# Management Science Chapter 7 Homework Solutions

**Topics:**Regression analysis, Linear regression, Moving average

**Pages:**78 (1798 words)

**Published:**December 5, 2014

Problem Summary

Problem Solutions

7.1 See file Ch7.1.xls

a.

Yes, a stationary model seems appropriate

b.

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

20.16667

1.373732

14.6802

4.3E-08

17.1058

23.22753

17.1058

23.22753

Period

-0.07692

0.186653

-0.41212

0.688949

-0.49281

0.338967

-0.49281

0.338967

From regression output, t = -.412 and p = .689. A stationary model seems appropriate since the linear term, Period, is not significant.

7.1 c.

Forecast for January -- 19, for upcoming year – 12*19 = 228

7.1 d.

Forecast for January -- 20.4

e. 4 month moving average. MAD is 1.72

7.2 See files Ch7.2a.xls and Ch7.2b.xls

a.

Forecast for January -- 18.86

7.2 b. See file Ch7.2b.xls

Forecast for January -- 20.28

c. = .6 gives the lower MSE

7.3 See file Ch7.3.xls

a.

b.

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

406.6014

3.916368

103.8211

4.22E-31

398.4794

414.7235

398.4794

414.7235

Month

10.17522

0.274089

37.12382

2.44E-21

9.606792

10.74364

9.606792

10.74364

From regression output, t = 37.1238, p = 0

7.3 c.

From the above output we see that the forecast is as follows:

25 -- 660, 26 -- 671, 27 -- 681, 28 -- 692, 29 -- 702, 30 -- 712, 31 -- 722, 32 -- 732, 33 -- 742, 34 -- 753, 35 -- 763, 36 -- 773.

7.4 See file Ch7.4a.xls and Ch7.4b.xls

Forecast for upcoming 12 months:

Period

25

26

27

28

29

30

31

32

33

34

35

36

Forecast

665

675

685

695

706

716

726

736

746

756

766

776

7.4b See file Ch7.4b.xls

Forecast for upcoming 12 months:

Period

25

26

27

28

29

30

31

32

33

34

35

36

Forecast

659

665

671

676

682

688

693

699

705

710

716

722

c. = .5 and = .7

d. = .5 and = .7

7.5 See file Ch7.5.xls

Week 5: Su 318.89, M 371.72, Tu 353.72, W 397.54, Th 404.22, F 362.08, Sa 366.49,

Week 6: Su 326.62, M 380.70, Tu 362.24, W 407.08, Th 413.89, F 370.71, Sa 375.20.

7.6 See file Ch7.6.xls

a.

b.

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

67.175

3.120786

21.52503

3.96E-12

60.48157

73.86843

60.48157

73.86843

Week

0.457353

0.322744

1.417077

0.178329

-0.23486

1.149571

-0.23486

1.149571

From the regression output, t = 1.4171, p = .1783 so a stationary model seems appropriate since Week is not significant. 7.6 c.

Forecast for upcoming year = 52*71*100 = 369,200 bottles of shampoo.

7.7 See file Ch7.7.xls

Forecast for upcoming year = 52*70.6296*100 = 367,274 bottles of shampoo.

7.8 See file Ch7.8.xls

Quarter 1 -- Forecast = 5.71 - .0775*21 + 1.9275 = 6.01

Quarter 2 -- Forecast = 5.71 - .0775*22 + 6.0050 = 10.01

Quarter 3 -- Forecast = 5.71 - .0775*23 + 3.5625 = 7.49

Quarter 4 -- Forecast = 5.71 - .0775*24 = 3.85

7.9 See file Ch7.9.xls,

a.

b.

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

152.5421

7.57903

20.12686

8.64E-14

136.6191

168.4651

136.6191

168.4651

Period

-0.27068

0.632685

-0.42782

0.673855

-1.5999

1.058547

-1.5999

1.058547

From the regression output, t = -.428 and p = .674. Hence, one cannot conclude that linear trend is present.

7.9 c. See file Ch7.3.xls

Forecast for upcoming week is 143.8*5 = 719

7.9 d. See file Ch7.9.xls

Forecast for upcoming week = 147.2*5 = 736.

7.10 See file Ch7.10.xls

The optimal smoothing constant is = .11.

7.10 b.

c. The weighted moving average gives lower values for the MSE and hence it would be recommended.

7.11 See file Ch7.11.xls

The forecast is as follows:...

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