16.5 A study was designed to evaluate treatments for hypertension. The researchers were concerned that whether the patient smoked may impact the effectiveness of the treatments so they also recorded the number of cigarettes smoked daily by the patients. After one month on the treatment, the treating doctors assigned each patient an index based on blood pressure, cholesterol level, and amount of exercise, which reflected the patient's risk of cardiovascular disease (CVD). The index ranged from 0 to 100 with the higher values indicating a greater risk of CVD. The data are presented here with notation: RISK = risk index for CVD, NOCIG = number of
cigarettes smoked daily, C = standard treatment, I = new treatment 1, II = new treatment 2.

a. Write a model for the above experiment. Make sure to identify all variables and parameters in your model.

b. Provide a scatterplot of the data with regression lines which would allow a visual assessment of whether there is a significant relationship between risk index of CVD and the number of cigarettes smoked.

c. From your scatterplot in (b), do the three lines appear to have similar slopes?