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 variables y 5 VO2max (Lymin) x1 = weight (kg) x2 = age (yr) x3 = time necessary to walk 1 mile (min) x4 = heart rate at the end of the walk (beatsymin) 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" (Research Quarterly for Exercise and Sport, 1994: 152-158):
Y = 5.0 + .01x1 - .05x2 - .13x3 - .01x4 + e = .4
a. Interpret β1 and β3.
b. What is the expected value of VO2max when weight is 76 kg, age is 20 yr, walk time is 12 min, and heart rate is 140 b/m?
c. What is the probability that VO2max will be between 1.00 and 2.60 for a single observation made when the values of the predictors are as stated in part (b)?