## Concluding Examples

In concluding our discussion of heteroscedasticity we present two examples illustrating the main points made in this chapter.

### Park Test

Since there are two regressors, GNP and FLR, we can regress the squared residuals from regression {8.2.1) on either of these variables. Or, we can regress them on the estimated CM values { = CM) from regression {8.2.1). Using the latter, we obtained the following results.

Note: U, are^the residuals obtained from regression {8.2.1) and CM are the estimated values of CM from regression {8.2.1).

As this regression shows, there is no systematic relation between the squared residuals and the estimated CM values {why?), suggesting that the assumption of

{Cont,nued)

37However, as a practical matter, one may plot u2 against each variable and decide which X variable may be used for transforming the data. (See Fig. 11.9.)

38Sometimes we can use ln(Yi + k) or ln(Xi + k), where k is a positive number chosen in such a way that all the values of Y and X become positive.

39For example, if X1, X2, and X3 are mutually uncorrelated r12 = r13 = r23 = 0 and we find that the (values of the) ratios X1/X3 and X2/X3 are correlated, then there is spurious correlation. "More generally, correlation may be described as spurious if it is induced by the method of handling the data and is not present in the original material." M. G. Kendall and W. R. Buckland, A Dictionary of Statistical Terms, Hafner Publishing, New York, 1972, p. 143.

40For further details, see George G. Judge et al., op. cit., Sec. 14.4, pp. 415-420.