View source for Breusch-Pagan test

{{CMG}}
__NOTOC__


==Overview==

In [[statistics]], the '''Breusch-Pagan test''' is used to test for [[heteroskedasticity]] 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 equation

:<math>
y = x_0 + x_1\beta + u.\,
</math>

We can then estimate <math>\hat{u}</math>, the residual.  [[Ordinary least squares]] constrains these so that their mean is 0, so we can calculate the variance as the average squared values.  Even simpler is to simply regress the squared residuals on the independent variables, which is the Breusch-Pagan test:

:<math>
\hat{u}^2 = x_0 + x_1\beta + v.\,
</math>

If an [[F-test]] confirms that the independent variables are jointly significant then we can reject the hypothesis of no heteroskedasticity.

The Breusch-Pagan test tests for conditional heteroskadicity.  It is a [[chi-squared test]]: the test statistic is  [[chi-square distribution|''n''&chi;<sup>2</sup>]] with ''k'' degrees of freedom.  If the Breush-Pagan test shows that there is conditional heteroskadicity, it can be corrected by using the [[Hansen method]], using robust [[standard error]]s, or re-thinking the regression equation.

==See also==
[[White test]]

[[Category:Biostatistics]]
[[Category:Statistics]]

{{jb1}}
{{WikiDoc Help Menu}}
{{WikiDoc Sources}}