corrected by using the [[Hansen method]], using [[robust standard errors]], or re-thinking the regression equation.

			==Procedure==
			Under the classical assumptions, including [[homoscedasticity]], ordinary least squares is the [[best linear unbiased estimator]] (BLUE), i.e., it is unbiased and efficient. The efficiency is lost, however, in the presence of heteroscedastic disturbances. Before deciding upon an estimation method, one may conduct the Breusch–Pagan test to examine the presence of heteroscedasticity. The Breusch–Pagan test is based on models of the type <math>\sigma_i^2 = h(z_i'\gamma)</math> for the variances of the observations where <math>z_i = (1, z_{2i}, \dots, z_{pi})</math> explain the difference in the variances. The null hypothesis is equivalent to the <math>(p - 1)\, </math> parameter restrictions:
			:<math>
			\gamma_2 = \dots = \gamma_p = 0.
			</math>
			The following [[Lagrange multiplier]] (LM) yields the [[test statistic]] for the Breusch–Pagan test:{{citation needed\|date=June 2012}}
			:<math>
			LM=\left (\frac{\partial l}{\partial\theta} \right )'\left (-E\left [\frac{\partial^2 l}{\partial\theta \partial\theta'} \right ] \right )^{-1}\left(\frac{\partial l}{\partial\theta} \right ).
			</math>
			This test is analogous to following the simple three-step procedure:{{citation needed\|date=June 2012}}

			* ''Step 1'': Apply OLS in the model
			:<math>
			y = X\beta+\varepsilon.
			</math>
			and compute the regression residuals.
			* ''Step 2'': Perform the auxiliary regression
			:<math>
			e_i^2=\gamma_1+\gamma_2z_{2i}+\dots+\gamma_pz_{pi}+\eta_i.
			</math>
			* ''Step 3'': The test statistic is the result of the coefficient of determination of the auxiliary regression in Step 2 and sample size <math>n\, </math> with:
			:<math>
			LM=nR^{2}\, .
			</math>
			The test statistic is [[asymptotic distribution\|asymptotically distributed]] as <math>\chi^2 \left (p - 1 \right )</math> under the [[null hypothesis]] of homoscedasticity.{{citation needed\|date=June 2012}}

			==Software==
			In [[R (programming language)\|R]], this test is performed by function '''ncvTest''' available in the '''car''' [[R (programming language)#Packages\|package]], or by function '''bptest '''available in the '''lmtest''' package.

			In Stata, one specifies the full regression, and then enters the command "estat hettest" followed by all independent variables.

			In SAS, breusch pagan can be obtained using the Proc Model option.
			<!-- and R includes other references:

			R. Koenker (1981), A Note on Studentizing a Test for Heteroscedasticity. Journal of Econometrics 17, 107–112.

			W. Krämer & H. Sonnberger (1986), The Linear Regression Model under Test. Heidelberg: Physica

			//-->

			==See also==
			* [[White test]]
			* [http://finzi.psych.upenn.edu/R/library/lmtest/html/bptest.html R documentation about bptest]

			{{no footnotes\|date=June 2012}}

			== References ==
			* {{cite journal
			\| last=Breusch \| first=T.S. \|authorlink=Trevor Breusch
			\| last2=Pagan \|first2=A.R. \|authorlink2=Adrian Pagan
			\| title=Simple test for heteroscedasticity and random coefficient variation
			\| journal=Econometrica
			\| year=1979
			\| volume=47
			\| issue=5
			\| pages=1287–1294
			\| mr=545960
			\| doi=10.2307/1911963
			\| jstor=1911963
			\| publisher=The Econometric Society
			}}.

			* {{ Cite book
			\| last=Heij
			\| first=C.
			\| coauthor=P. de Boer
			\| title= Econometric Methods with Applications in Business and Economics
			\| publisher=Oxford University Press
			\| year=2004
			\| pages=334–353
			}}.

			{{Expert-subject\|statistics\|date=November 2008}}

			{{DEFAULTSORT:Breusch-Pagan Test}}
			[[Category:Statistical tests]]
			[[Category:Regression diagnostics]]

94.210.41.151: Remove the "real life example" section as it is clearly not written for use in a wikipedia article and does not add anything to the article

2012-05-17T10:43:49Z

Remove the "real life example" section as it is clearly not written for use in a wikipedia article and does not add anything to the article

New page

Greetings. The author's title is Phebe and she feels comfy when people use the full title. South Dakota is her birth location but she needs to move because of her family. Bookkeeping is what I do. To do aerobics is a thing that I'm completely addicted to.<br><br>Here is my website; [http://www.associazioneitalianafotografi.it/community/gruppi/points-to-know-when-confronted-with-candidiasis/ http://www.associazioneitalianafotografi.it]

Scatchard equation - Revision history

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q2229066

94.210.41.151: Remove the "real life example" section as it is clearly not written for use in a wikipedia article and does not add anything to the article