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 (Dataset "Stroke"). 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.
a. Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood-pressure level.
a) Risk = -110.942 + 1.515 Age + 0.296 Blood Pressure
b) Risk = -110.942 + 1.315 Age + 0.296 Blood Pressure
c) Risk = -108.942 + 1.315 Age + 0.296 Blood Pressure
d) Risk = -110.942 + 1.315 Age + 0.396 Blood Pressure
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.
a) Risk = -123.16 + 1.51 Age + 0.45 Blood Pressure + 8.87 Smoker – 0.013 Age*Blood Pressure
b) Risk = -123.16 + 1.51 Age + 0.45 Blood Pressure + 8.97 Smoker – 0.003 Age*Blood Pressure
c) Risk = -123.16 + 1.41 Age + 0.45 Blood Pressure + 8.87 Smoker – 0.003 Age*Blood Pressure
d) Risk = -123.16 + 1.51 Age + 0.45 Blood Pressure + 8.87 Smoker – 0.003 Age*Blood Pressure
c. At a 0.05 level of significance, test to see whether the addition of the interaction term and the smoker variable contributes significantly to the estimated regression equation developed in part (a).
a) F = 26.54; p-value is 0.000; The addition of the two terms is significant.
b) F = 4.23; p-value is between 0.01 and 0.025; The addition of the two terms is significant.
c) F = 4.23; p-value is between 0.05 and 0.1; The addition of the two terms is not significant.
d) F = 4.23; p-value is between 0.025 and 0.05; The addition of the two terms is significant.
d. Refer to the model developed in part (b). Conduct a test at α = 0.05 to determine whether age and blood-pressure level interact to affect the risk of stroke (i.e., test to see whether the interaction term is significant).
a) F = 26.54; p-value is 0.000; age and blood-pressure level interact to affect the risk of stroke.
b) t = 1.297; p-value is 0.214; age and blood-pressure level don't interact to affect the risk of stroke.
c) t = 1.941; p-value is 0.071; age and blood-pressure level don't interact to affect the risk of stroke.
d) t = -0.573; p-value is 0.575; age and blood-pressure level don't interact to affect the risk of stroke.
