Question

A -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 this study. Risk is interpreted as the probability (times ) that the patient will have a stroke over the next -year period. For the smoking variable, define a dummy variable with  indicating a smoker and  indicating a nonsmoker.

Risk		Age		Pressure		Smoker
12		57		153			No
24		67		163			No
13		58		153			No
56		86		175			Yes
28		59		194			No
51		76		188			Yes
18		56		157			Yes
31		78		121			No
37		80		136			Yes
15		78		98			No
22		71		154			No
36		70		173			Yes
15		67		135			Yes
48		77		207			Yes
15		60		199			No
36		82		117			Yes
8		66		168			No
34		80		124			Yes
3		62		115			No
37		59		209			Yes

a. 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.

Please round your answers to three decimal places. Enter negative value as negative number.

        

b. Is smoking a significant factor in the risk of a stroke? Explain. Use .

Compute the  test statistic for the significance of smoking (to 2 decimals). Use t table.

The -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6

What is your conclusion?

Smoking - Select your answer -isis notItem 7 significant factor.

c. What is the probability of a stroke over the next  years for Art Speen, a -year-old smoker who has blood pressure of ?

(to 2 decimals).

Which of the following factors will the doctor recommend Art work on?

- Select your answer -b1 and b2b1 and b3b2 and b3b1, b2 and b3Item 9

Answer 1

Using Excel

0/1 for smoker - =IF(H2="YES",1,0)

Risk	Age	Pressure	Smoker
12	57	153	0
24	67	163	0
13	58	153	0
56	86	175	1
28	59	194	0
51	76	188	1
18	56	157	1
31	78	121	0
37	80	136	1
15	78	98	0
22	71	154	0
36	70	173	1
15	67	135	1
48	77	207	1
15	60	199	0
36	82	117	1
8	66	168	0
34	80	124	1
3	62	115	0
37	59	209	1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.932917464
R Square	0.870334994
Adjusted R Square	0.846022805
Standard Error	5.827840282
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	3647.530442	1215.843481	35.7982988	2.50915E-07
Residual	16	543.4195576	33.96372235
Total	19	4190.95
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-92.4208	15.5591	-5.9400	0.0000	-125.4046
Age	1.0875	0.1691	6.4330	0.0000	0.7291
Pressure	0.2515	0.0460	5.4644	0.0001	0.1539
Smoker	8.7356	3.0405	2.8731	0.0110	2.2900

y^= -92.421 + 1.088 Age + 0.252 Pressure + 8.736 Smoker

b)

p-value of smoker = 0.011

p-value between 0.01 and 0.025

Conclusion

we reject the null hypothesis

Smoking is a significant factor

c)

for smoker

y^= -92.421 + 1.088 Age + 0.252 Pressure + 8.736

just put the value of age and pressure to get y^

p-value of all three factors are less than 0.05

hence

all three b1,b2,b3