# RECORD 0e568775e77ac2d90b96f6f8ecad954135ed43b0
# TITLE: Listing price estimation of apartments: A generalised linear model
# YEAR: 2019.0  VENUE: Journal of Economic and Financial Sciences  DOI: 10.4102/jef.v12i1.204
# AUTHORS: Dane Bax; Mihalis Chasomeris
# PAGES: 11  CANDIDATE TABLE PAGES (1-based): [7]
# ABSTRACT: Orientation:  Residential property is an important segment of the property market in South Africa. Residential property transactions are typically infrequent and relate to a highly differentiated set of items making measurement techniques complex and difficult. Research purpose:  The aim of this research was to develop a statistical model to estimate listing prices of apartments in KwaZulu-Natal, South Africa, and build a software application to disseminate the results thereof. Motivation for the study:  This study presents a novel alternative to the log linear (ordinary least squares) method of deriving a hedonic price function for residential property where the arithmetic mean is computed as the expected value and not the geometric mean. Research design, approach and method:  Using a data set of 1314 residential apartments provided by Private Property (Pty) Ltd, this research derives a hedonic price function for residential property using a generalised linear model based on the gamma distribution and log-link function. Main findings:  The results showed that floor area, number of bedrooms, number of bathrooms and a dummy variable for suburb (location) were statistically significant determinants of listing prices. Practical/managerial implications:  A software application, called the  listing price calculator , was developed to disseminate the results of the model for commercial use by real estate buyers, sellers and agents, bridging the gap between academia and business. Contribution/value-add:  This study derives a hedonic price function for residential property using a generalised linear model based on the gamma distribution and log-link function, which is novel in South African research.


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https://www.jefjournal.org.za
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Journal of Economic and Financial Sciences 
ISSN: (Online) 2312-2803, (Print) 1995-7076
Page 1 of 11
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Authors:
Dane Bax1 
Mihalis G. Chasomeris1 
Affiliations:
1Graduate School of Business 
and Leadership, University of 
KwaZulu-Natal, Durban, 
South Africa
Corresponding author:
Mihalis Chasomeris, 
chasomerism1@ukzn.ac.za
Dates:
Received: 26 Mar. 2018
Accepted: 18 Jan. 2019
Published: 25 July 2019
How to cite this article:
Bax, D. & Chasomeris, M.G., 
2019, ‘Listing price 
estimation of apartments: 
A generalised linear model’, 
Journal of Economic and 
Financial Sciences 12(1), 
a204. https://doi.org/​
10.4102/jef.v12i1.204
Copyright:
© 2019. The Authors. 
Licensee: AOSIS. This work 
is licensed under the 
Creative Commons 
Attribution License.
Introduction
Residential property is perceived as a fundamental barometer of individual and collective wealth, 
where its cumulative value is closely tracked by government statistical bureaus, banks and other 
economic establishments. Individual households, financial institutions and policymakers closely 
monitor residential property price trends to gauge real house price growth and financial stability, 
as well as to monitor the activity and condition of the credit market (De Haan & Erwin 2011).
Residential property is an important segment of the property market in South Africa; the large 
portfolio of residential property contributes significantly towards the wealth of the country where 
it’s capitalised on the household balance sheet in the set of national accounts (South African 
Reserve Bank 2015). Residential property transactions are typically infrequent and relate to a 
highly differentiated set of items, rendering effective measurement techniques complex and 
difficult (Hill 2011). The main objective of this research was to construct a hedonic pricing model 
to estimate listing prices for apartments within three KwaZulu-Natal coastal regions based on 
statistically significant structural and locational attributes. It appears that no similar study has 
been conducted on any property segment in KwaZulu-Natal province of South Africa. This study 
develops a hedonic price function using a generalised linear model based on the gamma 
distribution and log-link function, which has not been attempted before in South African research, 
and finding global research employing this methodology has proven difficult where no existing 
studies have been identified. This study presents an alternative to the log linear (ordinary least 
squares) method of deriving a hedonic price function for residential property where the arithmetic 
Orientation: Residential property is an important segment of the property market in South 
Africa. Residential property transactions are typically infrequent and relate to a highly 
differentiated set of items making measurement techniques complex and difficult.
