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 that the following data are from a portion of the study. Risk is interpreted as the probability that the patient will have a stroke over the next 10 year period. For the smoking variable, define a dummy variable 1 with indicating a smoker and 0 indicating a non-smoker.

Risk	Age	Pressure	Smoker
12	57	152	0
24	67	163	0
13	58	155	0
56	86	177	1
28	59	196	0
51	76	189	1
18	56	155	1
31	78	120	0
37	80	135	1
15	78	98	0
22	71	152	0
36	70	173	1
15	67	135	1
48	77	209	1

SUMMARY OUTPUT
Regression Statistics

Multiple R	0.967777
R Square	0.936593
Adjusted R Square	0.917571
Standard Error	4.231574
Observations	14

ANOVA

	df	SS	MS	F	Significance F
Regression	3				2.7E-06
Residual	10
Total	13

	Coefficients	Standard Error	t Stat	P-value
Intercept	-96.245	12.16893	-7.90908	1.3E-05
Age	1.096419	0.132705	8.262106
Pressure	0.294972			4.09E-05
Smoker	3.906635	2.616022	1.493349

A) Construct a 90% confidence interval estimate for the coefficient for Age.
B) Is this regression model a good predictor for risk of stroke? Explain how you know.
C) Predict the risk for a 60 year old smoker wiht blood pressure of 160.
D) Is Smoker a significant independent variable? How do you know?

Answer 1

A) a 90% confidence interval estimate for the coefficient for Age

B) Since R² = 0.9365 is quite close to 1, so we can sau that the regression model is a significantly good predictor.

c) The predicted risk for a 60 year old smoker wiht blood pressure of 160

= -96.245 + (1.096419*60) + (0.294972*160) + (3.906635*1)

= 20.642

d) P-value for Smoker

Since P-value = 0.083105 > 0.05, so at 5% level of significance, we can conclude that smoker is a not a significant independent variable.