Problems


[Page 705 ( continued )]
1.

The Saki motorcycle dealer in the MinneapolisSt. Paul area wants to make an accurate forecast of demand for the Saki Super TXII motorcycle during the next month. Because the manufacturer is in Japan, it is difficult to send motorcycles back or reorder if the proper number is not ordered a month ahead. From sales records, the dealer has accumulated the following data for the past year:


[Page 706]

Month

Motorcycle Sales

January

9

February

7

March

10

April

8

May

7

June

12

July

10

August

11

September

12

October

10

November

14

December

16


  1. Compute a 3-month moving average forecast of demand for April through January (of the next year).

  2. Compute a 5-month moving average forecast for June through January.

  3. Compare the two forecasts computed in (a) and (b), using MAD . Which one should the dealer use for January of the next year?

2.

The manager of the Carpet City outlet needs to make an accurate forecast of the demand for Soft Shag carpet (its biggest seller). If the manager does not order enough carpet from the carpet mill, customers will buy their carpet from one of Carpet City's many competitors . The manager has collected the following demand data for the past 8 months:

Month

Demand for Soft Shag Carpet (1,000 yd.)

1

8

2

12

3

7

4

9

5

15

6

11

7

10

8

12


  1. Compute a 3-month moving average forecast for months 4 through 9.

  2. Compute a weighted 3-month moving average forecast for months 4 through 9. Assign weights of .55, .33, and .12 to the months in sequence, starting with the most recent month.

  3. Compare the two forecasts by using MAD . Which forecast appears to be more accurate?

3.

The Fastgro Fertilizer Company distributes fertilizer to various lawn and garden shops . The company must base its quarterly production schedule on a forecast of how many tons of fertilizer will be demanded from it. The company has gathered the following data for the past 3 years from its sales records:


[Page 707]

Year

Quarter

Demand for Fertilizer (tons)

1

1

105

 

2

150

 

3

93

 

4

121

2

5

140

 

6

170

 

7

105

 

8

150

3

9

150

 

10

170

 

11

110

 

12

130


  1. Compute a three-quarter moving average forecast for quarters 4 through 13 and compute the forecast error for each quarter.

  2. Compute a five-quarter moving average forecast for quarters 6 through 13 and compute the forecast error for each quarter.

  3. Compute a weighted three-quarter moving average forecast, using weights of .50, .33, and .17 for the most recent, next recent, and most distant data, respectively, and compute the forecast error for each quarter.

  4. Compare the forecasts developed in (a), (b), and (c), using cumulative error. Which forecast appears to be most accurate? Do any of them exhibit any bias?

4.

Graph the demand data in Problem 3. Can you identify any trends, cycles, or seasonal patterns?

5.

The chairperson of the department of management at State University wants to forecast the number of students who will enroll in production and operations management (POM) next semester, in order to determine how many sections to schedule. The chair has accumulated the following enrollment data for the past eight semesters:

Semester

Students Enrolled in POM

1

400

2

450

3

350

4

420

5

500

6

575

7

490

8

650


  1. Compute a three-semester moving average forecast for semesters 4 through 9.

  2. Compute the exponentially smoothed forecast ( a = .20) for the enrollment data.

  3. Compare the two forecasts by using MAD and indicate the more accurate of the two.

6.

The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months:


[Page 708]

Month

Gasoline Demanded (gal.)

October

800

November

725

December

630

January

500

February

645

March

690

April

730

May

810

June

1,200

July

980


  1. Compute an exponentially smoothed forecast, using an a value of .30.

  2. Compute an adjusted exponentially smoothed forecast (with a = .30 and b = .20).

  3. Compare the two forecasts by using MAPD and indicate which seems to be more accurate.

7.

The Victory Plus Mutual Fund of growth stocks has had the following average monthly price for the past 10 months:

Month

Fund Price

1

62.7

2

63.9

3

68.0

4

66.4

5

67.2

6

65.8

7

68.2

8

69.3

9

67.2

10

70.1


Compute the exponentially smoothed forecast with a = .40, the adjusted exponential smoothing forecast with a = .40 and b = .30, and the linear trend line forecast. Compare the accuracy of the three forecasts, using cumulative error and MAD , and indicate which forecast appears to be most accurate.

8.

