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 + ϵ σ = 0.4 (a) Interpret β1. Holding all other variables constant, a 1 kg increase in weight will result in a 0.01 L/min decrease in VO2max. correct 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 0.01 kg increase in weight will result in a 1 L/min decrease in VO2max. Holding all other variables constant, a 0.01 kg increase in weight will result in a 1 L/min increase in VO2max. Correct: Your answer is correct. Interpret β3. correct 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 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 0.13 min increase in walk time will result in a 1 L/min increase in VO2max. Correct: Your answer is correct. (b) What is the expected value of VO2max when weight is 78 kg, age is 23 yr, walk time is 15 min, and heart rate is 134 b/m? 1.34 Correct: Your answer is correct. L/min (c) What is the probability that VO2max will be between 0.82 and 1.86 for a single observation made when the values of the predictors are as stated in part (b)? (Round your answer to four decimal places.)

Answer 1