Unformatted text preview: DEPARTMENT OF ECONOMICS & FINANCE
Programme: MSc in Finance EF5070
Econometrics
Hedonic Pricing in Property Sales and Property Rent Instructor:
Student Name:
Date: Dr. Fred Y. Kwan
CHAN Tsz Kin (Student ID: student )
CHENG Chung Hon (Student ID: student)
December 6, 2004 TABLE OF CONTENTS
I EXECUTIVE SUMMARY..................................................................................2 II INTRODUCTION................................................................................................3 III OBJECTIVES ......................................................................................................3
IV METHODOLOGY ..............................................................................................3
V DATA COLLECTION .........................................................................................6 VI FINDINGS ............................................................................................................7
1)
2)
3) SALES ...............................................................................................................7
RENT ...............................................................................................................10
OVERALL.......................................................................................................13 VII PREDICTION ....................................................................................................13
VIII LIMITATIONS...................................................................................................14
IX CONCLUSION ..................................................................................................15
X APPENDICES – COMPUTER OUTPUT OF SAS ENTERPRISE GUIDE V2
..............................................................................................................................17
1)
2)
3)
4)
5) SUMMARY STATISTICS (DATA BEFORE TRANSFORMATION) ............17
SUMMARY STATISTICS (SALES) ...............................................................18
LINEAR REGRESSION RESULTS (SALES) ................................................19
SUMMARY STATISTICS (RENT) .................................................................23
LINEAR REGRESSION RESULTS (RENT)..................................................24 XI REFERENCES...................................................................................................28
1)
2) LITERATURES ...............................................................................................28
WEBSITES ......................................................................................................28 1 I EXECUTIVE SUMMARY Since housing supply is limited in Hong Kong compared to some other countries, the
transaction in property market is active. The property owners could make two forms of
transaction, which are property sale and property rent.
This study applies the hedonic pricing model to Property Sales and Property Rent and the
aim is to investigate whether the Property Sales and Property Rent are affected by
different factors. If this is the case, the property owners, or potential property owners, are
then suggested to pay more attention to the specific factors of sale or rent according to
their own interest.
Two log forms of hedonic pricing models, with the same set of independent variables, are
applied to Property Sales and Property Rent. The quantitative variables in our dataset are
“Gross Area” and “Building Age” of a property and the dummy variables are defined to
represent different qualitative attributes of the property in order to test if the attributes are
considered as significant factors of Sales and Rent.
Five of the most active transaction housing estates are chosen for data collection. 50
transaction records are collected for Property Sales and Property Rent in the five selected
housing estates respectively, which form a dataset of sample size of 500. Property
transaction records and other attribute details are collected through the websites of real
estate agencies, online map, as well as the Education and Manpower Bureau.
The findings indicate that there are 6 common factors that affect the Property Sales and
Property Rent. They are “Gross Area”, “Building Age”, “No. of Flats in the Building”,
“Sea View”, “MTR/KCR” and “No. of Bus/Minibus Routes”, while the specific factor for
Sales is “High Level of Floor”, and for Rent are “South Direction” and “No. of Band 1
Schools”.
In addition, we find five special points which should be noted by property owners. First,
“Building Age” is important to both Sales and Rent cases, but it has a stronger effect in
Rent cases. Second, “High Level of floor” only affects Sales cases. Third, except “South
Direction” marginally affects Rent cases, “Direction” is not a factor for Sales and Rent
cases. Fourth, if “No. of Bus/Minibus Routes” is larger than average (32), it has an
adverse effect to both Sales and Rent cases. Finally, if “No. of Band 1 Schools” in a
district is more than average (12), it has a positive effect to Rent only. 2 II INTRODUCTION As we know, the property transaction market is active in Hong Kong because housing
supply is limited compared to some other countries. The property owners could make two
forms of transaction, which are property sale and property rent.
No any form of the transactions is dominant. Some property owners prefer to sell his
property in order to gain the profit of appreciation while some owners would like to rent
his property to tenants for earning a monthly rent.
