Question

The analytics department of a public transit service group is trying to forecast the future number of passengers using the University subway station during the Fall term. During the first 10 days of September, the team count the number of passengers entering and exiting the station between 8:00am to 10:00pm.
Day   # Passengers
1   2250
2   2100
3   2150
4   2450
5   2250
6   2500
7   2300
8   2650
9   2350
10   2600

a)   Compute manually (show your formulas) the forecast for days 1-4 using the exponential smoothing method with an alpha of 0.3.
b)   Now switch to Excel and compute the exponential smoothing forecasts for days 11 and 12 (again using an alpha of 0.3). (Show your Excel Formulas)
c)   Reforecast days 11 and 12 using an alpha of 0.7.
d)   Compare how well the model forecast for periods 8-10 for alpha = 0.3 vs alpha =0.7. Which one was better? Explain.

Answer 1

a)   Compute manually (show your formulas) the forecast for days 1-4 using the exponential smoothing method with an alpha of 0.3.

Day #	Passengers	Alpha = 0.3
1	2250
2	2100	2250
3	2150	2205
4	2450	2188.5

b)   Now switch to Excel and compute the exponential smoothing forecasts for days 11 and 12 (again using an alpha of 0.3). (Show your Excel Formulas)

11		2459.946651
12		1721.962655

c)   Reforecast days 11 and 12 using an alpha of 0.7.

11		2543.642362
12		763.0927086

d)   Compare how well the model forecast for periods 8-10 for alpha = 0.3 vs alpha =0.7. Which one was better? Explain.

For alpha =0.3:

8	2650	2323.31385
9	2350	2421.319695
10	2600	2399.923787

For alpha =0.7:

8	2650	2340.45785
9	2350	2557.137355
10	2600	2412.141207

Alpha = 0.3 is better since it has lower MSE.