The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
SLUM
s
A
B
C
D
E
F
G
Com
muni
ty
Roof
15.
29.
75.
26.
9.
19.
10.
302.
Area
22
79
83
79
96
24
96
989
Expect
ed
Popula
tion
(1st
Order)
4
7
14
6
3
5
4
71
Expect
ed
Popula
tion
(3 rd
Order)
3
6
66
4
7
7
4
5
35
Actual
Popula
tion
4
5
9
6
4
4
6
70
Table 4. Validation Data Showing Number of Residents in
Slum Area
highest as usual. The sample plot in the third order, correlation
factor, and the regression equations for slums are shown in
Figure 4 and Table 2 below. The area is measured in square
meters. The sample plot for semi-formal is shown in Figure 5
and Regression Equation in Table 3.
Figure 4. Third Order Regression Plot of Slum Area
1 st Order
2 nd Order
3 rd Order
R 2
0.090750
0.154538
0.160570
Regressi
on
Equation
Y-hat
2.3306145 +
0.1662026* [Are
a]
Y-hat
26.2106264 +
2.4328515*
[Area]
0.0442838*
[Area A 2]
Y-hat
39.5889753
5.6473600*
[Area] +
0.2826836*
[Area A 2]
0.0043599*
[Area A 3]
Table 2. Slums Regression Equation
Sc-sttfift'ict tf Iknkt# wit?? tab« se?*?ifen??_?*5r*ss
Setectifig festitfes fr&mcne »1 features from, t&e other
2 SO + BHA?*a] * S2~fAr* 3 '2j ♦ Sl'jAtsz’ l]
R-S-3 o a re>i * 0. * 4 . Ad| a ste-s R -Sq : o« ? ed * CM 1$1
Figure 5. Third Order Regression Plot of Semi-formal Area
6.2 Validation
The formulated equations for the two informal settlement types
have been validated by randomly selecting a number of
individual houses and several clusters of houses in the field. The
actual number of validation data, however, has been determined
by the feasibility and security involved in field data gathering.
Due to the limited time and resources for fieldwork, two sets of
data each for slums and semi-formal were collected. These data
were used to check the accuracy of predicting first, the number
of residents in one house and second, a selected community or
cluster of houses.
I s ’Order
2 nd Order
3 rd Order
R 2
0.107333
0.118824
0.147635
Regressi
on
Equation
Y-hat
5.2650832 +
0.0432388*
[Area]
Y-hat
3.3147666 +
0.1010005*
[Area]
0.0003618*
[Area A 2]
Y-hat = -4.5233895
+ 0.4459212*
[Area]
0.0047731*
[Area A 2] +
0.0000166*
[Area A 3]
Table 3. Semi-formal Regression Equation
6.2.1 Slum Area
The result of the validation shows that the third order function
did not consistently predicted with accuracy the number of
individual houses particularly those with large areas. This is
also true for the prediction of the cluster or community, with an
expected large number of people, because of the exponential
nature of higher order polynomials. The low or first order
equation provided a more realistic estimates both for the
individual houses and the community. Results is summarized in
Table 4.
6.2.2 Semi-formal Area
The result is the same as in the slum area showing the third
order function not consistently predicting with accuracy the
number of individual houses. The prediction of the cluster or
community with large number of people is also erroneous
(Table 5). The low or first order equation provided the same
realistic estimates for the individual houses and the community.
The use of this equation, however, is restricted by the fact that
this may be effective only for single level houses which actually
defined the premise for its formulation. All the field samples for
the regression analysis and the validation data indicated a great
percentage of multilevel houses. This will indeed render the
formulated equation for estimating population in semi-formal
houses useless.
Com
SEMI-
muni
FORMAL
A
B
C
D
E
F
G
ty
21
40.
52.
58.
61.
94.
1.
25
ROOF
27
24
86
98
44
55
0.6
770.0
AREA
1
6
9
2
3
1
84
46
Expected
Population
(1st Order)
7
7
7
7
9
14
16
67
Expected
Population
(3 rd Order)
6
8
8
8
9
33
68
140
Actual
Population
7
4
9
17
10
7
9
63
Table 5. Validation Data Showing Number of Residents in
Semi-formal Area.
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