f. Fit linear regression models to Rail and to Auto, similar

to the model you fit for Air. Remember to use only

pre-event data. Once the models are estimated, use them to

forecast each of the three postevent series.

i. For each series (Air, Rail, Auto), plot the complete

pre-event and postevent actual series overlayed with the

predicted series.

ii. What can be said about the effect of the September 11

terrorist attack on the three modes of transportation?

Discuss the magnitude of the effect, its time span, and any

other relevant aspects.

16.1 Impact of September 11 on Air Travel in the

United States: The Research and Innovative Technology

Administrations Bureau of Transportation Statistics (BTS)

conducted a study to evaluate the impact of the September

11, 2001, terrorist attack on U.S. transportation. The study

report and the data can be found at http://www.bts.gov/

publications/estimated_impacts_of_9_11_on_us_travel.

The goal of the study was stated as follows:

The purpose of this study is to provide a greater

understanding of the passenger travel behavior patterns of

persons making long distance trips before and after 9/11.

The report analyzes monthly passenger movement data

between January 1990 and May 2004. Data on three

monthly time series are given in File Sept11Travel.xls for

this period: (1) actual airline revenue passenger miles

(Air), (2) rail passenge r miles (Rail), and (3) vehicle miles

traveled (Car).

In order to assess the impact of September 11, BTS took

the following approach: using data before September 11, it

forecasted future data (under the assumption of no terrorist

attack). Then, BTS compared the forecasted series with the

actual data to assess the impact of the event. Our first step,

therefore, is to split each of the time series into two parts:

preand post-September 11. We now concentrate only on

the earlier time series.

a. Plot the pre-event Air time series.

i. Which time series components appear from the plot?

b. Figure 16.15 is a time plot of the seasonally adjusted

pre-Sept-11 Air series. Which of the following methods

would be adequate for forecasting this series?

Linear regression model with dummies

Linear regression model with trend

Linear regression model with dummies and trend

c. Specify a linear regression model for the Air series that

would produce a seasonally adjusted series similar to the

one shown in (b), with multiplicative seasonality. What is

the output variable? What are the predictors?

d. Run the regression model from (c). Remember to create

dummy variables for the months (XLMiner will treat April

as the reference category) and to use only pre-event data.

i. What can we learn from the statistical insignificance of

the coefficients for October and September?

ii. The actual value of Air (air revenue passenger miles) in

January 1990 was 35.153577 billion. What is the residual

for this month, using the regression model? Report the

residual in terms of air revenue passenger miles.

e. Create an ACF (autocorrelation) plot of the regression

residuals.

i. What does the ACF plot tell us about the regression

models forecasts?

ii. How can this information be used to improve the

model?