For the second regress the squared errors on other variables, testing to see if there is a relationship between these estimated residual "variances" and the other variables. If you want to do the Breusch-Pagan test you run:

e_i²/² = g + d*Z_i + u_i

If you want to do the White test you run:

You can do either test easily with TSP. After the first regression retrieve the residuals @RES and square them, then regress the new series on Z. For the Breusch-Pagan test you will also need the variance of the residuals @S2.

To compute the Breusch-Pagan divide the sum of squares for the second regression (RSS) by 2. The RSS can easily be obtained by multiplying the R² by TSS, the total sum of squares. Note that since R² is equal to RSS/TSS, RSS=@RSQ*@SSR/(1-@RSQ)). On the other hand, to carry out the White test you multiply the number of observations by the R² (@NOB*@RSQ). We compute both tests in Example 6.3.

Note that TSP version 4.4 automatically supplies a version of the White test where Z_i is the squared fitted values for Y_i in the regression output, as a general omnibus heteroskedasticity test.