However, most property owners do not know what factors are actually affecting the
selling and rental prices of their property, and in particular they do not recognize the
specific factors that influence Sales or Rental market respectively. As a result, a study of
hedonic pricing on Sales and Rent will provide a general guidance on this area. III OBJECTIVES
This study applies the hedonic pricing model to Property Sales and Property Rent. The
objectives are to:
i)
find out the common factors that affect both Sales and Rent, which means that all
property owners, or potential owners, are suggested to pay attention to them;
ii)
determine factors that affect Sales or Rent only. If these factors really exist,
property owners who are interested in making sale or rent transactions should
consider those factors respectively; and
iii) identify which factors have favorable effects on Sales and Rental pricing, and on
the contrary which factors have adverse effects. IV METHODOLOGY
Two hedonic pricing models, with the same set of independent variables, are applied to
Property Sales and Property Rent.
Log form of regressions, that is the natural logarithms of all quantitative variables except
the dummy variables, are used. The quantitative variables in our dataset are “Gross Area”
and “Building Age” of a property. The dummy variables are defined to represent different
qualitative attributes of the property and test if the attributes are considered to be
3 significant factors for Sales and Rent.
The descriptions and descriptive statistics of the variables before any transformation are
listed in the following table:
Table 1
Variable Descriptions Unit Mean Std
Dev Minimum Maximum Sales Sales of each
property Ten
thousand 302.008 132.740
HK$ 98 730 Rent Rent of each
property Hundred
103.424 46.141
HK$ 38 320 Gross Area Gross area of each
property Sq. ft. 389 1349 Building
Age Building age of
each property Year 7.141 1 27 224.752 65.733 108 332 No. of Flats No. of flats in the
in the
building of each
building
property Flat 722.974 210.886
14.534 High Level
of Floor 0 = The property
is not in high level
of floor
1 = The property
is in high level of
floor Dummy 0.406 0.492 0 1 Middle
Level of
Floor 0 = The property
is not in middle
level of floor
1 = The property
is in middle level
of floor Dummy 0.254 0.436 0 1 East
Direction 0 = The property
is not in East
direction
1 = The property
is in East direction Dummy 0.242 0.429 0 1 4 South
Direction 0 = The property
is not in South
direction
1 = The property
is in South
direction Dummy 0.262 0.440 0 1 West
Direction 0 = The property
is not in West
direction
1 = The property
is in West
direction Dummy 0.238 0.426 0 1 Sea View 0 = The property
does not have a
sea view
1 = The property
has a sea view Dummy 0.240 0.428 0 1 MTR/KCR 0 = The property
does not have a
MTR or KCR
station in nearby
0.12 sq. km.
1 = The property
has a MTR or
KCR
station
in nearby 0.12 sq.
km. Dummy 0.258 0.438 0 1 Bus/
Minibus
route 31.930 20.325 0 109 School 12.400 3.882 8 18 Number of
No. of
bus/minibus
Bus/Minibus routes in nearby
Routes
0.12 sq. km of
each property
No. of
Band1
Schools Number of band 1
primary/secondary
schools in the
district of each
property 5 No. of
Recreation
Venues Number of
recreation venues,
including club
houses,
gymnasiums,
Recreation
parks, libraries
venue
and selfstudy
rooms in nearby
0.48 sq. km of
each property 4.546 2.872 1 13 The variables “No. of Flats in the Building”, “No. of Bus/Minibus Routes”, “No. of Band
1 Schools” and “No. of Recreation Venues” are quantitative in nature, but it is more
appropriate to recode them into dummy variables. It is because we believe that, for
example, one more bus route would probably not affect the Sales and Rental pricing, but
it makes sense that they would be affected if the number of routes is above or below
average. As a result, we find out the means of the 4 variables, round off them and form
the cutoff values. If the values of the variables are smaller than the cutoff values (below
average), they are recoded into 0, or otherwise recoded into 1.
Finally, the hedonic pricing model of Property Sales is:
ln(Sales) = ln(Gross Area) + ln(Building Age) + Dummy No. of Flats in the Building +
High Level of Floor + Middle Level of Floor + East Direction + South
Direction + West Direction + Sea View + MTR/KCR + Dummy No. of
Bus/Minibus Routes + Dummy No. of Band 1 Schools + Dummy No. of
Recreation Venues
The hedonic pricing model of Property Rent is exactly the same as above except the
dependent variable is replaced by ln(Rent). V DATA COLLECTION Five housing estates of the most active transactions are chosen for data collection. They
are Taikoo Shing (Hong Kong Island), South Horizons (Hong Kong Island), Olympic
(Kowloon), Whampoa Garden (Kowloon) and City One Shatin (New Territories).
