Extrapolation Techniques and Population Forecasting a Study Conducted on Kuala Lumpur

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American University of Sharjah
College of Architecture, Art & Design
Department of Urban Planning
Spring 2014

Extrapolation Techniques and Population Forecasting
A study conducted on the city of Kuala Lumpur

Assignment 2
By

Nadia B. Azzam
ID 27379

Submitted to
Dr. Mahyar Arefi

Submission Date
June 1st, 2014

Table of Contents

1.0.        Introduction        

2.0.        Part 1: Extrapolation Techniques        

2.1.        The Liniear Curve        

2.2.        The Geometric Curve        

2.3.        The Parabolic Curve        

2.4.        Findings        

3.0. Part 2: Population by age group and gender for the city of Kuala Lumpur in 2010        

3.1. Findings        

4.0 References        

Table of Figures

Figure 1: Observed Population and Linear Estimate, 1950 to 201………………...……………..6

Figure 2: Observed Population and Geometric Estimate, 1950 to 2010…………………...…..…8

Figure 3: Observed Population and Parabolic Estimate, 1950 to 2010………………..…….......10

Figure 4: Population Pyramid of Kuala Lumpur in 2010……………………………………..…13

Table of Tables

Table 1: Observed Population Values (1950 to 2010)…………………………………………...4
Table 2: Linear Curve Computations for an  Odd Number of Observations …………………....5

Table 3: Geometric  Computations for an Odd Number of Observations …………….………...7

Table 4: Table 1: Parabolic Computations for an Odd Number of Observations…………..…..10

Table 5: Population of Kuala Lumpur by age group and gender in 2010……………………....12

1. Introduction

According to Klosterman (1990), population projection and forecasts are among the most importatnt tasks required by local, state and national planners. However, the forecasting process is often confronted with challenges such as lack of accurate, reliable, timely and consistent data.  Curve fitting techniques, also known as Extrapolation techniques, are among the most important methods to project the future using aggregate data from the past.This study is devided into two parts.

The first part of this study aims to use curve fitting/extrapolation techniques to forecast the population of a major metropolitan city, Kuala Lumpur, using three projection methods (Linear, Geometric and Parabolic). The study uses an odd number of observations on population data over seven decades (1950 to 2010) and, by comparing between the real data and projected estimates, it reports which projection estimate curve is most likely to fit with the population growth pattern in the city of Kuala Lumpur.

The second part of this study aims to provide a population chart by age and gender reflecting the demographic data for the male and female cohorts for Kuala Lumpur in 2010.

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1. Part 1: Extrapolation Techniques

An odd number of obervations over the period between 1950 and 2010 is used. The observed data form the following table:

Table 2: Observed Population Values (1950 to 2010)

1. The Liniear Curve         

The Liniear curve equation is Yc = a + bX

With reference to Klosterman (1990), find the two unknowns, a and b, using the following formulas:

a =                b = [pic 3][pic 4]

Where:

N        =        Number of Observations

∑Y        =         Sum of Observed values

∑XY        =         Sum of Products of Observed and Index values

∑X2         =         Sum of Squared Index Values

a =  = 839,007
∑X2 =  = 28[pic 5][pic 6][pic 7]

Therefore,
b =  =  = 233,597[pic 8][pic 9]

Accordingly, the linear curve that best fits the observed population data the following equation:[pic 10]

Yc =839,007+ 233,598 X

 Using the linear computation method described by Klosterman for an odd number of observations, we get the following table:

Table 3: Linear Curve Computations for an  Odd Number of Observations