Treadmill stress tests were applied to patients with angina

Treadmill stress tests were applied to patients with angina pectoris before and 4 weeks after once-daily dosing with an experimental anti-anginal medication. The main objective for carrying out this study is to check if the improvement in exercise duration is dependent on the patient\'s disease history. The data file \"disease.txt\" represents the disease duration time (in years) since initial diagnosis and percent-improvement in treadmill walking times.

Patient_number Disease_duration Improvement

1               1                1          40

2               2                1          90

3               3                3          30

4               4                2          30

5               5                1          80

6               6                5          60

7               7                1          10

8               8                4         -10

9               9                2          50

10             10                6          40

11             11                1          60

12             12                4           0

13             13                2          50

14             14                2         100

15             15                3          20

16             16                3          70

17             17                5        -30

18             18                3          20

19             19                1          40

20             20                6           0

(a) Identify the response and the explanatory variables with proper reasoning

(b) Check graphically if the dependency between \"improvement\" and \"disease duration time\"

can be considered to be linear

(c) Now, use a formal test of hypothesis to check for the linear relationship in part (b) and

draw appropriate conclusion

(d) How does the disease duration effect the percentage improvement in exercise duration

(e) What assumption did you make to carry out the testing in part (c). Is there any other as-

sumptions required to formulate a linear model for \"improvement\" and \"disease duration

time\"

(f) Check all the model assumptions made in part (d) graphically and comment on the

violation or non violation of the model assumptions with proper reasoning

Solution