In a study published in Medicine and Science in Sports and Exercise (volume 17, no. 2,...

 

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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 (-0.874). The partial table shown. bere lists only the first nine rows of the data. Age Weight Height Neck Chest Abdom. (yr) (in.) (cm) (lb) 173.25 72.25 154.00 66.25 154.25 67.75 (cm) (cm) 38.5 93.6 34.0 95.8 36.2 93.1 73.50 42.1 99.6 35.5 92.1 38.0 77.50 96.6 71.25 34.4 97.3 74.75 39,0 70.75 35.7 2222 23 23 198.25 23 23 24 24 24 159.75 72.25 188.15 184.25 210.25 156,00 104.5 92.7 83.0 87.9 85.2 88.6 77.1 (a) (weight, neck) (c) (age, body fat) (e) (age, wrist) (g) (forearm, height) (i) (weight, body fat) (k) (hip, abdomen) 85.3 100.0 94,4 81.9 Hip (cm) 98.7 58.7 99.2 59,6 94.5 59.0 104.1 63.1 93.9 56.1 102.5 59.1 101.9 63.2 107.8 66.0 95.3 56.4 EXERCISES 1. Using your intuition, classify each (x,y) pair as having a weak correlation (0 <r< 0.5). a moderate correlation (0.5<r< 0.8), or a strong correlation (0.8 <r< 1.0). (b) (weight, height) (d) (chest, hip). (f) (ankle, wrist) (h) (bicep, forearm) (j) (knee, thigh) (1) (abdomen, hip) 130 2. Use technology to find the correlation coefficient for each pair in Exercise 1. Compare your results with those obtained by intuition. Hip and Abdomen Circumferences Thigh Knee Ankle Bicep Forearm Wrist Body (cm) (cm) (cm) (cm) (cm) (cm) 100 100 tin 115 Hip circumference (in centimeters) 37.3 234 38.9 24.0 37:3 41.7 36.1 37.6 42.2 42.0 36.5 30.5 28.8 23,2 24.0 25.6 22.0 32.0 21.9 25,0 35.6 30.0 22.7 30.5 27.2 28.9 31.8 32.2 35.7 33.5 25,2 27.4 Source: "Generalized Body Composition Prediction Equation for Men Using Simple Measurement Techniques" by KW, Penrose et al. (19 MEDICINE AND SCIENCE IN SPORTS AND EXERCISE, vol. 12 002, p. 189 29.7 27.7 30.6 28.3 18.2 16.6 17.1 19.2 18.2 18.3 17.7 18.8 17.3 6.1 25.3 12.3 11.7 94 103 28,7 20.9 14.2 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. 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 (-0.874). The partial table shown. bere lists only the first nine rows of the data. Age Weight Height Neck Chest Abdom. (yr) (in.) (cm) (lb) 173.25 72.25 154.00 66.25 154.25 67.75 (cm) (cm) 38.5 93.6 34.0 95.8 36.2 93.1 73.50 42.1 99.6 35.5 92.1 38.0 77.50 96.6 71.25 34.4 97.3 74.75 39,0 70.75 35.7 2222 23 23 198.25 23 23 24 24 24 159.75 72.25 188.15 184.25 210.25 156,00 104.5 92.7 83.0 87.9 85.2 88.6 77.1 (a) (weight, neck) (c) (age, body fat) (e) (age, wrist) (g) (forearm, height) (i) (weight, body fat) (k) (hip, abdomen) 85.3 100.0 94,4 81.9 Hip (cm) 98.7 58.7 99.2 59,6 94.5 59.0 104.1 63.1 93.9 56.1 102.5 59.1 101.9 63.2 107.8 66.0 95.3 56.4 EXERCISES 1. Using your intuition, classify each (x,y) pair as having a weak correlation (0 <r< 0.5). a moderate correlation (0.5<r< 0.8), or a strong correlation (0.8 <r< 1.0). (b) (weight, height) (d) (chest, hip). (f) (ankle, wrist) (h) (bicep, forearm) (j) (knee, thigh) (1) (abdomen, hip) 130 2. Use technology to find the correlation coefficient for each pair in Exercise 1. Compare your results with those obtained by intuition. Hip and Abdomen Circumferences Thigh Knee Ankle Bicep Forearm Wrist Body (cm) (cm) (cm) (cm) (cm) (cm) 100 100 tin 115 Hip circumference (in centimeters) 37.3 234 38.9 24.0 37:3 41.7 36.1 37.6 42.2 42.0 36.5 30.5 28.8 23,2 24.0 25.6 22.0 32.0 21.9 25,0 35.6 30.0 22.7 30.5 27.2 28.9 31.8 32.2 35.7 33.5 25,2 27.4 Source: "Generalized Body Composition Prediction Equation for Men Using Simple Measurement Techniques" by KW, Penrose et al. (19 MEDICINE AND SCIENCE IN SPORTS AND EXERCISE, vol. 12 002, p. 189 29.7 27.7 30.6 28.3 18.2 16.6 17.1 19.2 18.2 18.3 17.7 18.8 17.3 6.1 25.3 12.3 11.7 94 103 28,7 20.9 14.2 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. Case Study 497