The maximum volume of oxygen uptake (VO2 max) has been used as a measure of cardiac (heart) status in healthy individuals as well as in persons suffering from cardiac-related illnesses such as heart attacks. The VO2 max readings for 12 healthy adult males following strenuous exercise were recorded. The goal of the study was to determine whether duration of exercise (in minutes) can be used to predict VO2 max. Assume that a simple linear regression model is appropriate. You will find below an analysis of the data using R.

(A) Specify the response and predictor variables.

(B) Test whether there is a linear association between the VO2 max and duration of exercise, using a test with =0.05. State the alternatives, test statistic , critical value, and conclusion.

(C) Suppose the test in part (B) is carried out by means of a general linear test.

(i) State the full and reduced models.

(ii) Obtain the value of (1) (), (2) (), (3) , (4) , (5) test statistic , and (6) critical value.

(iii) State your conclusion of the test.

(iv)Are the general linear test and the test in part (B) equivalent? Justify. (Hint: Find the relation between in part (C-ii) and in part (B), and the relation between critical value in part (C-ii) and critical value in part (B); make sure to verify the numbers.)

(D) Obtain the coefficient of determination and interpret it in the context of the problem.

(E) Obtain the coefficient of correlation and interpret it in the context of the problem.

(F) Compute the residual for the healthy adult male with duration of exercise of 10 minutes and VO2 max reading of 82.

(G) Given =11.375 and =14.6025, find a 95% confidence interval for the mean VO2 max for adult males with duration of exercise of =11.0.