We saw the data for the women's 2004 Olympic heptathlon in Exercise 73. Are the two jumping events associated? Perform a regression of the long-jump results on the high-jump results.

a) What is the regression equation? What does the slope mean?
b) What percentage of the variability in long jumps can be accounted for by high-jump performances?
c) Do good high jumpers tend to be good long jumpers?
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 long-jump performance? (Compare the residual standard deviation to the standard deviation of the long 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