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.

Year	Visitors
2000	329
2001	319
⋮	⋮
2007	333

SOURCE: International Association of Amusement Parks and Attractions.
Click here for the Excel Data File

Year	Visitors
2000	329
2001	319
2002	308
2003	302
2004	308
2005	319
2006	357
2007	333

a. Estimate the linear trend model to make forecasts for 2008. (Round your answers to 2 decimal places.)

yˆ =

b. Estimate the exponential trend model to make forecasts for 2008. (Round your answers to 2 decimal places.)

yˆ =

Answer 1

a)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
1	329	12.25	50.77	-24.94
2	319	6.25	8.27	7.19
3	308	2.25	192.52	20.81
4	302	0.25	395.02	9.94
5	308	0.25	192.52	-6.94
6	319	2.25	8.27	-4.31
7	357	6.25	1233.77	87.81
8	333	12.25	123.77	38.94

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	36	2575	42	2204.9	128.50
mean	4.50	321.88	SSxx	SSyy	SSxy

sample size ,   n =   8          
here, x̅ = Σx / n=   4.50   ,     ȳ = Σy/n =   321.88  
                  
SSxx =    Σ(x-x̅)² =    42.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   128.5          
                  
estimated slope , ß1 = SSxy/SSxx =   128.5   /   42.000   =   3.0595
                  
intercept,   ß0 = y̅-ß1* x̄ =   308.1071          
                  
so, regression line is   Ŷ =   308.1071   +   3.0595   *x

Predicted Y at X=   9   is                  
Ŷ =   308.10714   +   3.059524   *   9   =   335.64
forecasts for 2008 = 335.64

..................

b)

exponential trend model to make forecasts for 2008 = 335.04