Quantitative Methods

l.'Y\<a!+ tu Q,ra;,e,4 Srs 18.4 CHAPTER 5 . FORECASTING

lbund ro be 1.30.0.90,0.70, and 1.10, rcspecrively.

The fbllowing table provides the Dow Jones Indus- trial Average (DJfA) opening index value on the f,rst working day ol' 1 994*201 3: Develop a trcnd line anti use it to predict the opening DJIA index value for years 201-1. 2015. and 2016. Find the MSE for this model.

YEAR DJLA YEAR DJIA

5-41 Refer to the DJIA data in Problem 5-39. (a) Use an exponential smoothing model with a

smoothing constant of 0.4 to predict the opening DJIA index value for 2014. Find the MSE for this.

&) Use QM forWindows orExcel and find the smoortr- ing constant that would provide the lowest MSE"

5-42 The following table gives the averagc monthly ex- change rate betwcen the U.S. dollar and thc curo lirr 2009. It shows that I curo was equivalcnt to 1.289 Ll.S. dollars in January 2009. Dcvelop a rrend line that could be used to predict the exchange rate for 2010. Use this model to predict the exchange rate for January 2010 and February 2010.

MONTH EXCHANGB R{TE January

Februarl

March

April

Mry

June

July

August

Septenrber

Octobr:r

Novembcr

Dcccmhr:r

5-zl3 For the data in Problerrr -5-42, develop an e.xponen- tial srnoothing model with a sinoothing constant of 0.3. Using the MSE. compare tliis wirh thc modcl in Problcrn 5-42.

2013

?"(il2

201 I

2010

2009

200Ii

2001

20a6

200-5

2004

I 3,1 04

12.392

1t .571

1t)..+-3 I

8.1'12

l -3.262

I2.,160

10.71 I 14.784

10.453

2003

2002

2(nr

2(XX)

1999

r 998

1991

t996 1 00<

I 994

8,3.+2

10.022

I0.79I

I 1.5()2

9,213

7.908

6.418

-5.1 l7

3.834

3.154

1.289

1.321

l.:121

1.311

1.280

I 254 1.230

1.2'+0

I 287 1.298

1.283

1.31 I 5-40 Llsing the DJIA data in Probiem -5-39, use expo-

nential smooth with trend adjustmcnt to forecast the opening DJIA value for 2014. Use a : 0.8 and F - A.Z. Compare rhe MSE {br this technique with thc MSE [br the trcnd line.

lnternet Homework Problems

See our Infernet home page, at www.pearsonhighered.com/render, for additional homework problems, Problems 5-44 to 5-52.

Case Study

the past, Judy Holmes's tire dealership sold an avcrage ol' 1,000 radials each year. In thu past two ycars. 200 and 250. rcspectivcly, wcrc sold in fall, 350 and 300 in winter. 150 and 165 in spring. and 300 and 285 in summer. With a major expansion planned, Judy projects sales next )/car to increase to

radials. What will the demand be each

Forecasting Attendance at SWU Football Games Southweslem University (SWU), a large state college in Stephenville, Texas, 30 miles southwest of the DallaslFort Worth metroplex, enrolls close to 20,000 students, In a rypical town-gown relationship, the school is a dominant force in the small city, with more students during fall and spring than per- rnanent residents.

A longtime football powerhouse, SWU is a member of the Big Eleven conference and is usually in the top 20 in college football rankings. To bolster its chances of reaching the elu- sive and long-desired number-one ranking, in 2008 SWU hired the legendary Billy Bob Taylor as its head coach. Although

thc numbcr-onc ranking rcmained out of rcach. atlendancc at the flve Saturday home games each year increased. prior to Taylor's arrival. attendance eene'rally averaged 25,000 to 29,000 pcr game. Season ricket sales bumped up by I 0,000 just with the announcement of the new coach's arrival. Srephenville and SWU were ready to rnovc to the big time!

The irnmediate issuc facing SWU. however. was not NCAA ranking. It was capacity. 1'he existing SWIJ stadium, built in 1953. has searing lor 54,(X)0 lans. The iirllowing table indicates attcndancc: at cach .ramc for the past six ycars.

Quantitative Analysis for Managemant, Twelfth Edition, by Barry Render, Ralph M. Stail Micfuel E. Hanna, and Trevor S. Hale. pubtished by prentice Hall. Copyright O 2015 by Pearson Education, Inc.