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?
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section: Chapter Questions
Problem 8CR
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Step 1: Determine the given variables.
VIEWStep 2: Find the regression equation. Also find SSE
VIEWStep 3: Find the error of the standard deviation.
VIEWStep 4: Find the standard deviation of the slope.
VIEWStep 5: Find the test statistic for the slope.
VIEWStep 6: Test the hypothesis for slope.
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