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To investigate the dependence of energy expenditure on body build, researchers used underwater weighing techniques to determine the fat-free body mass (x) for a group of 7 men. They also measured the total energy expenditure (y) for each man during the conditions of quiet sedentary activity. The results are shown in the table. Fat-Free Mass (kg) Energy Expenditure (kcal) 49.3 1894 59.3 68.3 47.1 2050 2353 1838 1948 57.6 78.1 2528 76.1 2568 Mean 62.257 2168.429 Standard deviation 12.296 308.254 r= 0.97985 a. State the linear regression equation and predict the energy expenditure of a man with 60 kg of fat-free mass, with a significance level of 0.01. Assume the pairs of data follow a bivariate normal distribution and that the scatterplot shows no evidence of a non-linear relationship in the data. b. Determine the percentage of energy expenditure that is explained by the linear relationship between fat-free mass and energy expenditure.

To investigate the dependence of energy expenditure on body build, researchers used underwater weighing techniques to determine the fat-free body mass (x) for a group of 7 men. They also measured the total energy expenditure (y) for each man during the conditions of quiet sedentary activity. The results are shown in the table. Fat-Free Mass (kg) Energy Expenditure (kcal) 49.3 1894 59.3 68.3 47.1 2050 2353 1838 1948 57.6 78.1 2528 76.1 2568 Mean 62.257 2168.429 Standard deviation 12.296 308.254 r= 0.97985 a. State the linear regression equation and predict the energy expenditure of a man with 60 kg of fat-free mass, with a significance level of 0.01. Assume the pairs of data follow a bivariate normal distribution and that the scatterplot shows no evidence of a non-linear relationship in the data. b. Determine the percentage of energy expenditure that is explained by the linear relationship between fat-free mass and energy expenditure.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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To investigate the dependence of energy expenditure on body build, researchers used underwater weighing techniques to determine the fat-free body mass (x) for a group of 7 men. They also measured the total energy expenditure (y) for each man during the conditions of quiet sedentary activity. The results are shown in the table. Fat-Free Mass (kg) Energy Expenditure (kcal) 49.3 1894 59.3 68.3 2050 2353 47.1 1838 57.6 1948 78.1 2528 76.1 2568 Mean 62.257 2168.429 Standard deviation 12.296 308.254 T = 0.97985 a. State the linear regression equation and predict the energy expenditure of a man with 60 kg of fat-free mass, with a significance level of 0.01. Assume the pairs of data follow a bivariate normal distribution and that the scatterplot shows no evidence of a nón-linear relationship in the data. b. Determine the percentage of energy expenditure that is explained by the linear relationship between fat-free mass and energy expenditure.
Transcribed Image Text:To investigate the dependence of energy expenditure on body build, researchers used underwater weighing techniques to determine the fat-free body mass (x) for a group of 7 men. They also measured the total energy expenditure (y) for each man during the conditions of quiet sedentary activity. The results are shown in the table. Fat-Free Mass (kg) Energy Expenditure (kcal) 49.3 1894 59.3 68.3 2050 2353 47.1 1838 57.6 1948 78.1 2528 76.1 2568 Mean 62.257 2168.429 Standard deviation 12.296 308.254 T = 0.97985 a. State the linear regression equation and predict the energy expenditure of a man with 60 kg of fat-free mass, with a significance level of 0.01. Assume the pairs of data follow a bivariate normal distribution and that the scatterplot shows no evidence of a nón-linear relationship in the data. b. Determine the percentage of energy expenditure that is explained by the linear relationship between fat-free mass and energy expenditure.
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