The Bayside Fountain Hotel is adjacent to County Coliseum, a 24,000-seat arena that is home to the city's professional basketball and ice hockey teams and that hosts a variety of concerts, trade shows, and conventions throughout the year. The hotel has experienced the following occupancy rates for the past 9 years, since the coliseum opened:

Year

Occupancy Rate (%)

1

83

2

78

3

75

4

81

5

86

6

85

7

89

8

90

9

86



[Page 709]

Compute an exponential smoothing forecast with a = .20, an adjusted exponential smoothing forecast with a = .20 and b = .20, and a linear trend line forecast. Compare the three forecasts, using MAD and average error ( ), and indicate which seems to be most accurate.

9.

Emily Andrews has invested in a science and technology mutual fund. Now she is considering liquidating and investing in another fund. She would like to forecast the price of the science and technology fund for the next month before making a decision. She has collected the following data on the average price of the fund during the past 20 months:

Month

Fund Price

1

$63 1/4

2

60 1/8

3

61 3/4

4

64 1/4

5

59 3/8

6

57 7/8

7

62 1/4

8

65 1/8

9

68 1/4

10

65 1/2

11

68 1/8

12

63 1/4

13

64 3/8

14

68 5/8

15

70 1/8

16

72 3/4

17

74 1/8

18

71 3/4

19

75 1/2

20

76 3/4


  1. Using a 3-month average, forecast the fund price for month 21.

  2. Using a 3-month weighted average with the most recent month weighted 0.60, the next most recent month weighted 0.30, and the third month weighted 0.10, forecast the fund price for month 21.

  3. Compute an exponentially smoothed forecast, using a = 0.40, and forecast the fund price for month 21.

  4. Compare the forecasts in (a), (b), and (c), using MAD , and indicate the most accurate.

10.

Eurotronics manufactures components for use in small electronic products such as computers, CD players, and radios at plants in Belgium, Germany, and France. The parts are transported by truck to Hamburg, where they are shipped overseas to customers in Mexico, South America, the United States, and the Pacific Rim. The company has to reserve space on ships months and sometimes years in advance. This requires an accurate forecasting model. Following are the number of cubic feet of container space the company has used in each of the past 18 months:


[Page 710]

Month

Space (1,000s ft. 3 )

1

10.6

2

12.7

3

9.8

4

11.3

5

13.6

6

14.4

7

12.2

8

16.7

9

18.1

10

19.2

11

16.3

12

14.7

13

18.2

14

19.6

15

21.4

16

22.8

17

20.6

18

18.7


Develop a forecasting model that you believe would provide the company with relatively accurate forecasts for the next year and indicate the forecasted shipping space required for the next 3 months.

11.

The Whistle Stop Cafe in Weems, Georgia, is well known for its popular homemade ice cream, made in a small plant in back of the cafe. People drive all the way from Atlanta and Macon to buy the ice cream. The two women who own the cafe want to develop a forecasting model so they can plan their ice cream production operation and determine the number of employees they need to sell ice cream in the cafe. They have accumulated the following sales records for their ice cream for the past 12 quarters:

Year

Quarter

Ice Cream Sales (gal.)

2003

1

350

 

2

510

 

3

750

 

4

420

2004

5

370

 

6

480

 

7

860

 

8

500

2005

9

450

 

10

550

 

11

820

 

12

570


Develop an adjusted exponential smoothing model with a = .50 and b = .50 to forecast demand and assess its accuracy using cumulative error ( E ) and average error ( ). Does there appear to be any bias in the forecast?


[Page 711]
12.

For the demand data in Problem 11, develop a seasonally adjusted forecast for 2004. (Use a linear trend line model to develop a forecast estimate for 2006.) Which forecast model do you perceive to be more accurate: the exponential smoothing model from Problem 11 or the seasonally adjusted forecast?

13.

Develop a seasonally adjusted forecast for the demand data for fertilizer found in Problem 3. Then use a linear trend line model to compute a forecast estimate for demand in year 4.

14.

Monaghan's Pizza delivery service has randomly selected 8 weekdays during the past month and recorded orders for pizza at four different time periods per day:

 

Day

Time Period

1

2

3

4

5

6

7

8

10:00 A.M. 3:00 P.M.

62

49

53

35

43

48

56

43

3:00 P.M. 7:00 P.M.

73

55

81

77

60

66

85

70

7:00 P.M. 11:00 P.M.

