solution

Railroad executives must understand how the costs incurred in a freight yard

are related to the output of the yard. The two most important services performed

by a yard are switching and delivery, and it seems reasonable to use the

number of cuts switched and the number of cars delivered during a particular

period as a measure of output. (A cut is a group of cars that rolls as a unit onto the same classifi cation track; it is often used as a unit of switching output.) A

study of one of the nation’s largest railroads assumed that

Ci = A + B1Si + B2Di + ei

where Ci is the cost incurred in this freight yard on the ith day, Si is the number

of cuts switched in this yard on the ith day, Di is the number of cars delivered

in this yard on the ith day, and ei is an error term. Data were obtained regarding

Ci, Si, and Di for 61 days. On the basis of the procedures described in this

chapter, these data were used to obtain estimates of A, B1, and B2. The resulting

regression equation was Cn i = 4,914 + 0.42Si + 2.44Di

where Cn i is the cost (in dollars) predicted by the regression equation for the

ith day. a. If you were asked to evaluate this study, what steps would you take to

determine whether the principal assumptions underlying regression

analysis were met? b. If you were satisfied that the underlying assumptions were met, of what

use might this regression equation be to the railroad? Be specific.

c. Before using the study’s regression equation, what additional statistics

would you like to have? Why? d. If the Durbin-Watson statistic equals 2.11, is there evidence of serial correlation in the residuals?