Medicine and Clinical Studies
Some physicians use the cholesterol ratio (CR = total cholesterol/HDL cholesterol) as a measure of a patient's risk of heart disease. In addition, the triglyceride concentration (TG) is associated with coronary artery disease in many patients. In a study of the relationship between these two variables, a random sample of adults was obtained, and the triglyceride level (x1, mg/dL) and cholesterol ratio (y) was obtained for each person.
a. Carefully sketch a scatter plot of these data (y versus x1). The relationship does not appear to be linear. Can you describe this relationship between y and x1?
b. Compute the natural logarithm of each difference (x1 2 129). That is, find the values of a new predictor variable, x2 = ln(x1 - 129).
c. Carefully sketch a scatter plot of y versus the new predictor variable x2. Describe this relationship.
d. Find the estimated regression line, and complete the ANOVA table using x2 as the predictor variable.