42

38

45

50

29

37

35

44

11:00 P.M. 12:00 A.M.

35

40

36

39

26

25

36

31


Develop a seasonally adjusted forecasting model for daily pizza demand and forecast demand for each of the time periods for a single upcoming day.

15.

The Cat Creek Mining Company mines and ships coal. It has experienced the following demand for coal during the past 8 years:

Year

Coal Sales (tons)

1

4,260

2

4,510

3

4,050

4

3,720

5

3,900

6

3,470

7

2,890

8

3,100


Develop an adjusted exponential smoothing model ( a = .30, b = .20) and a linear trend line model and compare the forecast accuracy of the two by using MAD . Indicate which forecast seems to be more accurate.

16.

The Northwoods Outdoor Company is a catalog sales operation that specializes in outdoor recreational clothing. Demand for its items is very seasonal, peaking during the Christmas season and during the spring. It has accumulated the following data for orders per season (quarter) during the past 5 years:

 

Orders (1,000s)

Quarter

2001

2002

2003

2004

2005

JanuaryMarch

18.6

18.1

22.4

23.2

24.5

AprilJune

23.5

24.7

28.8

27.6

31.0

JulySeptember

20.4

19.5

21.0

24.4

23.7

OctoberDecember

41.9

46.3

45.5

47.1

52.8



  1. [Page 712]
  2. Develop a seasonally adjusted forecast model for these order data. Forecast demand for each quarter for 2006 (using a linear trend line forecast estimate for orders in 2006).

  3. Develop a separate linear trend line forecast for each of the four seasons and forecast each season for 2006.

  4. Which of the two approaches used in (a) and (b) appears to be the more accurate? Use MAD to verify your selection.

17.

Metro Food Vending operates vending machines in office buildings , the airport, bus stations , colleges, and other businesses and agencies around town, and it operates vending trucks for building and construction sites. The company believes its sandwich sales follow a seasonal pattern. It has accumulated the following data for sandwich sales per season during the past 4 years:

 

Sandwich Sales (1,000s)

Season

2002

2003

2004

2005

Fall

42.7

44.3

45.7

40.6

Winter

36.9

42.7

34.8

41.5

Spring

51.3

55.6

49.3

47.3

Summer

62.9

64.8

71.2

74.5


Develop a seasonally adjusted forecast model for these sandwich sales data. Forecast demand for each season for 2006 by using a linear trend line estimate for sales in 2006. Do the data appear to have a seasonal pattern?

18.

The emergency room at the new Community Hospital selected every other week during the past 5 months to observe the number of patients during two parts of each weekthe weekend (Friday through Sunday) and weekdays (Monday through Thursday). They typically experience greater patient traffic on weekends than during the week:

 

Number of Patients

Week

Weekend

Weekdays

1

116

83

2

126

92

3

125

97

4

132

91

5

128

103

6

139

88

7

145

96

8

137

106

9

151

95

10

148

102


Develop a seasonally adjusted forecasting model for the number of patients during each part of the week for week 11.


[Page 713]
19.

Aztec Industries has developed a forecasting model that was used to forecast during a 10-month period. The forecasts and actual demand were as follows :

Month

Actual Demand

Forecast Demand

1

160

170

2

150

165

3

175

157

4

200

166

5

190

183

6

220

186

7

205

203

8

210

204

9

200

207

10

220

203


Measure the accuracy of the forecast by using MAD, MAPD , and cumulative error. Does the forecast method appear to be accurate?

20.

RAP Computers assembles personal computers from generic parts it purchases at a discount, and it sells the units via phone orders it receives from customers responding to the company's ads in trade journals. The business has developed an exponential smoothing forecast model to forecast future computer demand. Actual demand for the company's computers for the past 8 months as well as a forecast are shown in the following table:

Month

Demand

Forecast

March

120

April

110

120.0

May

150

116.0

June

130

129.6

July

160

129.7

August

165

141.8

September

140

151.1

October

155

146.7

November

150.0


  1. Using a measure of forecast accuracy of your choice, ascertain whether the forecast appears to be accurate.

  2. Determine whether a 3-month moving average would provide a better forecast.

21.

Develop an exponential smoothing forecast with a = .20 for the demand data in Problem 1. Compare this forecast with the 3-month moving average computed in part (a) of Problem 1, using MAD , and indicate which forecast seems to be more accurate.

