Question

The demand for a certain rail transit system shows stable growth over the past decade as shown in Table 1 below. An analyst seeks to estimate the expected demand at year 2008 when the system is due for improvement. (Note well: (1) use spreadsheet software such as MS Excel to generate the responses to (i) and (ii) below. (2) the “time” variable used in the analysis should be year since 1990)

i. Use linear functional form to predict the expected demand in that year.

ii. Use the exponential functional form to predict the expected demand in that year.

iii. What are the concerns with using trend analysis for demand estimation?

Table 1: Annual Ridership of a Rail Transit System

Year	1990	1992	1994	1996	1998	2000	2002	2004
Demand (Millions of Passengers per year)	1.25	1.37	1.45	1.58	1.72	1.95	2.31	2.48

Answer 1

i) The linear functional form on an excel gives the following trendline equation-

y= 0.178x+0.962

where, y= Demand, x=year (represented as 1-8 for the years 1990-2004)

Based on the above, the demand for 2008 comes as- y= 0.178 * 10 + 0.962 = 2.74 Mn. passengers

ii) The exponential functional form on an excel gives the following trendline equation-

y= 1.095 * exp(0.099x)

where, y= Demand, x=year (represented as 1-8 for the years 1990-2004)

Based on the above, the demand for 2008 comes as- y= 1.095 * exp(0.099 * 10) = 2.95 Mn. passengers

iii) Concerns of using trend analysis are that the trend in past years may not continue during the forthcoming years. Demand may vary due to some externalities and may not follow the trend of past years.