8.21. Refer to Exercise 8.20. Convert the national track records for men in Table 8.6 to speeds measured in meters per second. Notice that the records for 800 m, 1500 m, 5000 m, 10,000 m and the marathon are given in minutes. The marathon is 26.2 miles, or 42,195 meters, long. Perform a principal component analysis using the covariance matrix S of the speed data. Compare the results with the results in Exercise 8.20. Which analysis do you prefer? Why?Table 8.6 National Track Records for Men 100 m 200 m 400 m 800 m 1500 m 5000 m 10,000 m Marathon Country (0) () (min) (min) (min) (min) (min) Argentina 10.23 2037 46.18 1.77 3.68 13.33 27.65 129.57 Australia 9.93 20.06 44.38 1.74 153 12.93 27 53 12751 Austria 10.15 20.45 45.80 1.77 3.58 13.26 27.72 132 12 Belgium 10.14 20.19 45.02 1.73 357 12.83 26 87 127.20 Bermuda 10.27 20.30 45.26 1.79 3.70 14.64 30.49 146.37 Brazil 10.00 19 89 44.29 1.70 3.57 13.48 28 13 126.05 Canada 9.84 20.17 44.72 1.75 353 13.23 27.60 130.019 Chile 10.10 20.15 45.92 1.76 3.65 13.39 28.09 132.19 China 10.17 20.42 45.25 1.77 3.61 13.42 28.17 129.18 Columbia 10.29 20.85 45.84 1 80 3.72 13.49 27.88 131.17 Cook Islands 10.97 22.46 51.40 1.94 424 16.70 35.38 171.26 Costa Rica 10.32 20.95 46.42 1-57 3.84 13.75 28 81 133.23 Czech Republic 10.24 20.61 45.77 1.75 3.58 13.42 27.80 131.57 Denmark 10.20 20.52 45.89 1.69 3.52 13.42 27.91 129.43 DominicanRepublic 10.16 20.65 44.90 1.81 3.73 14.31 30.43 146,00 Finland 10.21 20.47 45.49 1.74 3.61 13.27 27 52 131.15 France 10.02 20.16 44.64 1-72 3.48 12.98 27 38 126.36 Germany 10.06 20.23 44.33 1.73 3.53 12.91 27.36 128.47 Great Britain 9.87 19.94 44.36 1.70 3.49 13.01 27 30 127.13 Greece 10,11 19.85 45.57 1-75 3.61 13.48 28.12 132/04 Guatemala 10.32 21.09 48.44 1.82 3.74 13.98 29 34 132.53 Hungary 10.08 20.11 45,43 1.76 3.39 13,45 132.10 India 10.33 20.73 45.48 1.76 363 13.50 28.81 132.00 Indonesia 10.20 20.93 46.37 1.83 3.77 14.21 29 65 139.18 Ireland 10.35 20.54 45.58 1.75 13.07 27 7A 129.15 Israel 10.20 20.89 45.59 1.80 3.70 13.66 28.72 134 21 Italy 10.01 19.72 45.26 1-73 3.35 13,09 27 28 127.29 Japan 10.00 20.03 44.78 1.77 3.62 13.22 27 58 126.16 Kenya 10.28 20.43 44,18 1.70 3.44 12.66 26 46 124.55 Korea, South 10.34 20.41 45.37 1.74 3.64 13.84 28 51 127.20 Korea, North 10.60 21.23 46.95 1.82 3.77 13.90 28 45 129.26 Luxembourg 10.41 20.77 47.90 1.76 3.67 13.64 28.77 134 03 Malaysia 10.30 20.92 46.41 1.79 3.76 14.11 29.50 149.27 Mauritius 10.13 20106 44.69 1.80 3.83 14.15 29 84 143.07 Mexico 10.21 20.40 44.31 1.78 3.63 13.13 27_14 127.19 Myanmar( Burma) 10.64 21.52 48.63 1.80 3.80 14.19 20162 139.57 Netherlands 10.19 20.19 45.68 1.73 3.55 13.22 27.44 128 31 New Zealand 10.11 20.42 46.09 1.74 3 54 13.21 27.70 128.59 Norway 10.08 20.17 46.11 1.71 13.11 2754 130.17 Papua New Guinea 10.40 21.18 46.77 1.80 400 14.72 31.36 148.13 Philippines 10 57 21,43 45.57 1.80 3.80 13.97 29 04 138.44 Poland 10.00 19.93 44.62 1.72 3.59 13.29 27_89 129.23 Portugal 9.86 20.12 46.11 1.75 3.50 13.05 27.21 126.36 Romania 10.21 20.75 45.77 1.76 3.57 13.25, 27.67 132.30 Russia 10.11 20.23 44.60 1.71 3.54 13.20 27.90 129.16 Samoa 10.78 21.86 49.98 1.94 4.01 16.28 34.71 161.50 Singapore 10.37 21.14 47.60 1.84 3,86 14,96 31.32 144.22 Spain 10.17 20.59 44.96 1.73 3.48 13.04 27.24 127.23 Sweden 10 18 20,43 45.54 1.76 3.61 13.29 27.93 13038 Switzerland 10.16 20.41 44,99 1.71 13.13 27.90 129.56 Taiwan 10 36 20.81 46.72 1.79 3.77 13.91 29.20 134 35 Thailand 10 23 20.69 46.05 1.81 3.77 14.25 29.67 139.33 Turkey 10.38 21.04 46.63 1.78 3.59 13.45 28.33 130.25 U.S.A. 9.78 19.32 43.18 1.71 3.46 12.97 27.23 125.38 Source: LAARATES Track and Field Salaries Handbook for the Hehinki 205 Olympic Courtesy of Onavio Castellini