An exercise physiologist used skinfold measurements to estimate the total body fat, expressed as a percentage of body weight, for 10 male participants in a physical fitness program. The body fat percentages and the body weights are shown in the table below. Using this information and the output from R, interpret the strength and direction of the linear relationship between body weight and body fat for men. Participant Weight Fat X (kg) Y (%) 1 89 28 2 88 27 3 66 24 4 59 23 5 93 27 6 73 26 7 82 29 8 77 25 9 100 33 10 67 29 Pearson's product-moment correlation data: weight and fat t = 2.911, df = 8, p-value = 0.01956 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: 0.1596912 0.9278440 sample estimates: cor 0.7172055
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This problem uses the dataset BodyFat, which gives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (in pounds), Height (in inches), and circumference (in cm) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. Using Weight to Predict Body Fat Figure 1 shows the data and regression line for using weight to predict body fat percentage. For the case with the largest positive residual, estimate the values of both variables. In addition, estimate the predicted body fat percent and the residual for that point. Using weight to predict percent body fat Click here for the dataset associated with this question. Weight: lbs Body fat: % Predicted body fat: % Residual: %
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Predicting Percent Body Fat This problem uses the dataset BodyFat, which gives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (in pounds), Height (in inches), and circumference (in cm) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. Using Weight to Predict Body Fat The figure shows the data and regression line for using weight to predict body fat percentage. For the case with the largest positive residual, estimate the values of both variables. In addition, estimate the predicted body fat percent and the residual for that point. Using weight to predict percent body fat Click here for the dataset associated with this question. Weight: Body fat: Predicted body fat: Residual:
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Use the dataset BodyFat, which gives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (in pounds), Height (in inches), and circumference (in $\mathrm{cm}$ ) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. $^{78}$ Figure 2.74 shows the data and regression line for using abdomen circumference to predict body fat percentage. (a) Which scatterplot, the one using Weight in Figure 2.73 or the one using Abdomen in Figure 2.74, appears to contain data with a larger correlation? (b) In Figure 2.74 , one person has a very large abdomen circumference of about $127 \mathrm{~cm} .$ Estimate the actual body fat percent for this person as well as the predicted body fat percent. (c) Use Figure 2.74 to estimate the abdomen circumference for the person with about $40 \%$ body fat. In addition, estimate the residual for this person.
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Two Quantitative Variables: Linear Regression
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