Respond to…
Read Problem 6 in Chapter 6 of your textbook. Calculate and answer parts a through d. Include all calculations and spreadsheets in your post. Explain why the moving average method was used instead of another forecasting method. What might be another forecasting method that could prove to be just as useful?
The figures below indicate the number of mergers that took place in the savings and loan industry over a 12-year period.
Year
Mergers
2000
46
2001
46
2002
62
2003
45
2004
64
2005
61
2006
83
2007
123
2008
97
2009
186
2010
225
2011
240
Calculate a 5-year moving average to forecast the number of mergers for 2012.
f_2012= ((123+97+186+225+240))/5=174.2
This method is used to help offset years where there may have been unusual circumstances leading to an increase or decrease in total mergers (Vonderembse & White, 2013).
Use the moving average technique to determine the forecast for 2005 to 2011. Calculate measurement error using MSE and MAD.
Mean Squared Error (MSE)
Year
Mergers
Forecast
Error
Sq Error
2005
61
52.6
8.4
70.56
2006
83
55.6
27.4
750.76
2007
123
63
60
3600
2008
97
75.2
21.8
475.24
2009
186
85.6
100.4
10080.16
2010
225
110
115
13225
2011
240
142.8
97.2
9447.84
Total
37649.56
Average
5378.5
Mean Absolute Dev (MAD)
Year
Mergers
Forecast
Error
Signs Removed
2005
61
52.6
8.4
8.4
2006
83
55.6
27.4
27.4
2007
123
63
60
60
2008
97
75.2
21.8
21.8
2009
186
85.6
100.4
100.4
2010
225
110
115
115
2011
240
142.8
97.2
97.2
Total
430.2
Average
61.5
Mergers minus forecast equals total error. Total error squared is simply that. For the MAD calculation, all figures were positive, so no need to change signs.
Calculate a 5-year weighted moving average to forecast the number of mergers for 2012. Use weights of 0.10, 0.15, 0.20, 0.25, and 0.30, with the most recent year weighted being the largest.
Year
Mergers
Weight
2007
123
0.10
12.30
2008
97
0.15
14.55
2009
186
0.20
37.20
2010
225
0.25
56.25
2011
240
0.30
72.00
AVG
192.30
This method is used to show the most recent year with the highest weighting.
Use regression analysis to forecast the number of mergers in 2012.
X
Y
XY
X^2
Y^2
1
123
123
1
15129
2
97
194
4
37636
3
186
558
9
311364
4
225
900
16
810000
5
240
1200
25
1440000
15
871
2975
55
2614129
b=
1810
160
11.3
a=
4.5
Y?=
72.4
b=?n???XY???X/???Yn???X2??(??X)2
a=???Y/n?b???X/n
Ye = a + bX
Reference
Vonderembse, M. A., & White, G. P. (2013). Operations management [Electronic version]. Retrieved from https://content.ashford.edu/
Respond to…
The figures below indicate the number of mergers that took place in the savings and loan industry over a 12-year period.
Year
Mergers
2000
46
2001
46
2002
62
2003
45
2004
64
2005
61
2006
83
2007
123
2008
97
2009
186
2010
225
2011
240
A) Calculate a 5-year moving average to forecast the number of mergers for 2012.
(123+97+186+225+240)/5 = 174.2
B) Use the moving average technique to determine the forecast for 2005 to 2011. Calculate measurement error using MSE and MAD.
MSE/MAD
Year
Actual Mergers
Forecasted Mergers
Error
Squared Error
2005
61
(46 +46+62+45+64)/5 = 53
8
(8*8) = 64
2006
83
(46 +62+45+64+61)/5 = 56
27
(27*27) = 729
2007
123
(62+45+64+61+83)/5 = 63
60
(60*60) = 3600
2008
97
(45+64+61+83+123)/5 = 75
22
(22*22) = 484
2009
186
(64+61+83+123+97)/5 = 86
100
(100*100) = 10000
2010
225
(61+83+123+97+186)/5 = 110
115
(115*115) = 13225
2011
240
(83+123+97+186+225)/5 = 143
97
(97*97) = 9409
Total
429
53597
MSE (53597/7) = 7656.7
MAD (429/7) = 61.3
C) Calculate a 5-year weighted moving average to forecast the number of mergers for 2012. Use weights of 0.10, 0.15, 0.20, 0.25, and 0.30, with the most recent year weighted being the largest.
(0.30 * 240) + (0.25 * 225) + (0.20 * 186) + (0.15 * 97) + (0.10 * 123) = 192
D) Use regression analysis to forecast the number of mergers in 2012.
Year
X
Mergers
XY
X^2
Y^2
2000
1
46
(1*46) = 46
(1^2) = 1
(46^2) = 2116
2001
2
46
(2*46) = 92
(4^2) = 4
(46^2) = 2116
2002
3
62
(3*62) = 186
(3^2) = 9
(62^2) = 3844
2003
4
45
(4*45) = 180
(4^2) = 16
(45^2) = 2025
2004
5
64
(5*64) = 320
(5^2) = 25
(64^2) = 4096
2005
6
61
(6*61) = 366
(6^2) = 36
(61^2) = 3721
2006
7
83
(7*83) = 581
(7^2) = 49
(83^2) = 6889
2007
8
123
(8*123) = 984
(8^2) = 64
(123^2) = 15129
2008
9
97
(9*97) = 873
(9^2) = 81
(97^2) = 9409
2009
10
186
(10*186) = 1860
(10^2) = 100
(186^2) = 34596
2010
11
225
(11*225) = 2475
(11^2) = 121
(225^2) = 50625
2011
12
240
(12*240) = 2880
(12^2) = 144
(240^2) = 57600
Totals
78
1278
10843
650
192166
b = 12 * 10,843 78 * 1278 / 12 * 650 78^2 = 13116 99,684 / 7800 6084 = 30,432 / 1716 = 17.73
a = 1278 / 12 17.7 * 78 / 12 = 106.5 115.245 = -8.75
r = 12 * 10,843 78 * 1,278 / ? 12 * 650 -78^2 12 * 198,514 – 1,278^2 = 130,16 -99,684 / ? 7,800 6084 2,382,168 1,633,284 = 1,258,084,944 = 30,432 / 35848.08 = .84892
Explain why the moving average method was used instead of another forecasting method. What might be another forecasting method that could prove to be just as useful?
The moving average was used instead of another forecasting method because it provides the most reasoned prediction according to Vonderembse and White (2013). This type of forecasting method also helps with smoothing out the peaks and valleys with all the fluctuations within the data. With utilizing forecasting testing, utilizing models such as exponential smoothing could be considered useful in considering qualitative factors. Exponential smoothing is a procedure for continualy revising an estimate to include more recent data, and is based upon averaging past values (Vonderembse & White, 2013). Altogether forecasting by the use of testing, is a great way to help predict the future.
References
Vonderembse, M. A., & White, G. P. (2013). Operations management [Electronic version]. Retrieved from https://content.ashford.edu/
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