21.(20 points) 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.

Use the following R linear regression output to answer questions.

Call: lm(formula = Oxygen ~ RunPulse, data = oxy)  Coefficients:  Estimate Std. Error t value Pr(>|t|) (Intercept) 82.42903 15.044 5.481 0.001 *** RunPulse -0.20691 0.089 -2.336 0.027 ***  Residual standard error: 4.971 on 29 degrees of freedom Multiple R-squared: 0.1582, Adjusted R-squared: 0.1291 F-statistic: 5.423 on 1 and 29 DF, p-value = 0.027 

1. (2 points) What is the equation of the least squares regression line?

1. (2 points) How is the estimated slope for running heart rate interpreted here?

1. (2 points) What percent of the variability in oxygen intake is explained by running heart rate?

1. (4 points) What is the residual for a man with running heart rate of 170 and oxygen intake rate of 50 ml per kg body weight per minute?

1. (10 points)Previous studies indicate that oxygen consumption decreases with an increasing heart rate while running. Does the study support this finding? Use a significance level of 5% (or 0.05).

i.(2 points) Write down the null and alternative hypotheses.

ii.(2 points) What is the standard error of the slope?

iii.(2 points) Find the value of the test statistic.

iv.(2 points) Find the p-value.

v.(2 points) State your conclusion in terms of the problem.