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. Data from a portion of this study follow. Risk is interpreted as the probability (times 100) that a person will have a stroke over the next 10-year period. For the smoker variable, 1 indicates a smoker and 0 indicates a nonsmoker Risk Age 59 67 68 63 65 74 Blood Pressure 220 129 170 198 173 172 159 173 Smoker 10 59 30 S2 28 32 20 40 41 25 56 36 32 26 28 18 36 73 68 80 62 82 67 61 61 78 75 90 76 209 176 110 151 191 208 112 125 129 184 153

Risk		Age	Blood Pressure		Smoker
10		59	220		1
33		67	129		0
14		68	170		0
59		63	198		0
30		65	173		0
52		74	172		1
9		77	159		0
28		73	173		0
32		68	117		1
20		80	209		1
40		62	176		1
41		82	110		0
25		67	151		1
56		55	191		0
36		61	208		1
32		61	112		1
26		78	125		0
28		75	129		0
18		90	184		1
36		76	153		1

Answer 1

a)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.3447
R Square	0.1188
Adjusted R Square	0.0151
Standard Error	13.7920
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	436.01	218.00	1.15	0.3413
Residual	17	3233.74	190.22
Total	19	3669.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	77.4348	33.33646226	2.322827337	0.032852868	7.101058467
Age	-0.5524	0.365775689	-1.510241623	0.149345077	-1.324128917
Blood pressure	-0.0460	0.096245603	-0.477487909	0.639096071	-0.249016586

Risk = 77.4348 -0.5524 Age -0.0460 Blood Pressure

s = 13.7920

R^2 = 0.1188

R sq adj = 0.0151

ANOVA
	df	SS	MS	F	Significance F
Regression	2	436.01	218.00	1.15	0.3413
Residual	17	3233.74	190.22
Total	19	3669.75

b)

Risk	Age	Blood pressure	Smoker	AgeBlood Press
10	59	220	1	12980
33	67	129	0	8643
14	68	170	0	11560
59	63	198	0	12474
30	65	173	0	11245
52	74	172	1	12728
9	77	159	0	12243
28	73	173	0	12629
32	68	117	1	7956
20	80	209	1	16720
40	62	176	1	10912
41	82	110	0	9020
25	67	151	1	10117
56	55	191	0	10505
36	61	208	1	12688
32	61	112	1	6832
26	78	125	0	9750
28	75	129	0	9675
18	90	184	1	16560
36	76	153	1	11628

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.3763
R Square	0.1416
Adjusted R Square	-0.0873
Standard Error	14.4915
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	4	519.71	129.93	0.62	0.6560
Residual	15	3150.04	210.00
Total	19	3669.75
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-4.5398	151.3921208	-0.029987319	0.976472522	-327.224511
Age	0.6188	2.141899624	0.288881354	0.776626242	-3.946596115
Blood pressure	0.4244	0.842470241	0.503700146	0.621788703	-1.371330429
Smoker	-0.4745	7.197444628	-0.065924818	0.948308317	-15.81548031
AgeBlood Press	-0.0067	0.012160861	-0.554319766	0.587530033	-0.032661266

Risk = -4.5395 + 0.6188 Age + 0.4244 Blood Pressure -0.4745 Smoker -0.0067 AgeBlood Press

s= 14.4915

R^2 =0.1416

R-sq adj = -0.0873

ANOVA
	df	SS	MS	F	Significance F
Regression	4	519.71	129.93	0.62	0.6560
Residual	15	3150.04	210.00
Total	19	3669.75