Question

Weekly sales of the Weber Dicamatic food processor for the past ten weeks have been: Week...

Weekly sales of the Weber Dicamatic food processor for the past ten weeks have been:

Week

Sales

Week

Sales

1

980

6

990

2

1040

7

1030

3

1120

8

1260

4

1050

9

1240

5

960

10

1100


Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average model gives a better forecast for this problem.

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Answer #1

Answer:

Given that,

Weekly sales of the Weber Dicamatic food processor for the past ten weeks have been:

Week

Sales

Week

Sales

1

980

6

990

2

1040

7

1030

3

1120

8

1260

4

1050

9

1240

5

960

10

1100

Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average model gives a better forecast for this problem.

Mean Square Error (MSE)=\sum(Actual-Forecast)2/(n-1)
Error Error2
Month Demand 3 Month MA Absolute error Square error
A B C=A-B D=C2
1 980
2 1040
3 1120
4 1050 1046.6667 3.3333 11.1111
5 960 1070.0000 -110.0000 12100.0000
6 990 1043.33333 -53.3333 2844.4444
7 1030 1000.0000 30.0000 900.0000
8 1260 993.3333 266.6667 21511.1111
9 1240 1093.3333 146.6667 21511.1111
10 1100 1176.6667 -76.6667 5877.7778
-160.0000 14955.5556
Eg Forecast Calculation
Month 4 =(month 1+month 2 +month 3)/3
=(980+1040+1120)/3
=3140/3=1046.6667
MSE=14955.5556/(7-1)
=2492.593
Error Error2
Month Demand 4 Month MA Absolute error square error
A B C=A-B D=C2
1 980
2 1040
3 1120
4 1050
5 960 1047.5000 -87.5000 7656.2500
6 990 1042.5000 -52.5000 2756.2500
7 1030 1030.0000 0.0000 0.0000
8 1260 1007.5000 252.5000 63756.2500
9 1240 1060.0000 180.0000 32400.0000
10 1100 1130.0000 -30.0000 900.0000
-140.0000 10412.5000
Eg Forecast Calculation
Month 5 =(month 1+month 2+month 3+ month 4)/4
=(980=1040+1120+1050)/4
=4190/4=1047.50
MSE=10412.50/(6-1)
=2082.50
Four month moving average gives better forecast,
Forecast for period 11
Using 3 month moving average
=(month 8+ month 9+ month 10)/3
=(1260+1240+1100)/3
=3600/3
=1200
Using 4 month moving average
=(month 7+month 8+month 9+month 10)/4
=(1030+1260+1240+1100)/4
=4630/4
=1157.50
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