Cardiorespiratory Fitness Is Widely Recognized as a Major Component of Overall

Essay

Cardiorespiratory fitness is widely recognized as a major component of overall physical well-being. Direct measurement of maximal oxygen uptake $\left( \mathrm { VO } _ { 2 } \max \right)$ 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 $\mathrm { VO } _ { 2 } \max$ in terms of easily obtained quantities. Consider the variables $y = V O _ { 2 } \max ( L / \min )$ $x _ { 1 } = \text { weight (kg) }$ $x _ { 2 } = \operatorname { age } ( \mathrm { y } )$ $x _ { 3 } = \text { time necessary to } \text { walk } 1 \mathrm {~m} \text { ile (min) }$
$x _ { 4 } = \text { heart } \mathrm { r } \text { ate at the end of the } \text { walk (beats/min) }$
Here is one possible model, for male students: $Y = 5.0 + .015 x _ { 1 } - .053 x _ { 2 } - .134 x _ { 3 } - .011 x _ { 4 } + \varepsilon$ , and $\sigma = .4$
a. Interpret $\beta _ { 1 } \text { and } \beta _ { 3 }$
.
b. What is the expected value of $\mathrm { VO } _ { 2 } \max$
when weight 75 kg. age is 20 yr, walk time is 15 minutes, and heart rate is 140 b/m?
c. What is the probability that $\mathrm { VO } _ { 2 } \max$
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)?