50 Sales and 50 Rent records in the 5 selected housing estates are collected, which form a
6 dataset of sample size of 500.
Records and other details are collected from 4 sources. They are Centaline Property
Agency Limited (www.centanet.com), Midland Realty Group (www.midland.com.hk),
Centamap (www.centamap.com) and the Education and Manpower Bureau
(www.emb.gov.hk). We trace each transaction record and find the details inside in the first
two homepages of the real estate agencies. We also go into an online map called
Centamap to find out other attribute details such as “No. of Recreation Venues” near the
property. Moreover, we find the information of band 1 schools in the Education and
Manpower Bureau website. VI FINDINGS
1) SALES
After compiling regression analysis for the Sales data in SAS Enterprise Guide V2
Program, first we would like to see if there is an overall significance for the regression
model. As shown in the following Table 2 and Table 3, the pvalue of the ANOVA is
smaller than 0.0001, it provides a strong evidence for the overall significance. Besides,
the RSquare statistic is 0.9488, it is very large and indicates that the model is good.
Table 2
Analysis of Variance
Sum of Mean
DF Squares Square Source F
Value Pr > F 13 53.90808 4.14678 336.37 <.0001 Model
Error 236 2.90942 0.01233 Corrected
Total 249 56.81750 Table 3
Root MSE 0.11103 RSquare 0.9488 Dependent Mean 5.60600 Adj RSq 0.9460
Coeff Var 1.98059 Since significant level of 0.05 is considered, the variables that have pvalue small than
0.05 are indicated as significant. In the Sales model there are 7 significant variables. They
7 are ln(Gross Area), ln(Building Age), Dummy “No. of Flats in the building”, “High Level
of Floor”, “Sea View”, “MTR/KCR” and Dummy “No. of Bus/Minibus Routes”. Please
refer to Table 4 for the statistics.
Besides, the parameter estimates indicate the “effect direction” and “effect magnitude” of
the variables. For quantitative variables, for example the ln(Gross Area), the parameter
estimate is 1.29216, which shows that it has a favorable effect to Sales. If the Gross Area
increases 10%, the Sales would increase by around 13%. With respect to the dummy
variables such as Dummy “No. of Bus/Minibus Routes”, the parameter estimate is
0.07962, which demonstrates that it has an adverse effect to Sales. If the number of
bus/minibus routes nearby the property is more than average (32), the Sales would
decrease by around 0.8%.
Table 4
Parameter Estimates
Parameter Standard
t Value
Estimate
Error Variable DF Pr > t Intercept 1 2.72723 0.28982 9.41 <.0001 ln(Gross Area) 1 1.29216 0.03904 33.10 <.0001 ln(Building Age) 1 0.07190 0.02770 2.60 0.0100 Dummy No. of Flats in the
building 1 0.09706 0.02802 3.46 0.0006 High Level of Floor 1 0.06428 0.01777 3.62 0.0004 Middle Level of Floor 1 0.02667 0.01847 1.44 0.1500 East Direction 1 0.00018193 0.02032 0.01 0.9929 South Direction 1 0.03346 0.02073 1.61 0.1079 West Direction 1 0.02268 0.01984 1.14 0.2541 Sea View 1 0.07968 0.02437 3.27 0.0012 MTR/KCR 1 0.14344 0.02352 6.10 <.0001 Dummy No. of Bus/Minibus
Routes 1 0.07962 0.01696 4.70 <.0001 Dummy No. of Band1
Schools 1 0.04435 0.03849 1.15 0.2504 Dummy No. of Recreation
Venues 1 0.02453 0.01889 1.30 0.1954 8 Heteroskedasticity test for the model is performed. The pvalue of it is 0.3259, which is
much larger than the significant level of 0.05, so the homoskedasticity assumption is not
violated. Furthermore, in the residual plot it does not show any heteroskedastic pattern,
that further supports the homoskedasticity conclusion. As a result, we conclude that the
standard errors computed for the least squares estimators are correct and the hypothesis
tests in Table 4 are valid. Please refer to Table 5 and Figure 1 for the test result and
residual plot.
Table 5
Test of First and Second
Moment Specification
DF ChiSquare Pr >
ChiSq 89 0.3259 94.47 Figure 1 To sum up the above results, we produce the following summary table that lists all the
significant factors which would affect the Property Sales.
