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Extrapolation Techniques and Population Forecasting a Study Conducted on Kuala Lumpur

Autor:   •  October 23, 2017  •  1,199 Words (5 Pages)  •  686 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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