Correlation of the residuals

[ilya49]

Testing for the Conditional Heteroskedasticity and Serial Correlation appears to involve correlation of the residuals. Does anybody know what I have to regress these residuals against in order to derive that residual correlation?
Thanks

 

[iaf10]

Testing for Heteroskedasticity, the BP test requires a regression of the Squared Residual (Yi-Ŷ1)2 on the independent variable(X)

Decision Rule
Heteroskedasticity exists: If X explains the variation in the squared residual.

Heteroskedasticity doesn’t exist:X doesn’t explain the variation.

BP test for Heteroskedasticity: χ2= nR2


Someone please correct me if I am wrong.