Research purpose: The aim of this research was to develop a statistical model to estimate 
listing prices of apartments in KwaZulu-Natal, South Africa, and build a software application 
to disseminate the results thereof.
Motivation for the study: This study presents a novel alternative to the log linear (ordinary 
least squares) method of deriving a hedonic price function for residential property where the 
arithmetic mean is computed as the expected value and not the geometric mean.
Research design, approach and method: Using a data set of 1314 residential apartments 
provided by Private Property (Pty) Ltd, this research derives a hedonic price function for 
residential property using a generalised linear model based on the gamma distribution and 
log-link function. 
Main findings: The results showed that floor area, number of bedrooms, number of bathrooms 
and a dummy variable for suburb (location) were statistically significant determinants of 
listing prices. 
Practical/managerial implications: A software application, called the listing price calculator, 
was developed to disseminate the results of the model for commercial use by real estate buyers, 
sellers and agents, bridging the gap between academia and business.
Contribution/value-add: This study derives a hedonic price function for residential property 
using a generalised linear model based on the gamma distribution and log-link function, 
which is novel in South African research.
Keywords: residential property; listing price estimation; hedonic valuation; economics; 
geospatial modelling; generalised linear model.
Listing price estimation of apartments: 
A generalised linear model
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mobile device 
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Page 7 of 11
Original Research
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is less than null deviance indicating that the saturated model 
is a better fit than the null model.
Interpretation of the coefficients of the generalised linear 
model:
•	 A 1% increase in square metres or size of an apartment 
increases the price by approximately 0.733%.
•	 A one-unit increase in the number of bathrooms of an 
apartment increases the price by approximately 20.3%.
•	 A one-unit increase in the number of bedrooms of an 
apartment increases the price by approximately 3.85%.
•	 Each suburb coefficient is the percentage difference 
between the reference suburb.
The signs for all the coefficients are as expected based on a 
priori expectations, unlike what was experienced in the study 
by Dodds (2011). The number of bedrooms is statistically 
significant, which was not the case in the study of Els and 
Von Fintel (2010). The generalised linear model results show 
that there are 35 suburb coefficients, yet there is a total of 36 
in the data. This is because one of the suburbs was withheld 
from the model output that all the other suburbs were 
compared to. The suburb that was withheld is Albert Park, in 
Durban Central, a comparatively low-priced suburb. The 
suburb coefficients presented in the results of the model will 
always be in comparison with the Albert Park suburb.
The first plot in Figure 2 is the jacknife standardised deviance 
residuals against the fitted values, indicating homogeneous 
TABLE 4: Generalised linear model output.
