The following data were used in a regression analysis to estimate a demand equat
ID: 1114571 • Letter: T
Question
The following data were used in a regression analysis to estimate a demand equation for recreation visits to a regional park.
Year
Visits in Year t
County population
Income
Price of gasoline
Time Trend
2001
1500
10,000
9,800
1.25
1
2002
1600
10,500
9,950
1.35
2
2003
1900
11,500
10,200
1.15
3
2004
2100
13,000
10,900
1.19
4
2005
2290
14,000
12,000
1.10
5
2006
2300
14,250
12,700
1.15
6
2007
2250
14,500
13,000
1.35
7
2008
2450
16,000
14,000
1.12
8
(15 points) Use the regression output below along with the future values of the explanatory variables to estimate future recreation demand in 2033 and 2053.
Regression Output:
Constant
1511.1
Std Err of Y Est
60.0547
R Squared
0.98727
No. of Observations
8
Degrees of Freedom
3
Population
Income
Price of gas
Trend
Coefficient(s)
0.18308
-0.142
-399.08
64.5077
Std. Err. of Coef.
0.091109
0.07718
378.0335
85.05416
T-statistics
2.009508
-1.8425
-1.05567
0.758431
Future values of the explanatory variables
Year
Population
Income
Price of gas
Trend
2033
21,000
16,000
1.23
32
2053
40,000
18,000
1.23
52
(5 points) Estimate the future values for the results above if the price of gasoline doubles.
Year
Visits in Year t
County population
Income
Price of gasoline
Time Trend
2001
1500
10,000
9,800
1.25
1
2002
1600
10,500
9,950
1.35
2
2003
1900
11,500
10,200
1.15
3
2004
2100
13,000
10,900
1.19
4
2005
2290
14,000
12,000
1.10
5
2006
2300
14,250
12,700
1.15
6
2007
2250
14,500
13,000
1.35
7
2008
2450
16,000
14,000
1.12
8
Explanation / Answer
Given Model:
Future recreation demand = 0.18308*Pop. - 0.142*Income - 399.08*PG + 64.5077*Trend
In 2033,
Future recreation demand = 0.18308*21,000 - 0.142*16,000 - 399.08*1.23 + 64.5077*32 = 3,146.058
In 2053,
Future recreation demand = 0.18308*40,000 - 0.142*18,000 - 399.08*1.23 + 64.5077*52 = 7,630.732
If price of gasoline doubles:
In 2033,
Future recreation demand = 0.18308*21,000 - 0.142*16,000 - 399.08*2.46 + 64.5077*32 = 2,655.1896
In 2053,
Future recreation demand = 0.18308*40,000 - 0.142*18,000 - 399.08*2.46 + 64.5077*52 = 7,139.8636
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