A study was conducted to determine the factors involved in the rate of participation of discharged cardiac patients in a rehabilitation program. Data were collected from 516 treated patients. Among the variables used to predict participation (0 = no, 1 = yes) were the distance traveled to rehabilitation in kilometers, whether the person had a car (0 = no, 1 = yes), and the age of the person in years. The summarized data are:

a. State the logistic regression model.
b. Using the model in (a), predict the probability that a patient will participate in rehabilitation if he or she travels 20 km to rehabilitation, has a car, and is 65 years old.
c. Using the model in (a), predict the probability that a patient will participate in rehabilitation if he or she travels 20 km to rehabilitation, does not have a car, and is 65 years old.
d. Compare the results of (b) and (c).
e. A t the 0.05 level of significance, is there evidence that the distance traveled, whether the patient has a car, and the age of the patient each make a significant contribution to the model?
f. What conclusions can you reach about the likelihood of a patient participating in the rehabilitation program?

Intercept Distance Car Age Estimate 5.7765 0.0675 1.9369 -0.0599 Standard Error 0.8619 0.0111 0.2720 0.0119 Z Value p-value 6.702 0.0000 -6.113 0.0000 7.12 0.0000 5.037 0.0000