Cardiorespiratory fitness is widely recognized as a major component of overall p
ID: 3276200 • Letter: C
Question
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 +
= 0.4
(b) What is the expected value of VO2max when weight is 77 kg, age is 20 yr, walk time is 10 min, and heart rate is 130 b/m?
(c) What is the probability that VO2max will be between 1.57 and 2.77 for a single observation made when the values of the predictors are as stated in part (b)? (Round your answer to four decimal places.)
Explanation / Answer
b) The expected vlaue of VO2max is
Y = 5.0 + 0.01(77) 0.05(20) 0.13(10) 0.01(130) = 2.17
c) E(Y) = 2.17 of a single observation
Var(Y) = 0.42 = 0.16
P(1.57<Y<2.77) = P((1.57-2.17)/0.16 < Z< (2.77-2.17)/0.16) = P(-3.75<Z<3.75) = 0.9999