Question

A 10-year study conducted by the American Heart Association provided data on how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.

Risk	Age	Pressure
12	57	152
24	67	163
13	58	155
56	86	177
28	59	196
51	76	189
18	56	155
31	78	120
37	80	135
15	78	98
22	71	152
36	70	173
15	67	135
48	77	209
15	60	199
36	82	119
8	66	166
34	80	125
3	62	117
37	59	207

1.       Develop an estimated regression equation that relates risk of a stroke to the person’s age

2.       Develop an estimated regression equation that relates risk of a stroke to the systolic blood pressure

3.       Which model is more deterministic?

Use excel’s data analysis option to obtain regression equations

Answer 1

Answer 3. Model 1 that relates risk of a stroke to the person’s age is more deterministic since the model explains 42.3% of total variability in risk of stroke relative to 15.1% of Model 2.

In simple linear regression, if the response and explanatory variables have an exact relationship, then that relationship is deterministic. So, we make this judgement based on R-square of the model. The one with higher R-square is more deterministic.