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 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 Smoker 12 57 151 No 24 67 164 No 13 58 156 No 56 86 178 Yes 28 59 197 No 51 76 187 Yes 18 56 156 Yes 31 78 122 No 37 80 137 Yes 15 78   95 No 22 71 150 No 36 70 171 Yes 15 67 135 Yes 48 77 207 Yes 15 60 199 No 36 82 119 Yes 8 66 168 No 34 80 127 Yes 3 62 116 No 37 59 208 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. Risk = ___ + ___ Age + ___ Pressure + ___ Smoker b. Is smoking a significant factor in the risk of a stroke? Explain. Use Alpha = .05. Compute the t-test statistic for the significance of smoking (to 2 decimals). Use t table. _____ The P-value is [- Select your answer-] (less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10 What is your conclusion? Smoking [- Select your answer -]    is / is not a significant factor. c. 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? _____ (to 2 decimals). Which of the following factors will the doctor recommend Art work on? [- Select your answer -] (b1 and b2, b1 and b3, b2 and b3, b1, b2 and b3)

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.935164
R Square	0.874533
Adjusted R Square	0.851007
Standard Error	5.732733
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	3665.122	1221.707	37.17438	1.93E-07
Residual	16	525.8277	32.86423
Total	19	4190.95
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-92.2751	15.21072	-6.06645	1.63E-05	-124.52	-60.0298	-124.52	-60.0298
Age	1.082097	0.165617	6.53372	6.89E-06	0.731004	1.433189	0.731004	1.433189
Pressure	0.252896	0.045136	5.60302	3.96E-05	0.157212	0.348579	0.157212	0.348579
smoker	8.661873	2.992392	2.894632	0.010558	2.318285	15.00546	2.318285	15.00546

a)

Risk = -92.275+ 1.082Age + 0.253Pressure + 8.662 Smoker

b)

t stat for smoking=2.895

0.01<p value<0.025

Decison : Reject Ho

Smoking is a significant factor. [because p value <α=0.05]

c)

Risk = -92.275+ 1.082*68 + 0.253*175 + 8.662*1=34.23

all three factor are significant

so, answer is : b1, b2 and b3