A recent 10-year study conducted by a research team at the Medical School was conducted to assess how age, 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. Risk Age Blood Pressure Smoker
12 57 150 No 26 60 165 No 11 59 155 No 57 86 170 Yes 28 59 196 Yes 50 76 189 Yes 17 56 155 Yes 32 78 120 No 37 80 135 No 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 Yes 48 77 209 Yes 14 60 199 No 36 82 119 Yes 8 65 166 No 34 82 125 No 3 61 117 No 39 60 208 Yes
(a) Develop an estimated multiple regression equation that relates risk of a stroke to the person's age, blood pressure, and whether the person is a smoker. Let x1 represent the person's age. Let x2 represent the person's blood pressure. Let x3 represent whether the person is a smoker. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
(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 Art Speen, a 67-year-old smoker who has a blood pressure of 171? If required, round your answer to two decimal places.
(d) What other factors could be included in the model as independent variables? (i) Family History of Stroke (ii) Weight/obesity (iii) Gender (iv) All of the above