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 + ϵσ = 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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Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter2: Exponential, Logarithmic, And Trigonometric Functions

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Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...

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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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