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. 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	Blood Pressure		Smoker
10		85	150		1
30		68	207		1
11		64	104		0
61		86	127		0
39		70	139		0
49		83	155		0
7		68	179		1
36		84	176		0
41		57	169		0
25		66	161		1
39		69	122		0
37		90	101		0
26		89	124		0
63		81	118		0
35		84	181		0
33		89	176		0
30		66	156		1
34		66	164		1
15		74	210		1
32		76	160		1

a. Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood pressure level. Enter negative value as negative number. Use Table 4 in Appendix B.

The regression equation is (to 4 decimals)

Risk=_______+________ age+________ blood pressure

S=____ (to 4 decimals) R^2=_____ (to 4 decimals) R^2 adj____ (to 4 decimals)

Analysis of Variance

SOURCE DF SS (to 2 decimals) MS (to 2 decimals) (to 2 decimals) -value (to 4 decimals) Regression Residual Total

b. Consider adding two independent variables to the model developed in part (a), one for the interaction between age and blood pressure level and the other for whether the person is a smoker. Develop an estimated regression equation using these four independent variables. Enter negative value as negative number. Use Table 4 in Appendix B.

The regression equation is (to 4 decimals)

Risk=______+______ age+_______ blood pressure

S= (to 4 decimals) R^2= (to 4 decimals) R^2 adj= (to 4 decimals)

Analysis of Variance

SOURCE DF SS (to 2 decimals) MS (to 2 decimals) (to 2 decimals) -value (to 4 decimals) Regression Residual Total

c. At a  level of significance, test to see whether the addition of the interaction term and the smoker variable contribute significantly to the estimated regression equation developed in part (a). Use Table 4 in Appendix B.

What is the value of the F test statistic?

(to 2 decimals)

P-value is - Select your answer -lower than 0.01between 0.01 and 0.025between 0.025 and 0.05between 0.05 and 0.10greater than 0.10Item 36 , so the addition of the two independent variables - Select your answer -is not is 37 statistically significant.

Answer 1

a. Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood pressure level. Enter negative value as negative number. Use Table 4 in Appendix B.

The regression equation is (to 4 decimals)

Risk=27.8343+0.3062 age+(-0.1194) blood pressure

S=____ (14.7882) R^2=_____ (0.1249) R^2 adj____ (0.0220)

ANOVA
	df	SS	MS	F
Regression	2	530.8051	265.4026	1.2136
Residual	17	3717.7449	218.6909
Total	19	4248.5500

Regression Analysis
Regression Statistics
Multiple R	0.3535
R Square	0.1249
Adjusted R Square	0.0220
Standard Error	14.7882
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	530.8051	265.4026	1.2136	0.3216
Residual	17	3717.7449	218.6909
Total	19	4248.5500
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	27.8343	34.2284	0.8132	0.4274	-44.3814	100.0499
Age	0.3062	0.3434	0.8917	0.3850	-0.4183	1.0307
Blood Pressure	-0.1194	0.1121	-1.0649	0.3018	-0.3559	0.1171

b. Consider adding two independent variables to the model developed in part (a), one for the interaction between age and blood pressure level and the other for whether the person is a smoker. Develop an estimated regression equation using these four independent variables. Enter negative value as negative number. Use Table 4 in Appendix B.

The regression equation is (to 4 decimals)

Risk=-143.4202+2.3621 age+1.2060blood pressure+(-0.0156) ageBp+(-18.7861)smoker

S= (13.1818) R^2= (0.3865) R^2 adj= (0.2229)

ANOVA
	df	SS	MS	F
Regression	4	1642.1534	410.5384	2.3627
Residual	15	2606.3966	173.7598
Total	19	4248.5500

Regression Analysis
Regression Statistics
Multiple R	0.6217
R Square	0.3865
Adjusted R Square	0.2229
Standard Error	13.1818
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	4	1642.1534	410.5384	2.3627	0.0999
Residual	15	2606.3966	173.7598
Total	19	4248.5500
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-143.4202	126.7083	-1.1319	0.2755	-413.4925	126.6521
Age	2.3621	1.6233	1.4551	0.1662	-1.0979	5.8221
Blood Pressure	1.2060	0.8502	1.4185	0.1765	-0.6062	3.0183
age*Bp	-0.0156	0.0109	-1.4328	0.1724	-0.0388	0.0076
Smoker	-18.7861	7.8138	-2.4042	0.0296	-35.4409	-2.1313

c. At a  0.05 level of significance, test to see whether the addition of the interaction term and the smoker variable contribute significantly to the estimated regression equation developed in part (a). Use Table 4 in Appendix B.

	df	SS	MS	F
Regression(part a)	2	530.8051
Regression	4	1642.153403	410.538
Regression addition 2 variable	2	1111.3483	555.674	3.1979
Residual	15	2606.396597	173.76
Total	19	4248.55

What is the value of the F test statistic? 3.20

(to 2 decimals)

P-value is - Select your answer

-lower than 0.01

between 0.01 and 0.025

between 0.025 and 0.05

correct option: between 0.05 and 0.10

greater than 0.10

Item 36 , so the addition of the two independent variables - Select your answer

-is not statistically significant.