EVERYONE should review this post and these numbers. The regression results are consistent with the facts that free-market health care results in adverse selection in insurance, moral hazard, and fails to price externalities.
The regression results show a statistically significant negative relationship (as public health care expenditures go up, health improves) between public health care expenditures and infant mortality rates, while showing a statistically insignificant positive relationship between private expenditures and infant mortality (the amount of private expenditures is not correlated with health).
The fact that the number of private health care dollars has no significant effect on health is consistent with theory. Consider the United States, health care services and insurance are provided privately and they are much more expensive as a result (US health care expenditures: Canada health care expenditures = 1.71:1) but we do not receive more services (US healthcare services received: Canada health care services received .71:1).
For those of you who do not speak econometrics - this means that public health care systems are more efficient and result in healthier nations, while market based systems are inherently inefficient due to market failures and, transitively, reduce a nation's health.