How can we solve part c in Excel?

     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.  For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.

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.

b)  Is smoking a significant factor in the risk of a stroke?  Explain.  Use a  .05.

c)   What is the probability of a stroke over the next 10 years for Art Speen, a 68-year-old smoker who has blood pressure of 175?  What action might the physician recommend for this patient? (15/38)

a.     The Excel output is shown below:

Regression Statistics
Multiple R	0.9346
R Square	0.8735
Adjusted R Square	0.8498
Standard Error	5.7566
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	3	3660.7396	1220.247	36.8230	2.06404E-07
Residual	16	530.2104	33.1382
Total	19	4190.95
	Coefficients	Standard Error	t Stat	P-value
Intercept	-91.7595	15.2228	-6.0278	1.76E-05
Age	1.0767	0.1660	6.4878	7.49E-06
Pressure	0.2518	0.0452	5.5680	4.24E-05
Smoker	8.7399	3.0008	2.9125	0.0102

                 = -91.7595 + 1.0767 Age + .2518 Pressure + 8.7399 Smoker

         b.     Since the p-value corresponding to t = 2.9125 is .0102 < a = .05, smoking is a significant factor.

         c.     The point estimate is 34.27; the 95% prediction interval is 21.35 to 47.18.  Thus, the probability of a stroke (.2135 to .4718 at the 95% confidence level) appears to be quite high.  The physician would probably recommend that Art quit smoking and begin some type of treatment designed to reduce his blood pressure.

Part c: first calculate the point estimate: yhat = - 91.7595 + 10.767*68 + 0.2518*175 + 8.7399 = 34.27

The question says that the probabilities are mulliplied by 100 (see highlighted section above). So we would divide 34.27/100 = 0.3427. This is the risk that this patient runs.