Ms. Carrie Allover, the manager of the commuter rail transportation system of our fair city has contracted us to analyze how various factors affect the number of riders who use the rail system. Her Supervisory Board wants this information for long-range planning. Accordingly, she has sent along some data on the weekly ridership (number of people who use the train during a week) of commuters taking the train into the city, as well as some data on various factors thought to have an influence on the ridership. These data contain the following variables: Weekly riders, Price per ride, Population, Income, and Parking rate. The latter variable, Parking rate, refers to the cost of downtown parking.

To deal with Ms. Allover’s requests, you will have to build several regression models with Weekly riders as the response variable, but before you proceed with this I want some common sense predictions on whether the coefficients of each of these explanatory variables will have a positive or negative sign; that is, whether the variable will have a positive or negative effect on the weekly ridership. Of course, you have to provide an explanation for your prediction. Some of these will be clear cut, but there may be a couple that are not so easy to predict and you won’t know the answer until you actually run the model. But don’t change your analysis if you prove to be wrong. Ms. Allover needs this kind of verbal, up-front analysis (whether right or wrong) so that she will be prepared to deal with possible responses, as well as misunderstandings, on the part of the Board.

After you have explained how you anticipate each variable will affect the number of weekly riders, go ahead and formulate the different models, one for each possible explanatory variable. Explain what each of the models means, using the coefficients in the regression output. In particular, describe how each explanatory variable actually affects the response variable, Weekly riders, including all appropriate units. This is extremely valuable information, Ms. Allover insists. Let’s provide her with a brief analysis of how well the models fit the data as well as how accurate we can anticipate the predictions of the models will be.

Attachment: Data file C08 Rail System.xls [.rda]