Question

Cardiorespiratory fitness is widely recognized as a major component of overall physical weliibeing. Direct measurement of maximal oxygen uptake (VOQmax) is the single best measure of such fitness, but direct measurement is timeiconsuming and expenswe. It is therefore desirable to have a prediction equation for VOZrnax in terms of easily obtained quantities. ConSider the variables y : VOZmax (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) Consider the model of the entire population. Y: .30 + 31X1 +32X2 + 33X3 + 34x4 t 5: Here is one possible model for male students: Y: 5.0 + 0.012x1 7 ().05x2 7 0.12x3 7 0.0m4 + s a : 0.4 (a) Interpret [31. Holding all other variables constant, a 1 kg increase in weight will result in a 0.012 lein increase in VOZmax. 0 Holding all other variables constant, a 0.012 kg increase in weight will result in a 1 lein increase in VOZmax. 0 Holding all other variables constant, a 1 kg increase in weight will result in a 0.012 L/min decrease in VOZmax. 0 Holding all other variables constant, a 0.012 kg increase in weight Will result in a 1 Lfmin decrease in VOZmax. Interpret ,5'3. 0 Holding all other variables constant, a 0.12 min increase in walk time will result in a 1 L/rnin decrease in V02max. 0 Holding all other variables constant, a 0.12 min increase in walk time will result in a 1 L/min increase in VOZmax. Holding all other variables constant, a 1 min increase in walk time will result in a 0.12 L/min decrease in VOZmax. 0 Holding all other variables constant, a 1 min increase in walk time will result in a 0.12 L/min increase in VOZmax. J (b) What is the expected value of VOzmax, .uy, when weight is 76 kg, age is 22 yr, walk time is 10 min, and heart rate is 134 b/m? 2,272 4 L/min (c) What is the probability VOZmax is between 1.832 and 2.712, when weight is 76 kg, age is 22 yr, walk time is 10 min, and heart rate is 134 b/m? S X Hint: The response varies normally with a mean of y and a standard deviation of a