# Breusch Pagan

Can someone clear something up for me please? In detecting heteroskad, the BP tests calls for a regression of the squared residuals on the indepenant variables, or on the residuals of the independant variables? In other words, are we regressing residuals against residuals, or residuals against variables? Thanks

It tests whether the estimated variance of the residuals from a regression are dependent on the values of the independent variables.

Thanks mcpass. I understand what it’s testing FOR, it’s HOW it’s testing it that I’m not clear on. In got bagged in a test on this. So you’re saying that the residuals are regressed against the actual indep. variables?

yes

Suppose that we estimate the equation y = x0 + x1CAP + e We can then estimate , 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: e-squared = x0 + x1CAP + e

Sometimes I don’t even know what I’m saying but I believe that’s correct.

Smarshy Wrote: ------------------------------------------------------- > Can someone clear something up for me please? > > In detecting heteroskad, the BP tests calls for a > regression of the squared residuals on the > indepenant variables, or on the residuals of the > independant variables? i dont think there is such a thing as residual of the indep variable. you can have residuals of a regression .

its the squared of the residuals that your doing the test on BP = n * R^2 of residuals n = number of samples with K degrees of freedom

thanks everyone

smarshy just a small note… for Conditional Heteroskedasticity in linear multiple regression - everything said above is correct BUT when you’re using Time Series…For ARCH - to check for conditional heteroskedasticity you need to regress residuals from one time period against the residuals from one lagged time period… this was on one of the mocks…don’t mix up the two…