What is the t-ratio for exp does it indicate that


1. The following regression results relate to a study of the salaries of public school teachers in a midwestern city:

Variable

Coefficient

Standard
Error

t-ratio

Constant

2Q720

6,820

3.04

EXP

805

258

 

R-squared = 0.6R4; n =

105.

 

 

R-squared = 0.6R4; n = 105.
Standard error of the estimate = 2,000.
FXP is the experience of teachers in wars of fall-time combing.

a. What is the t-ratio for EXP? Does it indicate that experience is a statistically signi?cant determinant of salary if a 95 percent con?dence level is desired?

b. What percentage of the variation in salary is explained by this model?

c. Determine the point estimate of salary for a teacher with 20 years of experience.

d. What is the approximate 95 percent con?dence interval for your point estimate from part (c)?

2. Mid-Valley Travel Agency (MVTA) has of?ces in 12 cities. The company believes that its monthly airline bookings are related to the mean income in those cities and has collected the following data:

(c4p6)  Location   Bookings   Income
 

1

1,098

$43,299

 

2

1,131

45,021

 

3

1,120

40,290

 

4

1,142

41,893

 

5

971

30,620

 

6

1,403

48,105

 

7

855

27,482

 

8

1,054

33,025

 

9

1,081

34,687

 

10

982

28,725

 

11

1,098

37,892

 

12

1,387

46,198

a. Develop a linear regression model of monthly airline bookings as a function of income.

b. Use the process described in the chapter to evaluate your results.

c. Make the point and approximate 95 percent con?dence interval estimates of monthly airline bookings for another city in which MVTA is considering opening a branch, given that income in that city is $39,020.

3. Carolina Wood Products, Inc., a major manufacturer of household furniture, is interested in predicting expenditures on furniture (FURN) for the entire United States. It has the following data by quarter for 1998 through 2007:

(c4p9)

Year

 

FURN (in $ Billions)

 

1st
Quarter

2nd
Quarter

3rd
Quarter

4th
Quarter

1998

S 98.1

$ 96.8

$ 96.0

S 95.0

1999

93.2

95.1

96.2

98.4

2000

100.7

104.4

108.1

111.1

2001

114.3

117.2

119.4

122.7

2002

125.9

129.3

132.2

136.6

2003

137.4

141.4

145.3

147.7

2004

148.8

150.2

153.4

154.2

2005

159.8

164.4

166.2

169.7

2006

173.7

175.5

175.0

175.7

2007

181.4

180.0

179.7

176.3

 

 

 

 

 

a. Prepare a naive forecast for 2008Q1 based on the following model:

     NFURN1 = FURNi-1

Period            Naive Forecast

2008Q1

b. Estimate the bivariate linear trend model for the data where TIME ? 1 for 1998Q1 through TIME ? 40 for 2007Q4.

                 FURN = a + b(TIME)
FURN =_________ +/-__________ (TIME)
(Circle + or as appropriate)

c. Write a paragraph in which you evaluate this model, with particular emphasis on its usefulness in forecasting.

d. Prepare a time-trend forecast of furniture and household equipment expenditures for 2008 based on the model in part (b).

 

 

 

Period

TIME

Trend Forecast

2008Q1

41

 

2008Q2

42

 

2008Q3

43

 

2008Q4

44

 

 

 

e. Suppose that the actual values of FURN for 2008 were as shown in the following table. Calculate the RMSE for both of your forecasts and interpret the results. (For the naive forecast, there will be only one observation, for 2008Q1.)

Period

Actual FURN (S Billions)

2008Q1

177.6

2008Q2

180.5

2008Q3

182.8

2008Q4

178.7

4. Fifteen midwestern and mountain states have united in an effort to promote and forecast tourism. One aspect of their work has been related to the dollar amount spent per year on domestic travel (DTE) in each state. They have the following estimates for disposable personal income per capita (DPI) and DTE:

 

 

 

(i.Ap10)

State

DPI

DTE
(5 Millions)

Minnesota

$17,907

54,933

Iowa

15,782

1,766

Missouri

17,158

4,692

North Dakota

15,688

628

South Dakota

15,981

551

Nebraska

17,416

1,250

Kansas

17,635

1,729

Montana

15,128

725

Idaho

15,974

934

Wyoming

17,504

778

Colorado

18,628

4,628

New Mexico

14,587

1,724

Arizona

15,921

3,836

Utah

14,066

1,757

Nevada

19,781

6,455

 

 

 

a. From these data estimate a bivariate linear regression equation for domestic travel expenditures (DTE) as a function of disposable income per capita (DPI):

          DTE = a + b(DPI)
DTE =  ______+/-________ (DPI)
(Circle + or - as appropriate)

Evaluate the statistical signi?cance of this model.

b. Illinois, a bordering state, has asked that this model be used to forecast DTE for Illinois under the assumption that DPI will be $19,648. Make the appropriate point and approximate 95 percent interval estimates.

c. Given that actual DTE turned out to be $7,754 (million), calculate the percentage error in your forecast.

5. Collect data on population for your state (https://www.economagic.com may be a good source for these data) over the past 20 years and use a bivariate regression trend line to forecast population for the next ?ve years. Prepare a time-series plot that shows both actual and forecast values. Do you think the model looks as though it will provide reasonably accurate forecasts for the ?ve-year horizon? (c4p11)

6. The following data are for shoe store sales in the United States in millions of dollars after being seasonally adjusted (SASSS).

