National Life Expectancies. We continue the analysis begun in Exercises 1.7and 2.22

Now fit a regression model on LIFEEXP using three explananatural logarithmic transform of PRIVATEHEALTH).

a. Interpret the regression coefficient associated with public education.

b. Interpret the regression coefficient associated with health expenditures without using the logarithmic scale for expenditures.

c. Based on the model fit, is PUBLICEDUCATION a statistically significant variable? To respond to this question, use a formal test of hypothesis. State your null and alternative hypotheses, decision-making criterion, and decision-making rule.

d. The negative sign of the PUBLICEDUCATION coefficient is surprising, in that the sign of the correlation between PUBLICEDUCATION and LIFEEXP is positive and intuition suggests a positive relation. To check this result, an added variable plot appears d(i). For an added variable plot, describe its purpose and a method for producing it.
d(ii). Calculate the correlation corresponding to the added variable plot that appears in Figure 3.11.

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1.7. National Life Expectancies. Who is doing health care right? Health-care decisions are made at the individual, corporate, and government levels. Virtually every person, corporation, and government has a different perspec- tive on health care; these result in a wide variety of systems for managing health care. Comparing different health-care systems help us learn about approaches other than our own, which in turn help us make better decisions in designing improved systems. Here, we consider health-care systems from n = 185 countries through- out the world. As a measure of the quality of care, we use LIFEEXP, the life expectancy at birth. This dependent variable and several explanatory vari- ables are listed in Table 1.4. From this table, you will note that although there are 185 countries consider in this study, not all countries provided informa- tion for each variable. Data not available are noted under the column " Num Miss." The data are from the UN Human Development Report. a. Examine the distribution of the dependent variable, LIFEEXP. Do this by making a histogram and then a qq plot, comparing the empirical to a normal distribution.