Human Development Index. In given Exercise we saw that the United Nations Development Programme (UNDP) uses the Human Development Index (HDI) in an attempt to summarize the progress in health, education, and economics of a country with one number. The gross domestic product per capita (GDPPC) attempts to summarize the wealth produced by a country in one number. Here is a plot of GDPPC against HDI for 172 countries throughout the world:

a) GDPPC is measured in dollars. Incomes and other economic measures tend to be highly right skewed. Taking logs often makes the distribution more unimodal and symmetric. Compare the histogram of GDPPC to the histogram of log(GDPPC).

b) Use the log re-expression to make a scatterplot of log(GDPPC) against HDI. Comment on the relationship.

c) The HDR report classifies countries into High, Medium, and Low development based in part on their HDI. Looking at the scatterplot in b), why might it be a good idea to separate out the Low-development countries?

d) Look at the scatterplot of log(GDPPC) against HDI for only the 141 Medium- and High-development countries. Comment.

e) Find the correlation of log(GDPPC) with HDI for all 172 countries. Find the correlation for only the 141 Medium- and High-development countries. Which is higher? Which relationship is straighter?