Question

A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Assume 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. (See the Stroke file in the document section on regression).

Risk	Age	Pressure	Smoker
12	57	152	No
24	67	163	No
13	58	155	No
56	86	177	Yes
28	59	196	No
51	76	189	Yes
18	56	155	Yes
31	78	120	No
37	80	135	Yes
15	78	98	No
22	71	152	No
36	70	173	Yes
15	67	135	Yes
48	77	209	Yes
15	60	199	No
36	82	119	Yes
8	66	166	No
34	80	125	Yes
3	62	117	No
37	59	207	Yes

1. Develop an estimated regression equation that relates risk of a stroke to the person’s age, blood pressure, and whether the person is a smoker.
2. Is smoking a significant factor in the risk of a stroke? Explain. Use α = .05.
3. What is the probability of a stroke over the next 10 years for Art Speen, a 68-year-old smoker who has blood pressure of 175? What action might the physician recommend for this patient?

Answer 1

(a)

Go to Data --> Daya Analysis --> Regression and enter the following details:

E F G H I IK Regression ? X 57 Pressure Smoker 152 163 Input Input Y Range: | OK $A$1:$A$21 Cancel 177 Input X Range: $8$1:$D$21 Help Labels Confidence Level: Constant is Zero 95 % AB 1 Risk Age 2 12 3 24 4 13 58 5 56 86 6 28 59 7 51 76 8 18 56 9 31 78 10 37 80 11 15 78 12 22 71 13 36 70 14 15 67 15 48 77 16 15 60 17 36 82 18 8 66 19 34 80 20 3 62 135 SM$2 Output options Output Range: New Worksheet Ply: New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots 152 173 135 209 199 119 166 125 117 207 Normal Probability Normal Probability Plots 21

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.935
R Square	0.873
Adjusted R Square	0.850
Standard Error	5.757
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	3660.74	1220.25	36.82	2.06404E-07
Residual	16	530.21	33.14
Total	19	4190.95
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-91.76	15.22	-6.03	0.00	-124.03	-59.49
Age	1.08	0.17	6.49	0.00	0.72	1.43
Pressure	0.25	0.05	5.57	0.00	0.16	0.35
Smoker	8.74	3.00	2.91	0.01	2.38	15.10

So, the regression equation is as follows:

Risk = -91.76 + 1.08 * Age + 0.25 * Pressure + 8.74 * Smoker

(b)

The P-value for the slope coefficient of 'Smoker' is 0.01 which is less than α = 0.05. So, the null hypothesis that the coefficient is zero is rejected. So, the positive value of 8.74 is significant. Therefore, smoking a statistically significant factor in the risk of a stroke.

(c)

Age = 68
Pressure = 175
Smoker = Yes i.e. 1

So,

Risk = -91.76 + 1.08 * 68 + 0.25 * 175 + 8.74 * 1 = 34.17

So, the risk is about 34%