Coefficients
Estimate
SE
Pr(> |t|)
(Intercept)
9.46220
0.15252
***
log(Size)
0.73296
0.03107
***
NumBaths
0.20298
0.01878
***
NumBeds
0.03851
0.01830
*
Suburb_Ballito
1.16161
0.10722
***
Suburb_Beachfront
0.58267
0.10742
***
Suburb_Berea
0.74698
0.10904
***
Suburb_Brettenwood Coastal Estate
1.17038
0.23149
***
Suburb_Carrington Heights
0.48521
0.17941
**
Suburb_Congella
-0.43305
0.17914
*
Suburb_Dunkirk Estate
0.80940
0.14942
***
Suburb_Durban CBD
0.23417
0.11202
*
Suburb_Esplanade
0.27414
0.11193
*
Suburb_Essenwood
0.83692
0.13930
***
Suburb_Glenwood
0.54902
0.10918
***
Suburb_La Lucia
1.33553
0.11921
***
Suburb_Morningside
0.71846
0.10923
***
Suburb_Mt Edgecombe
1.07865
0.14735
***
Suburb_Musgrave
0.71563
0.11761
***
Suburb_New Town Centre Gateway
1.28471
0.11707
***
Suburb_Overport
0.41942
0.13919
**
Suburb_Palm Lakes Estate
0.76619
0.15888
***
Suburb_Point Waterfront
1.14713
0.10878
***
Suburb_Prestondale
0.95626
0.23121
***
Suburb_Salt Rock
0.98652
0.14048
***
Suburb_Seaward Estates
0.55325
0.18071
**
Suburb_Shakas Rock
1.19157
0.11020
***
Suburb_Sheffield Beach
0.89679
0.11114
***
Suburb_Sherwood
0.53323
0.23222
*
Suburb_Simbithi Ballito
0.86659
0.11347
***
Suburb_Sunningdale
0.75334
0.23265
**
Suburb_Sydenham
0.43097
0.16861
*
Suburb_Tinley Manor and surrounds
0.85732
0.23219
***
Suburb_Umbilo
0.32250
0.12199
**
Suburb_Umhlanga Ridge
1.38917
0.11254
***
Suburb_Umhlanga Rocks
1.71270
0.10895
***
Suburb_Westridge
0.58978
0.14650
***
Suburb_Windermere
0.77823
0.16723
***
Suburb_Zimbali
1.09251
0.12327
***
NumBeds, number of bedrooms; NumBaths, number of bathrooms; CBD, central business 
district, SE, standard deviation.
***, p < 0.001;**, p < 0.01;*, p < 0.05.
Null deviance: 1091.47 on 1313 degrees of freedom.
Residual deviance: 104.44 on 1275 degrees of freedom.
TABLE 3: Variance inflation factor results.
Variables
VIF
Size
3.23
NumBeds
2.89
NumBaths
3.59
Suburb
1.09
NumBeds, number of bedrooms; NumBaths, number of bathrooms; VIF, variance inflation 
factor.
–3
12
13
14
15
16
17
Linear predictor
Residuals
–1
1
3
0.0
0.00
0.02
0.2
0.4
0.6
0.8
1.0
h/(1-h)
Cook stasc
0
200
400
600
Case
0.00
Cook stasc
0.02
800
1,000
1,200
–3
Ordered deviance residuals
Quanles of standard
normal
–3
–1
1
3
–2
–1
0
1
2
 3
FIGURE 2: Generalised linear model residual plots.


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Page 8 of 11
Original Research
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Open Access
TABLE 5: Bootstrapped generalised linear model.
Variables
Original
BootBias
BootSE
BootMed
(Intercept)
9.462201
-0.008291175
0.139005
9.449233
log(Size)
0.732960
0.001169352
0.033635
0.734793
NumBaths
0.202984
0.000409610
0.021085
0.203209
NumBeds
0.038513
-0.000670899
0.019742
0.038008
Suburb_Ballito
1.161614
0.003347619
0.068875
1.164911
Suburb_Beachfront
0.582668
0.002622434
0.076079
0.584300
Suburb_Berea
0.746979
0.003865832
0.069661
0.749166
Suburb_Brettenwood Coastal Estate
1.170375
0.002221222
0.071806
1.172913
Suburb_Carrington Heights
0.485213
0.003705877
0.067818
0.490015
Suburb_Congella
-0.433046
-0.013349784
0.190698
-0.437814
Suburb_Dunkirk Estate
0.809397
-0.000937352
0.099751
0.813618
Suburb_Durban CBD
0.234167
0.002723281
0.072944
0.237637
Suburb_Esplanade
0.274145
0.002687679
0.067512
0.276546
Suburb_Essenwood
0.836923
0.001812316
0.080513
0.835307
Suburb_Glenwood
0.549024
0.003786160
0.068967
0.553202
Suburb_La Lucia
1.335534
0.003588477
0.088316
1.341386
Suburb_Morningside
0.718460
0.003579625
0.068544
0.721921
Suburb_Mt Edgecombe
1.078650
0.001625004
0.147574
1.085874
Suburb_Musgrave
0.715626
0.000504024
0.081211
0.717503
