Bus Rapid Transit study. Bus Rapid Transit (BRT) is a rapi

QUESTION:

Bus Rapid Transit study. Bus Rapid Transit (BRT) is a rapi -dly growing trend in the provision of public transportation in America. The Center for Urban Transportation Research(CUTR) at the University of South Florida conducted a survey of BRT customers in Miami (TransportationResearch Board Annual Meeting, Jan. 2003). Data onthe following variables (all measured on a 5-point scale,where 1 = very unsatisfied and 5 = very satisfied) werecollected for a sample of over 500 bus riders: overall satisfaction with BRT (y), safety on bus \(\left(x_1\right)\), seat availability \(\left(x_2\right)\), dependability \(\left(x_3\right)\), travel time \(\left(x_4\right)\), cost \(\left(x_5\right)\), information/maps \(\left(x_6\right)\), convenience of routes \(\left(x_7\right)\), traffic signals \(\left(x_8\right)\), safety at bus stops \(\left(x_9\right)\), hours of service \(\left(x_{10}\right)\), and frequency of service \(\left(x_{11}\right)\). CUTR analysts used stepwise regression to model overall satisfaction (y).

a. How many models are fit at step 1 of the stepwise regression?

b. How many models are fit at step 2 of the stepwise regression?

c. How many models are fit 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): \(x_{11}, x_4, x_2, x_7, x_{10}, x_1, x_9\), and \(x_3\). Write the equation for E(y) that results from stepwise regression.

e. The model, part d, resulted in \(R^2=.677\). Interpret this value.

f. Explain why the CUTR analysts should be cautious in concluding that the best model for E(y) has been found.