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	Blood 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
15	60	199	0
36	82	119	1
8	66	166	0
34	80	125	1
3	62	117	0
37	59	207	1

(a) Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood-pressure level. Use x₁ for age and x₂ for blood-pressure level. (Round your constant term to one decimal place and coefficients to three decimal places.)

=

(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. Use x₃ for whether the person is a smoker. (Round your constant term to one decimal place, the coefficient for x₃ to two decimal places and all other coefficients to three decimal places.)

=

(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).

State the null and alternative hypotheses.

H₀: One or more of the parameters is not equal to zero. H_a: ₁ = ₂ = 0

H₀: ₁ = ₂ = 0 H_a: One or more of the parameters is not equal to zero.

H₀: ₃ = ₄ = 0 H_a: One or more of the parameters is not equal to zero.

H₀: One or more of the parameters is not equal to zero. H_a: ₃ = ₄ = 0

(D) Find the value of the test statistic. (Round your answer to two decimal places.)

(E) Find the p-value. (Round your answer to three decimal places.)

p-value =

(F) Is the addition of the interaction term and the smoker variable significant?

Do not reject H₀. We conclude that the addition of the interaction term and the smoker variable is not significant.

Reject H₀. We conclude that the addition of the interaction term and the smoker variable is significant.

Do not reject H₀. We conclude that the addition of the interaction term and the smoker variable is significant.

Reject H₀. We conclude that the addition of the interaction term and the smoker variable is not significant.