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. 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. Risk Age Pressure Smoker 12 57 152 No 24 67 163 No 13 58 155 No 56 86 177 Yes 28 59 196 No 51 76 189 Yes 18 56 155 Yes 31 78 120 No 37 80 135 Yes 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 Yes 48 77 209 Yes 15 60 199 No 36 82 119 Yes 8 66 166 No 34 80 125 Yes 3 62 117 No 37 59 207 Yes
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. 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. Risk Age Pressure Smoker 12 57 152 No 24 67 163 No 13 58 155 No 56 86 177 Yes 28 59 196 No 51 76 189 Yes 18 56 155 Yes 31 78 120 No 37 80 135 Yes 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 Yes 48 77 209 Yes 15 60 199 No 36 82 119 Yes 8 66 166 No 34 80 125 Yes 3 62 117 No 37 59 207 Yes
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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. 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.
| Risk | Age | Pressure | Smoker |
|---|---|---|---|
| 12 | 57 | 152 | No |
| 24 | 67 | 163 | No |
| 13 | 58 | 155 | No |
| 56 | 86 | 177 | Yes |
| 28 | 59 | 196 | No |
| 51 | 76 | 189 | Yes |
| 18 | 56 | 155 | Yes |
| 31 | 78 | 120 | No |
| 37 | 80 | 135 | Yes |
| 15 | 78 | 98 | No |
| 22 | 71 | 152 | No |
| 36 | 70 | 173 | Yes |
| 15 | 67 | 135 | Yes |
| 48 | 77 | 209 | Yes |
| 15 | 60 | 199 | No |
| 36 | 82 | 119 | Yes |
| 8 | 66 | 166 | No |
| 34 | 80 | 125 | Yes |
| 3 | 62 | 117 | No |
| 37 | 59 | 207 | Yes |
(a)
Develop an estimated 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 age, x2 represent blood pressure, x3 represent whether the person is a smoker, and y represent risk. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker. Round your constant term to one decimal place and coefficients to two decimal places.)
ŷ =
(b)
Is smoking a significant factor in the risk of a stroke? Explain. Use ? = 0.05.
State the null and alternative hypotheses.
H0: β3 = 0
Ha: β3 ≠ 0H0: β3 ≤ 0
Ha: β3 > 0 H0: β3 = 0
Ha: β3 > 0H0: β3 ≥ 0
Ha: β3 < 0
Ha: β3 ≠ 0H0: β3 ≤ 0
Ha: β3 > 0 H0: β3 = 0
Ha: β3 > 0H0: β3 ≥ 0
Ha: β3 < 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value =
State your conclusion.
Do not reject H0. There is insufficient evidence to conclude that smoking is a significant factor.Do not reject H0. There is sufficient evidence to conclude that smoking is a significant factor. Reject H0. There is insufficient evidence to conclude that smoking is a significant factor.Reject H0. There is sufficient evidence to conclude that smoking is a significant factor.
(c)
What is the probability of a stroke over the next 10 years for Art Speen, a 69-year-old smoker who has blood pressure of 185? (Round your answer to four decimal places.)
What action might the physician recommend for this patient?
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