Aerobic fitness, measured by the ability to consume oxygen, relates to the heart, blood vessels, and lungs working together to deliver oxygen-rich blood to the muscles during exercise. A high level of aerobic fitness is associated with lower risks of several diseases, including high blood pressure and coronary heart disease. In a study of aerobic fitness, a sample of 31 men involved in a physical fitness course at a university was randomly selected. The measurements included Oxygen: the oxygen intake rate (ml per kg body weight per minute),
RunPulse: the heart rate while running.
Our goal is to examine whether oxygen consumption is dependent upon the heart rate while running.
The following is part of the SAS output:
Parameter Estimates Standard Variable Parameter Estimate DF Error t Value Pr? Intercept RunPulse 82.4582!5 -0.20680 15.04386 0.08852 5.48 -2.34 ?,0001 0.0266
a. Write down the fitted regression equation. How is the estimated regression coefficient for RunPulse interpreted here? Is the intercept estimate meaningful in this context?
b. Suppose that one subject had a runpulse of 170 and oxygen intake rate of 50 ml per kg body weight per minute, what is the residual for this subject?
Construct the 95% confidence interval for the average change in oxygen intake rate when the running heart rate is increased by one. Interpret the results.
c. Suppose that previous studies indicate that oxygen consumption decreases with an increasing heart rate while running. Does the study support this finding? Write down the hypotheses, calculate the test statistic and p-value, and state your conclusion in terms of the problem.
d. Given that R2 = 0.1584, SSE = 716.5368, complete the following ANOVA table:
Source DF Sum of squares Mean of square F Value P-value
Model
Error 29 716.5368
Corrected
Total 30 851.3815
e. What is the estimated standard deviation of the random errors in the model?
f. What is the correlation coefficient between oxygen consumption and hear rate while running?