Problem 1.17 Carbon dioxide (CO2) emissions are believed to be associated with the phenomenon of global warming. The following data come from a sample of the twenty countries with the highest CO2 emissions in 1989. Key to the variables: The four variables are: X1 = 1989 emissions, X2 = 1989 emissions per capita, X3 = 1987 GNP per capita, and X4 = 1987 emissions per GNP. The units were not given. 1989 1987 1987 1989 emissions GNP emissions emissions per capita per capita per GNP Country X1 X2 X3 X4 USA 1328.3 5.37 18529 2.8 Soviet Union 1038.2 3.62 8375 4.3 China 651.9 0.59 294 19.0 Japan 284.0 2.31 15764 1.3 India 177.9 0.21 311 6.1 FRG 175.1 2.86 14399 2.1 UK 155.1 2.70 10419 2.6 Canada 124.3 4.73 15160 2.9 Poland 120.3 3.15 1926 17.6 Italy 106.4 1.86 10355 1.7 France 97.5 1.74 12789 1.4 GDR 88.1 5.40 11300 4.9 Mexico 87.3 1.01 1825 5.4 South Africa 76.0 2.20 1870 12.5 Australia 70.3 4.22 11103 3.6 Czechoslovakia 61.8 3.95 9280 4.5 ROK 60.3 1.42 2689 4.4 Rumania 57.9 2.50 6030 4.2 Brazil 56.5 0.38 2021 1.9 Spain 55.5 1.42 5972 2.1 (Source: UN Conference on Trade and Development, UNCTAD/RDP/DFP/1, United Nations, New York, 1992. Note: The data for USSR, FRG, GDR and Czechoslovakia were obtained prior to the breakup of the Soviet Union and Czechoslovakia and prior to the reunification of Germany. In this data set the countries are ranked (in decreasing order) according to their total 1989 CO2 emissions data; this is simply a display of the order statistics corresponding to the variable X1.)

(a) Looking at the data one sees that the USA leads the world in total CO2 emissions. Now, rank the countries according to the variable X2 (1987 emissions per capita). What is the rank of the USA? of China?

(b) Rank the countries according to the variable X4 (1987 emissions per GNP). What is the rank of the USA? of China?

(c) How would you explain the differences in the rankings of the various countries according to the variables X2 and X4, respectively?