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. Data from a portion of this study are contained in the Excel Online file below. 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. Construct a spreadsheet to answer the following questions.

1. Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood-pressure level. Note: report R^2 and R-sq adj between 0 and 1.

   The regression equation is
   
   Risk = (___) + (___) Age + (___) Pressure (to 2 decimals)
   
   s= (___) (3 decimals)
   
   R^2 = (___) (3 decimals)
   
   R-sq adj = (___) (to 3 decimals)

2. 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.Note: report R^2 and R-sq adj between 0 and 1.

   The regression equation is
   
   Risk = (___) + (___) Age + (___) Pressure + (___) Smoker + (___) AgePress (to 2 decimals)
   
   s= (___) (to 3 decimals)
   
   R^2 = (___) (to 3 decimals)
   
   R-sq adj = (___) (to 3 decimals)

3. At a .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).

   What is the value of the F test statistic?

   (____) (to 4 decimals)

   What is the -value? (to 4 decimals)

   P-value is (____)
   
   

   Risk	Age	Blood Pressure	Smoker	AgePress
   55	67	214	1
   67	90	156	0
   45	86	147	1
   36	75	143	0
   19	57	178	0
   50	78	201	1
   43	65	218	0
   43	74	155	1
   20	74	123	1
   52	79	181	0
   31	80	130	1
   64	84	175	0
   51	74	216	0
   31	83	109	0
   34	58	198	1
   55	79	202	0
   41	57	214	0
   45	82	152	0
   34	85	105	1
   46	73	174	1

Answer 1

1. Risk = -112.59 + 1.28 Age + 0.35 Pressure (to 2 decimals)

s= 5.561 (3 decimals)

R^2 = 0.832 (3 decimals)

R-sq adj = 0.812 (to 3 decimals)

2. Risk = -186.81 + 2.24 Age + 0.75 Pressure - 0.34 Smoker - 0.01 AgePress (to 2 decimals)

s= 5.739 (3 decimals)

R^2 = 0.842 (3 decimals)

R-sq adj = 0.800 (to 3 decimals)

3. What is the value of the F test statistic?

19.9585 (to 4 decimals)

What is the -value? (to 4 decimals)

P-value is 0.0000.

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