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 mea sure of output. (A cut is a group of cars that rolls as a unit onto the same classification 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
Ĉi = 4,914 + 0.42Si + 2.44Di
where Ĉi 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?