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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

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.

1. 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.

1. 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

Yₑ=

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.

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

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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