We discussed the women's 2012 Olympic heptathlon in Chapter 6. Here are the results from the high jump, 800-meter run, and long jump for the 26 women who successfully completed all three events in the 2004 Olympics (www.espn.com):

Let's examine the association among these events.
Perform a regression to predict high-jump performance from the 800-meter results.
a) What is the regression equation? What does the slope mean?
b) What percent of the variability in high jumps can be accounted for by differences in 800-m times?
c) Do good high jumpers tend to be fast runners? (Be careful-low times are good for running events and high distances are good for jumps.)
d) What does the residuals plot reveal about the model?
e) Do you think this is a useful model? Would you use it to predict high-jump performance? (Compare the residual standard deviation to the standard deviation of the high jumps.)

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High 800-m Long Name Carolina Klüft Austra Skujyte Helly Sotherton Shelia Burrel elena Prokhorova Country Jump (m) (sec) Jump (m) SWE 1.91 134.15 6.51 1.76 135.92 6.30 GBR 185 32.27 6.5 USA 1035.32 6.25 179 131.31 6.21 GER 176 135.21 642 RUS Kesselschlaeger Marie Collonville FRA 185 133.62 6.19 Natalya Dobrynska UKR 182 137.01 623 Margaret Simpson GHA 1.79 137.72 6.02 Svetiana Sokolova RUS 1.70 133.23 5.84 1.1. Shobha Claudia Tonn Naide Gomes Michelle Perry Aryiro Strataki Karin Ruckstuhl NED 185 133.95 5.90 Karin Ertl Hylie Wheeler lanice Josephs Tiffany Lott Hogan USA 1.67 145.10 6.15 Magdalena INDI 1.67 137.28 6.36 182 130.77 6.35 POR 1.85 140.05 6.10 USA 1.70 133.69 6.02 GRE 1.79 137.90 5.97 GER 1.73 138.68 6.03 AUS 179 13765 636 RSA 1.70 138.47 6.21 POL 1.76 133.08 5.98 Szczepanska lina NaumenkoKAZ 1.79 13457 6.16 Yuliya Akulenko UKR 1.73 142.58 6.02 Soma Biswas Marsha Mark-Baird TRI 170 1412 .22 Michaela Hejnova CZE 1.70 145.68 570 IND 1.70 132.27 5.92 2