Regression analysis with prediction intervals.
Almost all U.S. light-rail systems make use of electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with accident rate of .99 accidents per million passenger miles as compare to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems (USA Today, January 7, 2003).
|
City
|
Miles of Track
|
Ridership (1000s)
|
|
Cleveland
|
15
|
15
|
|
Denver
|
17
|
35
|
|
Portland
|
38
|
81
|
|
Sacramento
|
21
|
31
|
|
San Diego
|
47
|
75
|
|
San Jose
|
31
|
30
|
|
St. Louis
|
34
|
42
|
a. Use these data to develop an estimated regression equation that could be used to predict the ridership given the miles of track.
Compute b0 and b1 (to 4 decimals).
Complete the estimated regression equation (to 2 decimals).
b. Compute the following (to 2 decimal):
SSE
SST
SSR
MSE
c. What is the coefficient of determination, i.e., r-squared (to 3 decimals)?
Does an estimated regression equation provide a good fit?
d. Develop a 95 percent confidence interval for the mean weekday ridership for all light-rail systems with 30 miles of track (to 1 decimal).
e. Suppose that Charlotte is considering construction of a light-rail system with 30 miles of track. Build up a 95 percent prediction interval for the weekday ridership for the Charlotte system (to 1 decimal).
Do you think that the prediction interval you developed would be of value of Charlotte planners in anticipating the number of weekday riders for their new light-rail system?