Question

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.

Risk Age Systolic 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

(c) What is the probability of a stroke over the next 10 years for Art Speen, a 66-year-old smoker who has a systolic blood pressure of 174? If required, round your answer to two decimal places. Do not round intermediate calculations.

Answer 1

Using excel, running a linear regression model, to predict the dependent variable 'Risk' using the possible predictors 'Age', 'Systolic blood pressure' and 'Smoking status',

The output is obtained as:

Hence, the fitted regression equation can be expressed as:

Risk = -97.19867 + 1.20952 (Age) + 0.23694 (Systolic blood pressure) + 7.44008 (Smoking status = 0 or 1)

For Age = 66, Systolic blood pressure = 174 and Smoking status = 1 (Smoker)

Risk = -97.19867 + 1.20952 (66) + 0.23694 (174) + 7.44008(1)

=31.30

Hence, the probability of a stroke over the next 10 years for Art Speen, a 66-year-old smoker who has a systolic blood pressure of 174 is 0.3130.