22.

The Jersey Dairy Products Company produces cheese, which it sells to supermarkets and food-processing companies. Because of concerns about cholesterol and fat in cheese, the company has seen demand for its products decline during the past decade . It is now considering introducing some alternative low-fat dairy products and wants to determine how much available plant capacity it will have next year. The company has developed an exponential smoothing forecast with a = .40 to forecast cheese. The actual demand and the forecasts from the model are as follows:


[Page 714]

Year

Demand (1,000 lb.)

Forecast

1

16.8

2

14.1

16.8

3

15.3

15.7

4

12.7

15.5

5

11.9

14.4

6

12.3

13.4

7

11.5

12.9

8

10.8

12.4


Assess the accuracy of the forecast model by using MAD and cumulative error. If the exponential smoothing forecast model does not appear to be accurate, determine whether a linear trend model would provide a more accurate forecast.

23.

The manager of the Ramona Inn Hotel near Cloverleaf Stadium believes that how well the local Blue Sox professional baseball team is playing has an impact on the occupancy rate at the hotel during the summer months. Following are the number of victories for the Blue Sox (in a 162-game schedule) for the past 8 years and the hotel occupancy rates:

Year

Blue Sox Wins

Occupancy Rate (%)

1

75

83

2

70

78

3

85

86

4

91

85

5

87

89

6

90

93

7

87

92

8

67

91


Develop a linear regression model for these data and forecast the occupancy rate for next year if the Blue Sox win 88 games .

24.

Carpet City wants to develop a means to forecast its carpet sales. The store manager believes that the store's sales are directly related to the number of new housing starts in town. The manager has gathered data from county records on monthly house construction permits and from store records on monthly sales. These data are as follows:

Monthly Carpet Sales (1,000 yd.)

Monthly Construction Permits

5

21

10

35

4

10

3

12

8

16

2

9

12

41

11

15

9

18

14

26



  1. [Page 715]
  2. Develop a linear regression model for these data and forecast carpet sales if 30 construction permits for new homes are filed.

  3. Determine the strength of the causal relationship between monthly sales and new home construction by using correlation.

25.

The manager of Gilley's Ice Cream Parlor needs an accurate forecast of the demand for ice cream. The store orders ice cream from a distributor a week ahead; if the store orders too little, it loses business, and if it orders too much, the extra must be thrown away. The manager believes that a major determinant of ice cream sales is temperature (i.e., the hotter the weather, the more ice cream people buy). Using an almanac, the manager has determined the average daytime temperature for 10 weeks, selected at random, and from store records he has determined the ice cream consumption for the same 10 weeks. These data are summarized as follows:

Week

Average Temperature (degrees)

Ice Cream Sold (gal.)

1

73

110

2

65

95

3

81

135

4

90

160

5

75

97

6

77

105

7

82

120

8

93

175

9

86

140

10

79

121


  1. Develop a linear regression model for these data and forecast the ice cream consumption if the average weekly daytime temperature is expected to be 85 degrees.

  2. Determine the strength of the linear relationship between temperature and ice cream consumption by using correlation.

26.

Compute the coefficient of determination for the data in Problem 25 and explain its meaning.

27.

Administrators at State University believe that decreases in the number of freshman applications that they have experienced are directly related to tuition increases . They have collected the following enrollment and tuition data for the past decade:

Year

Freshman Applications

Annual Tuition

1

6,050

$3,600

2

4,060

3,600

3

5,200

4,000

4

4,410

4,400

5

4,380

4,500

6

4,160

5,700

7

3,560

6,000

8

2,970

6,000

9

3,280

7,500

10

3,430

8,000



  1. [Page 716]
  2. Develop a linear regression model for these data and forecast the number of applications for State University if tuition increases to $9,000 per year and if tuition is lowered to $7,000 per year.

  3. Determine the strength of the linear relationship between freshman applications and tuition by using correlation.

  4. Describe the various planning decisions for State University that would be affected by the forecast for freshman applications.

28.

Develop a linear trend line model for the freshman applications data at State University in Problem 27.

  1. Does this forecast appear to be more or less accurate than the linear regression forecast developed in Problem 27? Justify your answer.

  2. Compute the correlation coefficient for the linear trend line forecast and explain its meaning.

29.

