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11.2.1 Diabetes and obesity are serious health concerns in the United States and much of the developed world. Measuring the amount of body fat a person carries is one way to monitor weight control progress, but measuring it accurately involves either expensive X-ray equipment or a pool in which to dunk the subject. Instead body mass index (BMI) is often used as a proxy for body fat because it is easy to measure: BMI = mass(kg)/ (height(m))² = 703 mass(lb)/(height(in))². In a study of 250 men at Brigham Young University, both BMI and body fat were mea- sured. Researchers found the following summary statistics: n n E x = 6322.28 Σ x ² = 162674.18 i=1 i=1 n Σ.y; = 4757.90 i=1 n Σy? = 107679.27 i=1 n Σ.xy; = 125471.10 i=1 a. Estimate the error standard deviation. b. Estimate the standard deviation of the slope. c. What is the value of the t-statistic for the slope? d. Test the hypothesis that ß₁ = 0 at x = 0.05. What is the P-value for this test?

11.2.1 Diabetes and obesity are serious health concerns in the United States and much of the developed world. Measuring the amount of body fat a person carries is one way to monitor weight control progress, but measuring it accurately involves either expensive X-ray equipment or a pool in which to dunk the subject. Instead body mass index (BMI) is often used as a proxy for body fat because it is easy to measure: BMI = mass(kg)/ (height(m))² = 703 mass(lb)/(height(in))². In a study of 250 men at Brigham Young University, both BMI and body fat were mea- sured. Researchers found the following summary statistics: n n E x = 6322.28 Σ x ² = 162674.18 i=1 i=1 n Σ.y; = 4757.90 i=1 n Σy? = 107679.27 i=1 n Σ.xy; = 125471.10 i=1 a. Estimate the error standard deviation. b. Estimate the standard deviation of the slope. c. What is the value of the t-statistic for the slope? d. Test the hypothesis that ß₁ = 0 at x = 0.05. What is the P-value for this test?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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11.2.1 Diabetes and obesity are serious health concerns in the United States and much of the developed world. Measuring the amount of body fat a person carries is one way to monitor weight control progress, but measuring it accurately involves either expensive X-ray equipment or a pool in which to dunk the subject. Instead body mass index (BMI) is often used as a proxy for body fat because it is easy to measure: BMI = mass(kg)/ (height(m))² = 703 mass(lb)/(height(in))². In a study of 250 men at Brigham Young University, both BMI and body fat were mea- sured. Researchers found the following summary statistics: n n Σ* = 6322.28 Σx = 162674.18 i=1 i=1 n n Σy; = 4757.90 Σy = 107679.27 i=1 i=1 n Σxy = 125471.10 i=1 a. Estimate the error standard deviation. b. Estimate the standard deviation of the slope. c. What is the value of the t-statistic for the slope? d. Test the hypothesis that ß₁ = 0 at α = = 0.05. What is the P-value for this test?
Transcribed Image Text:11.2.1 Diabetes and obesity are serious health concerns in the United States and much of the developed world. Measuring the amount of body fat a person carries is one way to monitor weight control progress, but measuring it accurately involves either expensive X-ray equipment or a pool in which to dunk the subject. Instead body mass index (BMI) is often used as a proxy for body fat because it is easy to measure: BMI = mass(kg)/ (height(m))² = 703 mass(lb)/(height(in))². In a study of 250 men at Brigham Young University, both BMI and body fat were mea- sured. Researchers found the following summary statistics: n n Σ* = 6322.28 Σx = 162674.18 i=1 i=1 n n Σy; = 4757.90 Σy = 107679.27 i=1 i=1 n Σxy = 125471.10 i=1 a. Estimate the error standard deviation. b. Estimate the standard deviation of the slope. c. What is the value of the t-statistic for the slope? d. Test the hypothesis that ß₁ = 0 at α = = 0.05. What is the P-value for this test?
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