Chapter 13, Problem 67SE

The article “Validation of the Rockport Fitness Walking Test in College Males and Females” (Research Quarterly for Exercise and Sport, 1994: 152–158) recommended the following estimated regression equation for relating y = VO₂max (L/min, a measure of cardiorespiratory fitness) to the predictors x₁ = gender (female = 0, male = 1, x₂ = weight (lb), x₃ = 1-mile walk time (min), and x₄ = heart rate at the end of the walk (beats/min):

     $y=3.5959+.6566x_1+.0096x_2-.0996x_3-.0080x_4$

a.    How would you interpret the estimated coefficient ${\hat{\beta }}_3=-.0996$?

b.    How would you interpret the estimated coefficient ${\hat{\beta }}_1=-.0996$?

c.    Suppose that an observation made on a male whose weight was 170 lb, walk time was 11 min, and heart rate was 140 beats/min resulted in VO₂max 5 3.15. What would you have predicted for VO₂max in this situation, and what is the value of the corresponding residual?

d.    Using SSE 5 30.1033 and SST 5 102.3922, what proportion of observed variation in VO₂max can be attributed to the model relationship?

e.    Assuming a sample size of n = 20, carry out a test of hypotheses to decide whether the chosen model specifies a useful relationship between VO₂max and at least one of the predictors.