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. 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. 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). 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).
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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.
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.
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).
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).
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