Question

Chapter 4 Forecasting Homework Assignment

1. Daily high temperatures in St. Louis for the last week were as follows: 34, 36, 37, 39, 35, 32, and 36 (yesterday).
   1. Forecast the high temperature today, using a 3-day moving average.  
   2. Forecast the high temperature today, using a 2-day moving average.  

For questions c-e use all the days where a 3-day forecast value is possible.

3. Calculate the mean absolute deviation based on a 3-day moving average.
4. Compute the mean squared error for the 3-day moving average.
5. Calculate the mean absolute percent error for the 3-day moving averag

2. Data collected on the yearly registrations for a Six Sigma seminar at the Quality College are shown in the following table:

Year	1	2	3	4	5	6
Registrations	4500	6500	6775	6225	8075	8520
Forecast (α=0.5)	5000
Forecast (α=0.1)	5000

1. Use exponential smoothing with a smoothing constant of 0.5 and 0.1 to forecast years 2-6.
2. What is the MAD value for each forecast (1-6)?
3. What is the MSE value for each forecast (1-6)?
4. Which forecast is better? Why?

Answer 1

a)

Forecast of high temperature today, using a 3-day moving average = Average of previous three days high temperature

= (35+32+36)/3

= 34.33

b)

Forecast of high temperature today, using a 2-day moving average = Average of previous three days high temperature

= (32+36)/2

= 34

Parts c) to e) are solved in the following spreadsheet

Mean Absolute Deviation (MAD) = 2.83

Mean Squared Error (MSE) = 10.50

Mean Absolute PErcent Error (MAPE) = 8.17 %

F13 - fx =AVERAGE(F5:F8) @ C A B DE Absolute Squared Deviation Error High temp 3-day MA Absolute Percent Error 1 3.33 2.33 35.67 37.33 37.00 35.33 34.33 11.11 5.44 25.00 0.44 8.55% 6.67% 15.63% 1.85% 6 36 5.00 0.67 8 (today) MSE MAD 2.83 MAPE 8.17% 10.50

EXCEL FORMULAS:

Day	High temp	3-day MA	Absolute Deviation	Squared Error	Absolute Percent Error
1	34
2	36
3	37
4	39	=AVERAGE(B2:B4)	=ABS(B5-C5)	=D5^2	=D5/B5
5	35	=AVERAGE(B3:B5)	=ABS(B6-C6)	=D6^2	=D6/B6
6	32	=AVERAGE(B4:B6)	=ABS(B7-C7)	=D7^2	=D7/B7
7	36	=AVERAGE(B5:B7)	=ABS(B8-C8)	=D8^2	=D8/B8
8 (today)		=AVERAGE(B6:B8)
			MAD	MSE	MAPE
			=AVERAGE(D5:D8)	=AVERAGE(E5:E8)	=AVERAGE(F5:F8)