Question

# A 10 year study conducted by the American Heart Association provided data on how age, blood...

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 the study. Risk is interpreted as the probability that the patient will have a stroke over the next 10 year period. For the smoking variable, define a dummy variable 1 with indicating a smoker and 0 indicating a non-smoker.

 Risk Age Pressure Smoker 12 57 152 0 24 67 163 0 13 58 155 0 56 86 177 1 28 59 196 0 51 76 189 1 18 56 155 1 31 78 120 0 37 80 135 1 15 78 98 0 22 71 152 0 36 70 173 1 15 67 135 1 48 77 209 1

SUMMARY OUTPUT
Regression Statistics

 Multiple R 0.967777 R Square 0.936593 Adjusted R Square 0.917571 Standard Error 4.23157 Observations 14

ANOVA

 df SS MS F Significance F Regression 3 2.7E-06 Residual 10 Total 13
 Coefficients Standard Error t Stat P-value Intercept -96.245 12.16893 -7.90908 1.3E-05 Age 1.096419 0.132705 8.262106 Pressure 0.294972 4.09E-05 Smoker 3.906635 2.616022 1.493349

A) Construct a 90% confidence interval estimate for the coefficient for Age.
B) Is this regression model a good predictor for risk of stroke? Explain how you know.
C) Predict the risk for a 60 year old smoker wiht blood pressure of 160.
D) Is Smoker a significant independent variable? How do you know?

#### Homework Answers

Answer #1

A) a 90% confidence interval estimate for the coefficient for Age

B) Since R2 = 0.9365 is quite close to 1, so we can sau that the regression model is a significantly good predictor.

c) The predicted risk for a 60 year old smoker wiht blood pressure of 160

= -96.245 + (1.096419*60) + (0.294972*160) + (3.906635*1)

= 20.642

d) P-value for Smoker

Since P-value = 0.083105 > 0.05, so at 5% level of significance, we can conclude that smoker is a not a significant independent variable.

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