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
|
20,720
|
6,820
|
3.04
|
|
EXP
|
805
|
258
|
|
R-squared = 0.6R4; n = 105.
Standard error of the estimate = 2,000.
EXP is the experience of teachers in years of full-rime teaching.
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:
|
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
|
448,105
|
|
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:
|
Year
|
|
FURN (in $ Billions)
|
|
|
1st
Quarter
|
2nd
Quarter
|
3rd
Quarter
|
4th
Quarter
|
|
1998
|
$ 98.1
|
5 96.8
|
4 96.0
|
4 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 (see Chapter 1):
NFURNt- FURNt-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
($ 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:
|
State
|
DPI
|
DTE ($ Millions)
|
|
Minnesota
|
$17,907
|
$4,933
|
|
Lowa
|
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
|
|
Ldaho
|
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).
|
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
|
Jui-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
|
Jun-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
|
lun-98
|
1,842
|
Jun-02
|
1,963
|
Jun-06
|
2,237
|
|
Jul-94
|
1,667
|
Jul-98
|
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
|
1,6%
|
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
|
Dec-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
|
|
|
|
Jun-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
|
|
Sept
|
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?