Suburb_New Town Centre Gateway
1.284705
0.003353466
0.072259
1.287007
Suburb_Overport
0.419416
0.001347456
0.101720
0.423324
Suburb_Palm Lakes Estate
0.766187
0.001666709
0.087186
0.769822
Suburb_Point Waterfront
1.147131
0.003243269
0.069162
1.152322
Suburb_Prestondale
0.956261
0.003711508
0.068127
0.957237
Suburb_Salt Rock
0.986517
-0.004324199
0.152297
0.987189
Suburb_Seaward Estates
0.553246
-0.000642886
0.099687
0.554347
Suburb_Shakas Rock
1.191571
0.002634724
0.070973
1.192938
Suburb_Sheffield Beach
0.896794
0.003826300
0.069548
0.901282
Suburb_Sherwood
0.533233
0.001232588
0.105212
0.533948
Suburb_Simbithi Ballito
0.866593
0.002369934
0.072558
0.869840
Suburb_Sunningdale
0.753337
0.004092389
0.073277
0.758305
Suburb_Sydenham
0.430975
-0.003935970
0.162656
0.430606
Suburb_Tinley Manor and surrounds
0.857316
0.003783832
0.066366
0.861646
Suburb_Umbilo
0.322495
0.001902980
0.083675
0.324751
Suburb_Umhlanga Ridge
1.389172
0.002586008
0.071693
1.392348
Suburb_Umhlanga Rocks
1.712698
0.002458290
0.074615
1.715394
Suburb_Westridge
0.589776
0.002838880
0.086824
0.594515
Suburb_Windermere
0.778229
-0.001156938
0.097210
0.782636
Suburb_Zimbali
1.092508
0.000032188
0.099351
1.091839
NumBeds, number of bedrooms; NumBaths, number of bathrooms; BootBias, represents the difference between the average bootstrapped value of the statistic and its original sample value; 
BootSE, are the bootstrap estimates of the standard errors which are computed as the standard deviation of the bootstrap replicates; BootMED, bootstrap estimate; CBD, central business district.
variance and no curvilinear pattern of the  standardised 
deviance residuals. The second plot is of the standardised 
deviance residuals, indicating normality thereof. The bottom 
two plots relate to observations with high influence. Upon 
inspection of these data points, no clear outliers are evident, 
indicating that these points may have high degrees of 
leverage or influence on the model.
Bourassa et al. (2010) found that property price predictions 
were more accurate when submarket dummy locational 
variables were used and the presence of spatial autocorrelation 
was mitigated. In order to formally test for the presence of 
spatial autocorrelation the Mantel test was computed. 
Distances between the apartments were computed in 
kilometres and saved as a distance matrix. The distance matrix 
was then passed to the Mantel test function along with a 
matrix of the residuals from the generalised linear model. The 
Mantel test then tested the null hypothesis of no relationship 
between the residuals and the distance matrix, providing a test 
of spatial autocorrelation. The correlation between the distance 
matrix and the residual matrix was −0.02411 and the p-value 
was 0.999, providing sufficient evidence not to reject the null 
hypothesis of no spatial autocorrelation. The use of the Mantel 
test to detect the presence of spatial autocorrelation in this 
study was consistent with the assertion of Borcard and 
Legendre (2012) and Diniz-Filho et al. (2013).
Reliability of results: Bootstrapping
Bootstrapping was used as a means of model validation 
where 5000 random samples were drawn with replacement. 
A model was then developed for each sample and the average 
of the 5000 models computed was performed. The results 
indicate that bootstrapped coefficients are similar to the 
generalised linear model coefficient which is evident by 
comparing the column headed ‘original’ with the column 
headed ‘bootMed’ in Table 5. Simulating many random 
sampling distributions provides a measure of reliability for