Table 6
Significant Factor Effect Direction Parameter Estimate Gross Area Positive 1.29216 Building Age Negative 0.07190 No. of Flats in the Negative 0.09706
9 Building
High Level of Floor Positive 0.06428 Sea View Positive 0.07968 MTR/KCR Positive 0.14344 Negative 0.07962 No.
of
Routes Bus/Minibus 2) RENT
The interpretation for Rent data is basically the same as those of Sales data. As shown in
the following Table 7 and Table 8, the pvalue of the ANOVA is smaller than 0.0001, it
indicates the overall significance of the model. Besides, the RSquare is 0.9161 which
indicates that the model is good.
Table 7
Analysis of Variance
Source Sum of Mean
DF Squares Square F
Value Pr > F Model 13 43.57951 3.35227 198.33 <.0001 Error 236 3.98892 0.01690 Corrected
Total 249 47.56843 Table 8
Root MSE 0.13001 RSquare 0.9161 Dependent Mean 4.54478 Adj RSq 0.9115
Coeff Var 2.86061 In the Rent model there are 8 significant variables. They are ln(Gross Area), ln(Building
Age), Dummy “No. of Flats in the building”, “South Direction”, “Sea View”,
“MTR/KCR”, Dummy “No. of Bus/Minibus Routes” and Dummy “No. of Band 1
Schools”. However, because the pvalue of South Direction is 0.0459, which is close to
the 0.05 significant level, we do not have strong evidence to conclude that it is a
significant variable in the model. In other words, the effect of "South Direction”, to a
certain extent, is still uncertain. Please refer to Table 9 in next page for the statistics.
10 There are five variables that have favorable effects on Rental market. For example, the
Sea View with parameter estimate of 0.08896, which shows a favorable effect on Rent. If
a property has a “Sea View”, the Rent would increase by around 0.9%. And there are 3
variables which have adverse effects on Rent. One of them is ln(Building Age). The
parameter estimate is 0.12864, which indicates an adverse effect on Rent. If the
“Building Age” increases by 10%, the Rent would decrease by around 1.3%.
Table 9
Parameter Estimates
Parameter Standard
t Value
Estimate
Error Variable DF Pr > t Intercept 1 3.50656 0.25998 13.49 <.0001 ln(Gross Area) 1 1.26143 0.03867 32.62 <.0001 ln(Building Age) 1 0.12864 0.01670 7.70 <.0001 Dummy No. of Flats in the
building 1 0.09277 0.02877 3.23 0.0014 High Level of Floor 1 0.01561 0.01980 0.79 0.4311 Middle Level of Floor 1 0.00808 0.02284 0.35 0.7237 East Direction 1 0.00518 0.02385 0.22 0.8282 South Direction 1 0.04591 0.02288 2.01 0.0459 West Direction 1 0.02158 0.02569 0.84 0.4018 Sea View 1 0.08896 0.02978 2.99 0.0031 MTR/KCR 1 0.16188 0.02403 6.74 <.0001 Dummy No. of Bus/Minibus
Routes 1 0.04418 0.01848 2.39 0.0176 Dummy No. of Band1
Schools 1 0.24860 0.04134 6.01 <.0001 Dummy No. of Recreation
Venues 1 0.00698 0.02189 0.32 0.7500 As shown in the Table 10 and Figure 2 in the next page, the pvalue of Heteroskedasticity
test for the Rent model is 0.3208, which is much larger than the significant level of 0.05,
so the homoskedasticity assumption is not violated. This conclusion is further supported
by the residual plot as it does not show any heteroskedastic pattern. Based on this result,
we conclude that the hypothesis tests in Table 9 are valid.
11 Table 10
Test of First and Second
Moment Specification
DF ChiSquare Pr >
ChiSq 87 0.3208 92.59 Figure 2 The 8 significant factors are summarized in the following Table 11 for easy reference.
Table 11
Significant Factor Effect Direction Parameter Estimate Gross Area Positive 1.26143 Building Age Negative 0.12864 No. of Flats in the
Building Negative 0.09277 South Direction Positive 0.04591 Sea View Positive 0.08896 MTR/KCR Positive 0.16188 No. of Bus/Minibus
Routes Negative 0.04418 No. of Band 1 Schools Positive 0.24860 12 3) OVERALL
After conducting the two analyses for Sales and Rent, we find out the common factors
which influence both of them. Specific factors of Sales or Rent also exist. The common
factors and specific factors are listed in the following table.
