The development level of a city is assessed by many indicators, such as population, total volume of passenger transport and freight transport. Table 5.14 shows six social and economic indicators for eight cities in China The column headings: IL, TGOV, TIOV, TVPT, TVFT and FB denote the total income level (in 10,000 yuan), total agricultural output (10 billion yuan), total industrial output (100 billion yuan), total transport values (100 million yuan), total freight transport value (100 million yuan) and financial budget (100 billion yuan), respectively. Use the principal component analysis (PCA) method to rank the development level of these cities. Give complete reasoning on the dimensionality reduction performed in ranking the cities. (Note: Prior to performing PCA, standardize the variables by dividing each observed value from the maximum for the given variable). Determine the number of relevant PCs based on Kaiser critetion and Joliffe’s cutoff of 80% cumulative percentage of variation.

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Table 5.14 Social and economic indicators of eight Chinese cities. City Beijing Tianjin ILP TGOV TIOV TVPT TVFT FB 1249.90 1.84 2.00 2.03 4.56 2.79 910.17 1.59 2.26 0.33 2.63 1.13 0.69 0.29 0.19 0.71 875.40 2.92 299.92 0.24 0.27 0.19 1.19 0.39 207.78 0.37 0.26 0.14 677.08 1.30 0.58 0.78 1.54 0.90 545.31 1.88 0.84 1.08 1.92 0.76 Changchun 691.23 1.85 0.60 0.48 0.48 0.95 0.48 Shijiazhuang Taiyuan Hohhot Shenyang Dalian °° 0.08 0.24 Table 5.14 Social and economic indicators of eight Chinese cities. City Beijing Tianjin ILP TGOV TIOV TVPT TVFT FB 1249.90 1.84 2.00 2.03 4.56 2.79 910.17 1.59 2.26 0.33 2.63 1.13 0.69 0.29 0.19 0.71 875.40 2.92 299.92 0.24 0.27 0.19 1.19 0.39 207.78 0.37 0.26 0.14 677.08 1.30 0.58 0.78 1.54 0.90 545.31 1.88 0.84 1.08 1.92 0.76 Changchun 691.23 1.85 0.60 0.48 0.48 0.95 0.48 Shijiazhuang Taiyuan Hohhot Shenyang Dalian °° 0.08 0.24

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To rank the development level of the eight cities in China using the PCA method we first need to sta... View the full answer