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 = VO2 max (L/min, a measure of cardio respiratory 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 + .6566x1 + .0096x2 -.0996x3 - .0080x4
a. How would you interpret the estimated coefficient β^3 = -.0996?
b. How would you interpret the estimated coefficient β^1 = .6566?
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 VO2 max = 3.15. What would you have predicted for VO2 max in this situation, and what is the value of the corresponding residual?
d. Using SSE = 30.1033 and SST = 102.3922, what proportion of observed variation in VO2 max 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 VO2 max and at least one of the predictors.