(c4p14)

 

 

 

 

 

 

 

 

Date

SASSS

Date

SASSS

Date

SASSS

Date

SASSS

 

Jan-92

1,627

Jan-96

1,745

Jan-00

1,885

Jan-04

1,969

 

Feb-92

1,588

Feb-96

1,728

Feb-00

1,885

Feb-04

1,989

 

Mar-92

1,567

Mar-96

1,776

Mar-00

1,925

Mar-04

2,040

 

Apr-92

1,578

Apr-96

1,807

Apr-00

1,891

Apr-04

1,976

 

May-92

1,515

May-96

1,800

May-00

1,900

May-04

1,964

 

Jun-92

1,520

Jun-96

1,758

Jun-00

1,888

Jun-04

1,947

 

Jul-92

1,498

Jul-96

1,784

Jul-00

1,865

Jul-04

1,961

 

Aug-92

1,522

Aug-96

1,791

Aug-00

1,921

Aug-04

1,931

 

Sep-92

1,560

Sep-96

1,743

Sep-00

1,949

Sep-04

1,960

 

Oct-92

1,569

Oct-96

1,785

Oct-00

1,923

Oct-04

1,980

 

Nov-92

1,528

Nov-96

1,765

Nov-00

1,922

Nov-04

1,944

 

Dec-92

1,556

Dec-96

1,753

Dec-00

1,894

Dec-04

2,014

 

Jan-93

1,593

Jan-97

1,753

Jan-01

1,908

Jan-05

2,013

 

Feb-93

1,527

Feb-97

1,790

Feb-01

1,855

Feb-05

2,143

 

Mar-93

1,524

Mar-97

1,830

Mar-01

1,858

Mar-05

2 002

 

Apr-93

1,560

Apr-97

1,702

Apr-01

1,941

Apr-05

2,090

 

May-93

1,575

May-97

1,769

May-01

1,938

May-05

2,104

 

Jun-93

1,588

lun-97

1,793

Jun-01

1,901

Jun-05

2,114

 

Jul-93

1,567

Jul-97

1,801

Jul-01

1,964

Jul-05

2,124

 

Aug-93

1,602

Aug-97

1,789

Aug-01

1,963

Aug-05

2,098

 

Sep-93

1,624

Sep-97

1,791

Sep-01

1,838

Sep-05

2,105

 

Oct-93

1,597

Oct-97

1,799

Oct-01

1,877

Oct-05

2,206

 

Nov-93

1,614

Nov-97

1,811

Nov-01

1,927

Nov-05

2,232

 

Dec-93

1,644

Dec-97

1,849

Dec-01

1,911

Dec-05

2,194

 

Jan-94

1,637

Jan-98

1,824

Jan-02

1,962

Jan-06

2,218

 

Feb-94

1,617

Feb-98

1,882

Feb-02

1,980

Feb-06

2,271

 

Mar-94

1,679

Mar-98

1,859

Mar-02

1,955

Mar-06

2,165

 

Apr-94

1,607

Apr-98

1,831

Apr-02

1,967

Apr-06

2,253

 

May-94

1,623

May-98

1,832

May-02

1,940

May-06

2,232

 

Jun-94

1,619

Jun-98

1,842

Jun-02

1,963

Jun-06

2,237

 

Jul-94

1,667

1u498

1,874

Jul-02

1,920

Jul-06

2,231

 

Aug-94

1,660

Aug-98

1,845

Aug-02

1,937

Aug-06

2,278

 

Sep-94

1,681

Sep-98

1,811

Sep-02

1,867

Sep-06

2,259

 

Oct-94

1,696

Oct-98

1,898

Oct-02

1,918

Oct-06

2,231

 

Nov-94

1,710

Nov-98

1,878

Nov-02

1,914

Nov-06

2,217

 

Dec-94

1,694

De -98

1,901

Dec-02

1,931

Dec-06

2,197

 

Jan-95

1,663

Jan-99

1,916

Jan-03

1,867

 

 

 

Feb-95

1,531

Feb-99

1,894

Feb-03

1,887

 

 

 

Mar-95

1,707

Mar-99

1,883

Mar-03

1,939

 

 

 

Apr-95

1,707

Apr-99

1,871

Apr-03

1,860

 

 

 

May-95

1,715

May-99

1,918

May-03

1,898

 

 

 

lun-95

1,735

Jun-99

1,943

Jun-03

1,924

 

 

 

Jul-95

1,692

Jul-99

1,905

Jul-03

1,967

 

 

 

Aug-95

1,695

Aug-99

1,892

Aug-03

1,994

 

 

 

Sep-95

1,721

Sep-99

1,893

Sep-03

1,966

 

 

 

Oct-95

1,698

Oct-99

1,869

Oct-03

1,943

 

 

 

Nov-95

1,770

Nov-99

1,867

Nov-03

1,973

 

 

 

Dec-95

1,703

Dec-99

1,887

Dec-03

1,976

 

 

 

 

 

 

 

 

 

 

a. Make a linear trend forecast for SASSS though the ?rst seven months of 2007. Given that the actual seasonally adjusted values for 2007 were the following, calculate the RMSE for 2007.

 

 

Date

SASSS

Jan-07

2,317

Feb-07

2,224

Mar-07

2,279

Apr-07

2,223

May-07

2,250

Jun-07

2,260

Jul-07

2,305

b. Reseasonalize the 2007 forecast and the 2007 actual sales using the following seasonal indices:

Month

SI

Jan

0.74

Feb

0.81

Mar

1.00

Apr

1.03

May

1.04

Jun

0.98

Jul

0.98

Aug

1.23

Sep

0.96

Oct

0.94

Nov

0.98

Dec

1.31

 

 

c. Plot the ?nal forecast along with the actual sales data. Does the forecast appear reasonable? Explain.

d. Why do you think the April, May, August, and December seasonal indices are greater than 1?

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