Explain the numerical value of the slope of the linear regression equation in Problem 25.

30.

Some members of management of the Fairface Cosmetics Firm believe that demand for its products is related to the promotional activities of local department stores where the cosmetics are sold. However, others in management believe that other factors, such as local demographics , are stronger determinants of demand behavior. The following data for local annual promotional expenditures for Fairface products and local annual unit sales for Fairface lip gloss have been collected from 20 stores selected at random from different localities:

Store

Annual Unit Sales (1,000s)

Annual Promotional Expenditures ($1,000s)

1

3.5

$12.6

2

7.2

15.5

3

3.1

10.8

4

1.6

8.7

5

8.9

20.3

6

5.7

21.9

7

6.3

25.6

8

9.1

14.3

9

10.2

15.1

10

7.3

18.7

11

2.5

9.6

12

4.6

12.7

13

8.1

16.3

14

2.5

8.1

15

3.0

7.5

16

4.8

12.4

17

10.2

17.3

18

5.1

11.2

19

11.3

18.5

20

10.4

16.7


Based on these data, does it appear that the strength of the relationship between sales and promotional expenditures is sufficient to warrant using a linear regression forecasting model? Explain your response.

31.

Employees at Precision Engine Parts Company produce parts according to exact design specifications. The employees are paid according to a piece-rate system, wherein the faster they work and the more parts they produce, the greater their chances for monthly bonuses. Management suspects that this method of pay may contribute to an increased number of defective parts. A specific part requires a normal, standard time of 23 minutes to produce. The quality control manager has checked the actual average times to produce this part for 10 different employees during 20 days selected at random during the past month and determined the corresponding percentage of defective parts, as follows.


[Page 717]

Average Time (min.)

Defective (%)

Average Time (min.)

Defective (%)

21.6

3.1

20.8

2.7

22.5

4.6

18.9

4.5

23.1

2.7

21.4

2.8

24.6

1.8

23.7

1.9

22.8

3.5

23.8

1.1

23.7

3.2

24.9

1.2

20.9

3.7

19.8

2.3

19.7

4.5

19.7

5.1

24.5

0.8

21.2

3.6

26.7

1.2

20.8

4.2


Develop a linear regression model relating average production time to percentage defects to determine whether a relationship exists and the percentage of defective items that would be expected with a normal production time of 23 minutes.

32.

Apperson and Fitz is a chain of clothing stores that caters to high school and college students. It publishes a quarterly catalog and operates a Web site that features provocatively attired males and females. The Web site is very expensive to maintain, and company executives are not sure whether the number of hits at the site relate to sales (i.e., people may be looking at the site's pictures only). The Web master has accumulated the following data for hits per month and orders placed at the Web site for the past 20 months:

Month

Hits (1,000s)

Orders (1,000s)

1

34.2

7.6

2

28.5

6.3

3

36.7

8.9

4

42.3

5.7

5

25.8

5.9

6

52.3

6.3

7

35.2

7.2

8

27.9

4.1

9

31.4

3.7

10

29.4

5.9

11

46.7

10.8

12

43.5

8.7

13

52.6

9.3

14

61.8

6.5

15

37.3

4.8

16

28.9

3.1

17

26.4

6.2

18

39.4

5.9

19

44.7

7.2

20

46.3

5.5



[Page 718]

Develop a linear regression model for these data and indicate whether there appears to be a strong relationship between Web site hits and orders. What would be the forecast for orders with 50,000 hits per month?

33.

The Gametime Hat Company manufactures baseball caps that have various team logos in an assortment of designs and colors. The company has had monthly sales for the past 24 months as follows:

Month

Demand (1,000s)

1

8.2

2

7.5

3

8.1

4

9.3

5

9.1

6

9.5

7

10.4

8

9.7

9

10.2

10

10.6

11

8.2

12

9.9

13

10.3

14

10.5

15

11.7

16

9.8

17

10.8

18

11.3

19

12.6

20

11.5

21

10.8

22

11.7

23

12.5

24

12.8


Develop a forecast model using the method you believe best and justify your selection by using a measure (or measures) of forecast accuracy.

34.

