The Center for Urban Transportation Research (CUTR) at the University of South Florida conducted a survey of Bus rapid transit (BRT) customers in Miami (Transportation Research Board Annual Meeting, Jan. 2003). Data on the following variables (all measured on a five-point scale, where 1 = "very unsatisfied" and 5 = "very satisfied") were collected for a sample of over 500 bus riders: overall satisfaction with BRT (y), safety on bus (x1), seat availability (x2), dependability (x3), travel time (x4), cost (x5), information/maps (x6), convenience of routes (x7), traffic signals (x8), safety at bus stops (x9), hours of service (x10), and frequency of service (x11). CUTR analysts used stepwise regression to model overall satisfaction (y).
a. How many models are fitted at step 1 of the stepwise regression?
b. How many models are fitted at step 2 of the stepwise regression?
c. How many models are fitted at step 11 of the stepwise regression?
d. The stepwise regression selected the following eight variables to include in the model (in order of selection): x11, x4, x2, x7, x10, x1, x9, and x3. Write the equation for E(y) that results.
e. The model in part d was tested and resulted in R2 = .677. Interpret this value.
f. Explain why the CUTR analysts should be cautious in concluding that the "best" model for E(y) has been found.