3.39 ▼ One factor in the development of tennis elbow, a malady that strikes fear into the hearts of all serious play- ers of that sport (including one of the authors), is the impact-induced vibration of the racket-and-arm system at ball contact. It is well known that the likelihood of getting tennis elbow depends on various properties of the racket used. Consider the accompanying scatterplot of x = racket resonance frequency (in hertz) and y = sum of peak-to- peak accelerations (a characteristic of arm vibration, in meters per second per second) for n = 23 different rackets (“Transfer of Tennis Racket Vibrations into the Human Forearm,” Medicine and Science in Sports and Exercise [1992]: 1134–1140). Discuss interesting features of the data and of the scatterplot.

 

y

 

38

36

34

32

30

28

26

24

 

22                                                                                     x

 

Engine	Age	Baseline	Reformulated	100    110   120   130    140    150   160   170   180    190
1	0	1.72	1.88
2	0	4.38	5.93
3	2	4.06	5.54
4	11	1.26	2.67
5	7	5.31	6.53
6	16	0.57	0.74
7	9	3.37	4.94
8	0	3.44	4.89
9	12	0.74	0.69
10	4	1.24	1.42

 

 

Q118

3.40  ● Stress can affect the physiology and behavior of

animals, just as it can with humans (as many of us know

all too well). The accompanying data on x = plasma corti-

sol concentration (in milligrams of cortisol per milliliter of

plasma) and y = oxygen consumption rate (in milligrams

per kilogram per hour) for juvenile steelhead after three

2-min disturbances were read from a graph in the paper

“Metabolic Cost of Acute Physical Stress in Juvenile Steel-

head” (Transactions of the American Fisheries Society

[1987]: 257–263). The paper also included data for un-

stressed fish.

 

x	25      36      48     59      62      72      80   100   100   137	asked whether or not it was a good time or a bad time to
y	155   184   180   220   280   163   230   222   241  350	buy a house.

 

a.    Is the value of y determined solely by the value of x? Explain your reasoning.

b.    Construct a scatterplot of the data.

c.    Does an increase in plasma cortisol concentration ap- pear to be accompanied by a change in oxygen consump- tion rate? Comment.