Infoworks is a large computer discount store that sells computers and ancillary equipment and software in the town where State University is located. Infoworks has collected historical data on computer sales and printer sales for the past 10 years, as follows:

Year

Personal Computers Sold

Printers Sold

1

1,045

326

2

1,610

510

3

860

296

4

1,211

478

5

975

305

6

1,117

506

7

1,066

612

8

1,310

560

9

1,517

590

10

1,246

676



  1. [Page 719]
  2. Develop a linear trend line forecast to forecast printer demand in year 11.

  3. Develop a linear regression model relating printer sales to computer sales in order to forecast printer demand in year 11 if 1,300 computers are sold.

  4. Compare the forecasts developed in (a) and (b) and indicate which one appears to be more accurate.

35.

Develop an exponential smoothing model with a = .30 for the data in Problem 34 to forecast printer demand in year 11 and compare its accuracy to the linear trend line forecast developed in (a).

36.

Arrow Air is a regional East Coast airline that has collected data for the percentage available seats occupied on its flights for four quarters(1) JanuaryMarch, (2) AprilJune, (3) JulySeptember, and (4) OctoberDecemberfor the past 5 years. Arrow Air also has collected data for the average percentage fare discount for each of these quarters, as follows:

Year

Quarter

Average Fare Discount (%)

Seat Occupancy (%)

1

1

63

21

 

2

75

34

 

3

76

18

 

4

58

26

2

1

59

18

 

2

62

40

 

3

81

25

 

4

76

30

3

1

65

23

 

2

70

28

 

3

78

30

 

4

69

35

4

1

59

20

 

2

61

35

 

3

83

26

 

4

71

30

5

1

60

25

 

2

66

37

 

3

86

25

 

4

74

30


  1. Develop a seasonally adjusted forecast model for seat occupancy. Forecast seat occupancy for year 6 by using a linear trend line forecast estimate for seat occupancy in year 6.

  2. Develop linear regression models relating seat occupancy to discount fares in order to forecast seat occupancy for each quarter in year 6. Assume a fare discount of 20% for quarter 1, 36% for quarter 2, 25% for quarter 3, and 30% for quarter 4.

  3. Compare the forecasts developed in (a) and (b) and indicate which one appears to be the best.

37.

Develop an adjusted exponential smoothing forecast model ( a = .40 and b = .40) for the data in Problem 36 to forecast seat occupancy and compare its accuracy to the seasonally adjusted model developed in (a).

38.

The consumer loan department at Central Union Bank and Trust wants to develop a forecasting model to help determine its potential loan application volume for the coming year. Because adjustable-rate home mortgages are based on government long- term treasury note rates, the department collected the following data for 3- to 5-year treasury note interest rates for the past 24 years:


[Page 720]

Year

Rate

Year

Rate

Year

Rate

1

5.77

9

9.71

17

7.68

2

5.85

10

11.55

18

8.26

3

6.92

11

14.44

19

8.55

4

7.82

12

12.92

20

8.26

5

7.49

13

10.45

21

6.80

6

6.67

14

11.89

22

6.12

7

6.69

15

9.64

23

5.48

8

8.29

16

7.06

24

6.09


Develop an appropriate forecast model for the bank to use to forecast treasury note rates in the future and indicate how accurate it appears to be compared to historical data.

39.

The busiest time of the day at the Taco Town fast-food restaurant is between 11:00 A.M. and 2:00 P.M. Taco Town's service is very labor dependent, and a critical factor for providing quick service is the number of employees on hand during this 3-hour period. To determine the number of employees it needs during each hour of the 3-hour lunch period, Taco Town requires an accurate forecasting model. Following are the number of customers served at Taco Town during each hour of the lunch period for the past 20 weekdays:

 

Hour

Day

1112

121

12

1

90

125

87

2

76

131

93

3

87

112

99

4

83

149

78

5

71

156

83

6

94

178

89

7

56

101

124

8

63

91

66

9

73

146

119

10

101

104

96

11

57

114

106

12

68

125

95

13

75

206

102

14

94

117

118

15

103

145

122

16

67

121

93

17

94

113

76

18

83

166

94

19

79

124

87

20

81

118

115


Develop a forecast model that you believe will best forecast Taco Town's customer demand for the next day and explain why you selected this model.


[Page 721]
40.

