We discussed the women’s 2016 Olympic heptathlon in Chapter 5. Here are the results from the high jump, 800-meter run, and long jump for the 27 women who successfully completed all three events in the 2016 Olympics:

Let’s examine the association among these events. Perform a regression to predict long jump performance from 800 m run times.

a) What is the regression equation? What does the slope mean?
b) What percent of the variability in long jumps can be accounted for by differences in 800-m times?
c) Do good long jumpers tend to be fast runners?
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.)

Name Evelis Aguilar Nadine Broersen Katerina Cachov Vanessa Chefer Ivona Dadic Jessica Ennis-Hill Alysbeth Felix Laura Ikauniece-Admidina Katarina Johnson-Thompson Akela Jones Hanna Kasyanova Eliska Klucinova Xenia Krizsan Heather Miller-Koch Antoinette Nana Djimou Ida Barbara Nwaba Jennifer Oeser Claudia Rath Yorgelis Rodriguez Carolin Schafer Brianne Theisen-Eaton Nafissatou Thiam High Jump 800 m Long Jump 134.32 6.23 137.55 6.15 138.95 5.91 134.2 6.1 135.64 6.05 129.07 6.34 135.32 6.22 129.43 6.12 130.47 6.51 161.12 6.3 136.58 5.88 142.81 6.08 133.46 6.08 126.82 6.16 140.36 6.43 131.61 5.81 133.82 6.19 127.22 6.55 34.65 6.25 6.2 6.48 6.58 6.1 6.35 6.31 1.74 1.77 1.77 1.68 1.77 1.89 1.68 1.77 1.98 1.89 1.77 1.8 1.77 1.8 1.77 1.83 1.86 1.74 1.861 1.83 1.86 1.98 Anouk Vetter 1.77 Nadine Visser 1.68 Kendell Williams 1.83 Sofia Yfantidou 1.65 Gyorgyi Zsivoczky-Farkas 1.86 131.76 136.52 129.5 136.54 137.71 134.47 136.24 150.08 5.51 6.31