A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker. The data is provided below: Risk of Strokes Age Systolic Blood Pressure Smoker 10 59 156 0 25 65 163 0 12 60 158 0 57 86 177 1 28 59 196 0 50 76 189 1 17 57 159 1 34 78 120 1 37 80 135 1 15 78 98 0 22 71 152 1 39 70 173 1 17 67 135 0 48 77 209 1 18 60 199 0 36 82 119 1 10 66 166 0 34 80 125 1 4 62 117 0 38 59 209 1 (a) Develop an estimated multiple regression equation that relates risk of a stroke (Y) to the person's age, systolic blood pressure, and whether the person is a smoker. Let x1 represent the person's age. Let x2 represent the person's systolic blood pressure. Let x3 represent whether the person is a smoker. (b) Is smoking a significant factor in the risk of a stroke? Explain. Use a 0.05 level of significance. (c) What is the probability of a stroke over the next 10 years for a 67-year-old smoker who has a systolic blood pressure of 175? What action might the physician recommend for this patient?
A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker. The data is provided below:
|
Risk of Strokes |
Age |
Systolic Blood Pressure |
Smoker |
|
10 |
59 |
156 |
0 |
|
25 |
65 |
163 |
0 |
|
12 |
60 |
158 |
0 |
|
57 |
86 |
177 |
1 |
|
28 |
59 |
196 |
0 |
|
50 |
76 |
189 |
1 |
|
17 |
57 |
159 |
1 |
|
34 |
78 |
120 |
1 |
|
37 |
80 |
135 |
1 |
|
15 |
78 |
98 |
0 |
|
22 |
71 |
152 |
1 |
|
39 |
70 |
173 |
1 |
|
17 |
67 |
135 |
0 |
|
48 |
77 |
209 |
1 |
|
18 |
60 |
199 |
0 |
|
36 |
82 |
119 |
1 |
|
10 |
66 |
166 |
0 |
|
34 |
80 |
125 |
1 |
|
4 |
62 |
117 |
0 |
|
38 |
59 |
209 |
1 |
|
(a) |
Develop an estimated multiple regression equation that relates risk of a stroke (Y) to the person's age, systolic blood pressure, and whether the person is a smoker. |
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Let x1 represent the person's age. |
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Let x2 represent the person's systolic blood pressure. |
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Let x3 represent whether the person is a smoker. |
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(b) |
Is smoking a significant factor in the risk of a stroke? Explain. Use a 0.05 level of significance. |
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(c) |
What is the probability of a stroke over the next 10 years for a 67-year-old smoker who has a systolic blood pressure of 175? What action might the physician recommend for this patient? |
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(d) |
Based on the four criteria we discussed in class determine the usefulness of the above model. |
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