Table 12
Common Factor Specific Factor to Sales Specific Factor to Rent Gross Area High Level of Floor South Direction Building Age No. of Band 1 Schools No. of Flats in the
Building
Sea View
MTR/KCR
No. of Bus/Minibus
Routes VII PREDICTION
Although using the two hedonic pricing models for predicting Sales and Rent is not our
main objective, we would also like to know the accuracy of the prediction. Other than the
500 records we have collected, we find another 5 records for Sales and 5 records for Rent.
The predictions are quite accurate, half of them are within 3% of absolute difference, and
only 1 record has difference more than 10%. The prediction results are listed in the
following table.
Table 13
Sales (in HK$)
Housing Estate Actual Sales Predicted
Sales Actual
Difference Percentage
of
Difference WHAMPOA GARDEN
PHASE 01 3,180,000.00 3,273,114.23 93114.23 2.93 WHAMPOA GARDEN
PHASE 05 3,150,000.00 3,217,295.07 67295.07 2.14
13 ISLAND
HARBOURVIEW 6,300,000.00 5,948,486.28 351513.72 5.58 SOUTH HORIZON 2,540,000.00 2,766,108.43 226108.43 8.90 TAIKOO SHING 3,120,000.00 3,088,943.36 31056.64 1.00 RMSE = 194345.22 Rent (in HK$)
Housing Estate Actual Rent Predicted
Rent Actual
Difference Percentage
of
Difference ISLAND
HARBOURVIEW 9,500.00 8,980.50 519.50 5.47 CITY ONE SHATIN
PHASE 2 5,000.00 4,958.54 41.46 0.83 CITY ONE SHATIN
PHASE 5 3,800.00 4,383.35 583.35 15.35 TAIKOO SHING 9,300.00 8,697.69 602.31 6.48 TAIKOO SHING 8,700.00 8,895.91 195.91 2.25 RMSE = 450.12 VIII LIMITATIONS Due to limited resources for data collection and defects of hedonic pricing technique itself,
limitations exist in this study. One of the limitations is that we can only investigate 5 of
the most active transaction housing estates because of time and manpower constraints.
Thus, the generalizability of this study is a doubt. As we only focus on 5 housing estates,
the application of the results to other areas is unwarranted. Besides, the primary limitation
of hedonic pricing technique is that it can only measure a subset of variables associated
with the market value of related good [Freeman, 1993]. Hence it is not likely to include
all the related variables in order to fully explain the variation of Property Sales and
Property Rent in this study. 14 IX CONCLUSION
As referring to the objectives, common factors and specific factors of Property Sales and
Property Rent are found out. Their effects to Sales and Rent are also identified. In
conclusion, the positive common factors are “Gross Area”, “Sea View” and “MTR/KCR”.
The three negative common factors are “Building Age”, “No. of Flats in the Building”
and “No. of Bus/Minibus Routes”. On the other hand, the positive specific factor, for
Sales is “High Level of Floor”, while the two positive specific factors for Rent are “South
Direction” and “No. of Band 1 Schools” in the district of the property.
The following figure recapitulates the factors and their corresponding effects in a
graphical presentation.
Figure 3 There are 5 special points to note for the property owners when deciding to make Sales
and Rent decisions.
First, “Building Age” is important to both Sales and Rent, but there is a stronger effect to
Rent. The “Building Age” increased by 10% would only cut down the Sales by 0.7%, but
it would decrease the Rent by 1.3%. In other words, tenants would attach more weight to
the “Building Age” than property buyers. 15 Second, “High Level of Floor” would affect Sales only and it does not have significant
effects on Rent. So, if a potential property owner wants to buy a flat and then sell it for a
profit, he/she is suggested to buy it in “Higher Level of Floor”.
Third, except “South Direction” affects Rent (it is in fact a marginal case), Direction is
generally not a factor for Sales and Rent cases. However, because in different housing
estates or even in different blocks within an estate, the atmosphere of different Direction
is not the same. So in one block the East Direction is superior while in another one the
South Direction is better. Thus, this result only applies in average cases, meaning there is
a possibility that Direction affects the Sales and Rent of a particular property.