The Wellton Fund is a balanced mutual fund that includes a mix of stocks and bonds . Following are the year-end share prices of the fund and Dow Jones Industrial Average (DJIA) for a 20-year period:

Year

Share Price

DJIA

1

$14.75

1,046

2

15.06

1,258

3

14.98

1,211

4

15.73

1,546

5

16.11

1,895

6

16.07

1,938

7

16.78

2,168

8

17.69

2,753

9

16.90

2,633

10

17.81

3,168

11

19.08

3,301

12

20.40

3,754

13

19.39

3,834

14

24.43

5,117

15

26.46

6,448

16

29.45

7,908

17

29.35

9,181

18

27.96

11,497

19

28.21

10,786

20

27.26

10,150


Develop a linear regression model for these data and forecast the fund share price for a DJIA of 12,000. Does there appear to be a strong relationship between the fund's share price and the DJIA?

41.

The Valley United Soccer Club has boys' and girls ' travel soccer teams at all age levels up to 18 years. The club has been successful and grown in popularity over the years; however, an obstacle to its continued growth is a shortage of practice and game soccer fields in the area. The club has tried to make a case to the town council and the parks and recreation committee that it needs more soccer fields to accommodate the increasing number of kids who want to play on club teams. The number of kids who have played soccer on club teams and the town's population for the past 15 years are as follows:

Year

Club Soccer Players

Town Population

1

146

18,060

2

135

18,021

3

159

18,110

4

161

18,125

5

176

18,240

6

190

18,231

7

227

18,306

8

218

18,477

9

235

18,506

10

231

18,583

11

239

18,609

12

251

18,745

13

266

19,003

14

301

19,062

15

327

19,114



[Page 722]

The soccer club wants to develop a forecasting model to demonstrate to the town council its expected growth in the future.

  1. Develop a linear trend line forecast to predict the number of soccer players the club can expect next year.

  2. The town planning department has told the soccer club that the town expects to grow to a population of 19,300 by next year and to 20,000 in 5 years. Develop a linear regression model, using the town's population as a predictor of the number of club soccer players, and compare this forecasting model to the one developed in part (a). Which forecasting model should the club use to support its request for new fields?

42.

The Port of Savannah is considering an expansion of its container terminal. The port has experienced the following container throughput during the past 12 years, expressed as TEUs (i.e., 20- foot equivalent units, a standard unit of measure for containers):

Year

TEUs (1,000s)

1

526.1

2

549.4

3

606.0

4

627.0

5

695.7

6

734.9

7

761.1

8

845.4

9

1,021.1

10

1,137.1

11

1,173.6

12

1,233.4


  1. Develop a linear trend line forecast for these data and forecast the number of TEUs for year 13.

  2. How strong is the linear relationship for these data?

43.

The admission data for freshmen at Tech during the past 10 years are as follows:

Year

Applicants

Offers

% Offers

Acceptances

% Acceptances

1

13,876

11,200

80.7

4,112

36.7

2

14,993

11,622

77.8

4,354

37.3

3

14,842

11,579

78.0

4,755

41.1

4

16,285

13,207

81.1

5,068

38.0

5

16,922

11,382

73.2

4,532

39.8

6

16,109

11,937

74.1

4,655

39.0

7

15,883

11,616

73.1

4,659

40.1

8

18,407

11,539

62.7

4,620

40.0

9

18,838

13,138

69.7

5,054

38.5

10

17,756

11,952

67.3

4,822

40.3


Tech's admission objective is a class of 5,000 entering freshmen, and Tech wants to forecast the percentage of offers it will likely have to make in order to achieve this objective.

  1. Develop a linear trend line to forecast next year's applicants and percentage of acceptances and use these results to estimate the percentage of offers that Tech should expect to make.


    [Page 723]
  2. Develop a linear trend line to forecast the percentage of offers that Tech should expect to make and compare this result with the result in (a). Which forecast do you think is more accurate?

  3. Assume that Tech receives 18,300 applicants in year 11. How many offers do you think it should make to get 5,000 acceptances?

44.

The State of Virginia has instituted a series of standards of learning (SOL) tests in math, history, English, and science that all high school students must pass with a grade of 70 before they are allowed to graduate and receive their diplomas. The school superintendent of Montgomery County believes the tests are unfair because the test scores are closely related to teacher salary and tenure (i.e., the years a teacher has been at a school). The superintendent has sampled 12 other county school systems in the state and accumulated the following data for average teacher salary and average teacher tenure:

School

Average SOL Score

Average Teacher Salary

Average Teacher Tenure (yr.)

