Salaries of public school teachers in a midwestern city

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Reference no: EM13743899

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)
Year	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):

NFURN_t- FURN_t-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?

Reference no: EM13743899

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