497 CASE STUDY Correlation of Body Measurements Case Study 497 In a study published in Medicine and Science in Sports and Exercise (volume 17, no. 2, page 189), the measurements of 252 men (ages 22–81) were taken. Of the 14 measurements taken of each man, some have significant correlations and others do not. For instance, the scatter plot at the right shows that the hip and abdomen circumferences of the men have a strong linear correlation 1r ≈ 0.8742. The partial table shown here lists only the first nine rows of the data. EXERCISES 1. Using your intuition, classify each 1x, y2 pair as having a weak correlation 10 6 r 6 0.52, a moderate correlation 10.5 6 r 6 0.82, or a strong correlation 10.8 6 r 6 1.02. (a) (weight, neck) (b) (weight, height) (c) (age, body fat) (d) (chest, hip) (e) (age, wrist) (f) (ankle, wrist) (g) (forearm, height) (h) (bicep, forearm) (i) (weight, body fat) (j) (knee, thigh) (k) (hip, abdomen) (l) (abdomen, hip) 2. Use technology to find the correlation coefficient for each pair in Exercise 1. Compare your results with those obtained by intuition. 3. Use technology to find the regression line for each pair in Exercise 1 that has a strong correlation. 4. Use the results of Exercise 3 to predict the following. (a) The hip circumference of a man whose chest circumference is 95 centimeters (b) The height of a man whose forearm circumference is 28 centimeters 5. Are there pairs of measurements that have stronger correlation coefficients than 0.85? Use technology and intuition to reach a conclusion. Age (yr) Weight (lb) Height (in.) Neck (cm) Chest (cm) Abdom. (cm) Hip (cm) Thigh (cm) Knee (cm) Ankle (cm) Bicep (cm) Forearm (cm) Wrist (cm) Body fat % 22 173.25 72.25 38.5 93.6 83.0 98.7 58.7 37.3 23.4 30.5 28.9 18.2 6.1 22 154.00 66.25 34.0 95.8 87.9 99.2 59.6 38.9 24.0 28.8 25.2 16.6 25.3 23 154.25 67.75 36.2 93.1 85.2 94.5 59.0 37.3 21.9 32.0 27.4 17.1 12.3 23 198.25 73.50 42.1 99.6 88.6 104.1 63.1 41.7 25.0 35.6 30.0 19.2 11.7 23 159.75 72.25 35.5 92.1 77.1 93.9 56.1 36.1 22.7 30.5 27.2 18.2 9.4 23 188.15 77.50 38.0 96.6 85.3 102.5 59.1 37.6 23.2 31.8 29.7 18.3 10.3 24 184.25 71.25 34.4 97.3 100.0 101.9 63.2 42.2 24.0 32.2 27.7 17.7 28.7 24 210.25 74.75 39.0 104.5 94.4 107.8 66.0 42.0 25.6 35.7 30.6 18.8 20.9 24 156.00 70.75 35.7 92.7 81.9 95.3 56.4 36.5 22.0 33.5 28.3 17.3 14.2 Source: “Generalized Body Composition Prediction Equation for Men Using Simple MeasurementTechniques” by K.W. Penrose et al. (1985). MEDICINE AND SCIENCE IN SPORTS AND EXERCISE, vol. 17, no.2, p. 189. Hip circumference (in centimeters) Abdomen circumference (in centimeters) 85 90 95 100 105 110 115 70 80 90 120 130 100 110 Hip and Abdomen Circumferences y x
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