A social scientist thinks that the level of activity in the shadow economy, Y, depends either positively on the level of the tax burden, X, or negatively on the level of government expenditure to discourage shadow economy activity, Z. Y might also depend on both X and Z. International cross-section data on Y, X, and Z, all measured in U.S. $ million, are obtained for a sample of 30 industrialized countries and a second sample of 30 developing countries. The social scientist regresses (1) log Y on both log X and log Z, (2) log Y on log X alone, and (3) log Y on log Z alone, for each sample, with the following results (standard errors in parentheses):
X was positively correlated with Z in both samples. Having carried out the appropriate statistical tests, write a short report advising the social scientist how to interpret these results.