a. Consider the regression using three explanatory variables, FERTILITY, PUBLICEDUCATION, and LNHEALTH that you did in Exercise 3.3.6. Test whether PUBLICEDUCATION and LNHEALTH are jointly statistically significant, using a partial \(F\)-test. State your null and alternative hypotheses, decision-making criterion, and decision-making rules. (Hint: use the coefficient of determination form for calculating the test statistic.) Provide an approximate \(p\)-value for the test.

b. We now introduce the REGION variable, summarized in Table 4.11. A box plot of life expectancies versus REGION is given in Figure of life expectancies versus REGION is given in Figure 4.8.
Describe what we learn from the table and box plot about the effect of REGION on LIFEEXP.

Table 4.11.

 Figure 4.8.

c. Fit a regression model using only the factor REGION. Is REGION a statistically significant determinant of LIFEEXP? State your null and alternative hypotheses, decision-making criterion, and decision-making rules.

d. Fit a regression model using three explanatory variables, FERTILITY, PUBLICEDUCATION, and LNHEALTH, as well as the categorical variable REGION.
d(i). You are examining a country that is not in the sample with values FERTILITY \(=2.0\), PUBLICEDUCATION \(=5.0\), and \(\mathrm{LNHEALTH}=1.0\). Produce two predicted life expectancy values by assuming that the country is from (1) an Arab state and (2) sub-Saharan Africa.
d(ii). Provide a \(95 \%\) confidence interval for the difference in life expectancies between an Arab state and a country from subSaharan Africa.
d(iii). Provide the (usual ordinary least squares) point estimate for the difference in life expectancies between a country from subSaharan Africa and a high-income OECD country.

Transcribed Image Text:

REGION Region Description Number Mean 1234567 Arab states 13 71.9 East Asia and the Pacific 17 69.1 Latin American and the Carribean 25 72.8 South Asia 7 65.1 Southern Europe 3 67.4 Sub-Saharan Africa 38 52.2 Central and Eastern Europe 24 71.6 8 High-income OECD 23 79.6 All 150 67.4 Note: OECD stands for Organization for Economic Co-operation and Development.