Extrapolation Techniques and Population Forecasting a Study Conducted on Kuala Lumpur
Autor: Sara17 • October 23, 2017 • 1,199 Words (5 Pages) • 776 Views
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With a squared deviation value equal to 38,650,523,119, the information provided in Table 2 translate into the following linear model:
[pic 11]
Figure 1: Observed Population and Linear Estimate, 1950 to 2010
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The Geometric Curve
The Geometric curve equation is Yc = abx or log Yc = log a + (log b)X
With reference to Klosterman (1990), to find the two unknowns, a and b, we first need to find log a and log b, using the following formulas:
log a = = 5.83[pic 12]
∑X2 = = 28[pic 13]
log b = =0.148[pic 14]
Therefore,
a = antilog (log a) = 678,411.75
b = antilog (log b) = 1.41
Accordingly, the geometric curve that best fits the observed population data the following equation:[pic 15][pic 16]
Yc = abx = (678,411)(1.41)X or Yc = log a + (log b)X = 5.83 + 0.148 X
Using the geometric computation method described by Klosterman for an odd number of observations, we get the following table:
Year
Observed value
(Y)
Logarithm of Observed Value
(Log Y)
Index Value
(X)
Index Value Squared
(X2)
Product of Logarithm and Observed Value
(X log Y)
Estimate/ Projection
(Yc )
Deviation
(Yc - Y)
Squared Deviation
(Yc - Y)²
1950
207,939
5.32
-3
9
-15.95
243,720
243,715
59,396,800,770
1960
343,527
5.54
-2
4
-11.07
342,840
342,835
117,535,634,163
1970
451,201
5.65
-1
1
-5.65
482,273
482,267
232,581,394,831
1980
920,647
5.96
0
0
0.00
954,320
954,314
910,715,806,525
1990
1,120,411
6.05
1
1
6.05
954,320
954,314
910,715,643,749
2000
1,305,582
6.12
2
4
12.23
1,342,440
1,342,434
1,802,129,183,536
2010
1,523,744
6.18
3
9
18.55
1,888,408
1,888,401
3,566,059,678,802
Sum
…
41
…
28
4
…
…
7,599,134,142,376
Table 4: Geometric Computations for an Odd Number of Observations
With a squared deviation value equal to 7,599,134,142,376, the information provided in Table 3 translate into the following geometric model:
[pic 17]
Figure 2: Observed Population and Geometric Estimate, 1950 to 2010
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The Parabolic Curve
The Parabolic curve equation is Yc = a + bX + cX2
With reference to Klosterman (1990), the following equations can be used to find the unknowns that satisfy the least squares
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