1

81

$34,300

9.3

2

78

28,700

10.1

3

76

26,500

7.6

4

77

36,200

8.2

5

84

35,900

8.8

6

86

32,500

12.7

7

79

31,800

8.4

8

91

38,200

11.5

9

68

27,100

8.3

10

73

31,500

7.3

11

90

37,600

12.3

12

85

40,400

14.2


  1. Using Excel or QM for Windows, develop the multiple regression equation for these data.

  2. What is the coefficient of determination for this regression equation? Do you think the superintendent is correct in his beliefs?

  3. Montgomery County has an average SOL score of 74, with an average teacher salary of $27,500 and an average teacher tenure of 7.8 years. The superintendent has proposed to the school board a salary increase that would raise the average salary to $30,000 as well as a benefits program, with the goal of increasing the average tenure to 9 years. He has suggested that if the board passes his proposals, then the average SOL score will increase to 80. Is he correct, according to the forecasting model?

45.

Tech administrators believe their freshman applications are influenced by two variables : tuition and the size of the applicant pool of eligible high school seniors in the state. The following data for an 8-year period show the tuition rates (per semester) and the sizes of the applicant pool for each year:

Tuition

Applicant Pool

Applicants

$ 900

76,200

11,060

1,250

78,050

10,900

1,375

67,420

8,670

1,400

70,390

9,050

1,550

62,550

7,400

1,625

59,230

7,100

1,750

57,900

6,300

1,930

60,080

6,100



  1. [Page 724]
  2. Using Excel, develop the multiple regression equation for these data.

  3. What is the coefficient of determination for this regression equation?

  4. Determine the forecast for freshman applicants for a tuition rate of $1,500 per semester, with a pool of applicants of 60,000.

46.

In Problem 34, Infoworks believes its printer sales are also related to the average price of its printers. It has collected historical data on average printer prices for the past 10 years, as follows:

Year

Average Printer Price

1

$475

2

490

3

520

4

420

5

410

6

370

7

350

8

300

9

280

10

250


  1. Using Excel, develop the multiple regression equation for these data.

  2. What is the coefficient of determination for this regression equation?

  3. Determine the forecast for printer sales, based on personal computer sales of 1,500 units and an average printer price of $300.

47.

The manager of the Bayville police department motor pool wants to develop a forecast model for annual maintenance on police cars, based on mileage in the past year and age of the cars. The following data have been collected for eight different cars :

Miles Driven

Car Age (yr.)

Maintenance Cost

16,320

7

$1,200

15,100

8

1,400

18,500

8

1,820

10,200

3

900

9,175

3

650

12,770

7

1,150

8,600

2

875

7,900

3

900


  1. Using Excel, develop a multiple regression equation for these data.

  2. What is the coefficient of determination for this regression equation?

  3. Forecast the annual maintenance cost for a police car that is 5 years old and will be driven 10,000 miles in 1 year.

48.

The dean of the college of business at Tech has initiated a fund-raising campaign. One of the selling points he plans to use with potential donors is that increasing the college's private endowment will improve its ranking among all business schools , as published each year by the magazine The Global News and Business Report . He would like to demonstrate that there is a relationship between funding and the rankings. He has collected the following data, showing the private endowments ($1,000,000s) and annual budgets ($1,000,000s) from state and private sources for eight of Tech's peer institutions plus Tech, and the ranking of each school:


[Page 725]

Private Endowment ($1,000,000s)

Annual Budget ($1,000,000s)

Ranking

$ 2.5

$ 8.1

87

52.0

26.0

20

12.7

7.5

122

63.0

33.0

32

46.0

12.0

54

27.1

16.1

76

23.3

17.0

103

46.4

14.9

40

48.9

21.8

98


  1. Using Excel, develop a linear regression model for the amount of the private endowment and the ranking and forecast a ranking for a private endowment of $70 million. Does there appear to be a strong relationship between the endowment and the ranking?

  2. Using Excel, develop a multiple regression equation for all these data, including private endowment and annual budget, and forecast a ranking for a private endowment of $70 million and an annual budget of $40 million. How does this forecast compare to the forecast in part (a)?




Introduction to Management Science
Introduction to Management Science (10th Edition)
ISBN: 0136064361
EAN: 2147483647
Year: 2006
Pages: 358

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