Breusch-Pagan test

This test is used in linear regressions to test for homoscedasticity of the error term.

For the regression $Y = \beta X + u$ verify homoscedastic $u_t$ using the Breusch-Pagan test.

Regress the squared $u_t$ back to the X:

$\hat{u_t}^2 = \beta X + v$

and calculate the test statistics: $nR^2$ .

This test statistics is Χ² with (k-1) d.f. distributed under the null hypothesis of homoscedasticity.