Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO2max) is the single best measure of such fitness, but direct measurement is time-consuming and expensive. It is therefore desirable to have a prediction equation for VO2max in terms of easily obtained quantities. Consider the following variables. y = VO2max (L/min) x1 = weight (kg) x2 = age (yr) x3 = time necessary to walk 1 mile (min) x4 = heart rate at the end of the walk (beats/min) Here is one possible model for male students, consistent with the information given in the article "Validation of the Rockport Fitness Walking Test in College Males and Females."† Y = 5.0 + 0.01x1 − 0.05x2 − 0.13x3 − 0.01x4 + ϵ σ = 0.4 (a) Interpret β1. Holding all other variables constant, a 0.01 kg increase in weight will result in a 1 L/min increase in VO2max.Holding all other variables constant, a 0.01 kg increase in weight will result in a 1 L/min decrease in VO2max. Holding all other variables constant, a 1 kg increase in weight will result in a 0.01 L/min increase in VO2max.Holding all other variables constant, a 1 kg increase in weight will result in a 0.01 L/min decrease in VO2max. Interpret β3. Holding all other variables constant, a 1 min increase in walk time will result in a 0.13 L/min increase in VO2max.Holding all other variables constant, a 0.13 min increase in walk time will result in a 1 L/min decrease in VO2max. Holding all other variables constant, a 1 min increase in walk time will result in a 0.13 L/min decrease in VO2max.Holding all other variables constant, a 0.13 min increase in walk time will result in a 1 L/min increase in VO2max. (b) What is the expected value of VO2max when weight is 78 kg, age is 19 yr, walk time is 14 min, and heart rate is 138 b/m? L/min (c) What is the probability that VO2max will be between 1.19 and 2.07 for a single observation made when the values of the predictors are as stated in part (b)? (Round your answer to four decimal places.)

Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO2max) is the single best measure of such fitness, but direct measurement is time-consuming and expensive. It is therefore desirable to have a prediction equation for VO2max in terms of easily obtained quantities. Consider the following variables. y = VO2max (L/min) x1 = weight (kg) x2 = age (yr) x3 = time necessary to walk 1 mile (min) x4 = heart rate at the end of the walk (beats/min) Here is one possible model for male students, consistent with the information given in the article "Validation of the Rockport Fitness Walking Test in College Males and Females."† Y = 5.0 + 0.01x1 − 0.05x2 − 0.13x3 − 0.01x4 + ϵ σ = 0.4 (a) Interpret β1. Holding all other variables constant, a 0.01 kg increase in weight will result in a 1 L/min increase in VO2max.Holding all other variables constant, a 0.01 kg increase in weight will result in a 1 L/min decrease in VO2max. Holding all other variables constant, a 1 kg increase in weight will result in a 0.01 L/min increase in VO2max.Holding all other variables constant, a 1 kg increase in weight will result in a 0.01 L/min decrease in VO2max. Interpret β3. Holding all other variables constant, a 1 min increase in walk time will result in a 0.13 L/min increase in VO2max.Holding all other variables constant, a 0.13 min increase in walk time will result in a 1 L/min decrease in VO2max. Holding all other variables constant, a 1 min increase in walk time will result in a 0.13 L/min decrease in VO2max.Holding all other variables constant, a 0.13 min increase in walk time will result in a 1 L/min increase in VO2max. (b) What is the expected value of VO2max when weight is 78 kg, age is 19 yr, walk time is 14 min, and heart rate is 138 b/m? L/min (c) What is the probability that VO2max will be between 1.19 and 2.07 for a single observation made when the values of the predictors are as stated in part (b)? (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake (VO₂max) is the single best measure of such fitness, but direct measurement is time-consuming and expensive. It is therefore desirable to have a prediction equation for VO₂max in terms of easily obtained quantities. Consider the following variables.

y = VO₂max (L/min)
x₁ = weight (kg)
x₂ = age (yr)
x₃ = time necessary to walk 1 mile (min)
x₄ = heart rate at the end of the walk (beats/min)

Here is one possible model for male students, consistent with the information given in the article "Validation of the Rockport Fitness Walking Test in College Males and Females."†

Y = 5.0 + 0.01x₁ − 0.05x₂ − 0.13x₃ − 0.01x₄ + ϵ

σ = 0.4

(a) Interpret β₁.

Holding all other variables constant, a 0.01 kg increase in weight will result in a 1 L/min increase in VO₂max.Holding all other variables constant, a 0.01 kg increase in weight will result in a 1 L/min decrease in VO₂max. Holding all other variables constant, a 1 kg increase in weight will result in a 0.01 L/min increase in VO₂max.Holding all other variables constant, a 1 kg increase in weight will result in a 0.01 L/min decrease in VO₂max.

Interpret β₃.

Holding all other variables constant, a 1 min increase in walk time will result in a 0.13 L/min increase in VO₂max.Holding all other variables constant, a 0.13 min increase in walk time will result in a 1 L/min decrease in VO₂max. Holding all other variables constant, a 1 min increase in walk time will result in a 0.13 L/min decrease in VO₂max.Holding all other variables constant, a 0.13 min increase in walk time will result in a 1 L/min increase in VO₂max.

(b) What is the expected value of VO₂max when weight is 78 kg, age is 19 yr, walk time is 14 min, and heart rate is 138 b/m?
L/min

(c) What is the probability that VO₂max will be between 1.19 and 2.07 for a single observation made when the values of the predictors are as stated in part (b)? (Round your answer to four decimal places.)

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