Question

Despite the growth in digital entertainment, the nation’s 400 amusement parks have managed to hold on to visitors. A manager collects data on the number of visitors (in millions) to amusement parks in the United States. A portion of the data is shown in the accompanying table.

B-1) Estimate a linear trend model and an exponential trend model for the sample. (Round your answers to 2 decimal places.)

Variable	Linear Trend	Exponential Trend
Intercept	?	?
T	?	?
Standard Error	?	?

B-2 Calculate the MSE for both trends. (Do not round estimates or intermediate calculations. Round final answers to 2 decimal places.)

	Linear Trend	Exponential Trend
MSE	?	?

b-3. By comparing MSE, which of the above methods perform better? Exponential or Linear?

c-1. Using the model of best fit, make a forecast for visitors to amusement parks in 2008. (Do not round estimates or intermediate calculations. Round your answer to 1 decimal place.)

Y Hat or Y^

?

Million Visitors

c-2. Using the model of best fit, make a forecast for visitors to amusement parks in 2009. (Do not round estimates or intermediate calculations. Round your answer to 1 decimal place.)

Y Hat or Y^

?

Million Views

Year	Visitors
2000	354
2001	338
2002	336
2003	310
2004	358
2005	375
2006	317
2007	305

Answer 1

a)

linear

y =a + b*t

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.33
R Square	0.11
Adjusted R Square	-0.04
Standard Error	25.33
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	476.72	476.72	0.74	0.42
Residual	6	3851.15	641.86
Total	7	4327.88
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	351.79	19.74	17.82	0.00	303.48	400.09
t	-3.37	3.91	-0.86	0.42	-12.93	6.20

exponential

ln y = a+ b*t

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.35
R Square	0.12
Adjusted R Square	-0.02
Standard Error	0.07
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.00	0.00	0.85	0.39
Residual	6	0.03	0.01
Total	7	0.04
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	5.86	0.06	100.92	0.00	5.72	6.01
t	-0.01	0.01	-0.92	0.39	-0.04	0.02

year	y	t	ln y	y^ linear	ei^2	y^ exponential	ei^2
2000	354	1	5.86929691	348.416667	31.1736111	348.5143794	30.0920335
2001	338	2	5.8230459	345.047619	49.6689342	344.8404123	46.79123988
2002	336	3	5.81711116	341.678571	32.2461735	341.2051753	27.09385032
2003	310	4	5.7365723	338.309524	801.429138	337.6082603	762.2160391
2004	358	5	5.88053299	334.940476	531.741638	334.0492633	573.6377892
2005	375	6	5.92692603	331.571429	1886.04082	330.5277844	1977.777956
2006	317	7	5.75890177	328.202381	125.493339	327.0434283	100.8704523
2007	305	8	5.72031178	324.833333	393.361111	323.5958035	345.8039096
		9		321.464286		320.1845229
		10		318.095238		316.8092033
					Linear		Exponential
				MSE	481.394345		483.0354088

Variable	Linear Trend	Exponential Trend
Intercept	351.79	5.86
T	-3.37	-0.01
Standard Error	25.33	0.07
b)
MSE	481.39	483.04
b-3	linear is better
c)	year	y^ linear
	2008	321.5
	2009	318.1

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