Question

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 three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

=______ +_________ x1 + ________x2 + ________x3

(c) What is the probability of a stroke over the next 10 years for Art Speen, a 68-year-old smoker who has a blood pressure of 173? If required, round your answer to two decimal places.

_____________

Answer 1

a)

The regression equation is defined as,

Now, the regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'Risk' column, Input X Range: 'Age, BP and Smoker' column then OK. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

The regression equation is,

c)

The regression equation is,

For, Age = 68, BP = 173, Smoker = 1

(c) What is the probability of a stroke over the next 10 years for Art Speen, a 68-year-old smoker who has a blood pressure of 173? If required, round your answer to two decimal places.