Furthermore, if “No. of Bus/Minibus Routes” nearby are more than average (32 routes in
this case), it has an adverse effect on both Sales and Rent. The possible reasons are that
more bus routes would cause busier traffic, and the noise pollution would also be
unfavorable.
Finally, if “No. of Band 1 Schools” in the district are more than average (12 schools in
this case), it has a positive effect on Rent but not on Sales. It is because probably some
parents would like to send their children to band 1 schools and this expectation is easier
be fulfilled when the district which they are living has more band 1 schools. However, if
it will cost them several millions to move to the districts with more band 1 schools, they
are not able to afford to it or not willing to do so, and they will rent a flat in one of the
districts instead. As a result, higher demand will push the Rent higher. 16 X APPENDICES – COMPUTER OUTPUT OF SAS ENTERPRISE GUIDE V2 1) SUMMARY STATISTICS (DATA BEFORE TRANSFORMATION)
Summary Statistics (Data before Transformation)
Results
The MEANS Procedure
Variable
Sales
Rent
Gross_Area
Building_Age
No_of_Flats
Lev_of_Flr_H
Lev_of_Flr_M
Direction_E
Direction_S
Direction_W
Sea_View
MTR_KCR
Bus
Band1_Sch
Recreation Maximum Mean Minimum Std Dev 730.0000000
320.0000000
1349.00
27.0000000
332.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
109.0000000
18.0000000
13.0000000 302.0080000
103.4240000
722.9740000
14.5340000
224.7520000
0.4060000
0.2540000
0.2420000
0.2620000
0.2380000
0.2400000
0.2580000
31.9300000
12.4000000
4.5460000 98.0000000
38.0000000
389.0000000
1.0000000
108.0000000
0
0
0
0
0
0
0
0
8.0000000
1.0000000 132.7397730
46.1409163
210.8860716
7.1410667
65.7325797
0.4915763
0.4357336
0.4287232
0.4401630
0.4262856
0.4275109
0.4379722
20.3252388
3.8820279
2.8719994 Generated by the SAS System (Local, WIN_PRO) on 01DEC2004 at 5:49 PM 17 2) SUMMARY STATISTICS (SALES)
Summary Statistics (Sales)
Results
The MEANS Procedure
Variable Maximum Mean Minimum Std Dev ln_Sales
ln_Gross_Area
ln_Building_Age
dummy_Flats
Lev_of_Flr_H
Lev_of_Flr_M
Direction_E
Direction_S
Direction_W
Sea_View
MTR_KCR
dummy_Bus
dummy_Band1
dummy_Recreation 6.5930445
7.1204444
3.2958369
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000 5.6060041
6.5705367
2.5289436
0.5440000
0.3920000
0.2960000
0.2320000
0.2200000
0.2760000
0.2800000
0.2880000
0.4680000
0.6000000
0.3840000 4.5849675
5.9635793
1.3862944
0
0
0
0
0
0
0
0
0
0
0 0.4776848
0.3008495
0.6338855
0.4990594
0.4891760
0.4574067
0.4229557
0.4150773
0.4479135
0.4498996
0.4537395
0.4999759
0.4908807
0.4873335 Generated by the SAS System (Local, WIN_PRO) on 01DEC2004 at 5:52 PM 18 3) LINEAR REGRESSION RESULTS (SALES)
Linear Regression (Sales)
Results
The REG Procedure
Model: Linear_Regression_Model
Dependent Variable: ln_Sales
Analysis of Variance Source DF Sum of
Squares Mean
Square F Value Pr > F Model 13 53.90808 4.14678 336.37 <.0001 Error 236 2.90942 0.01233 Corrected Total 249 56.81750 Root MSE 0.11103 RSquare 0.9488 Dependent Mean 5.60600 Adj RSq 0.9460 Coeff Var 1.98059 Parameter Estimates DF Parameter
Estimate Standard
Error t
Value Pr >
t 1 2.72723 0.28982 9.41 <.0001 ln_Gross_Area 1 1.29216 0.03904 33.10 <.0001 ln_Building_Age 1 0.07190 0.02770 2.60 0.0100 1 0.09706 0.02802 3.46 0.0006 Variable Label Intercept Intercept Dummy Variable
dummy_Flats for No. of Flats in
the Building 19 Parameter Estimates DF Parameter
Estimate Standard
Error t
Value Pr >
t Variable Label Lev_of_Flr_H Dummy Variable
for Level of Floor
(High) 1 0.06428 0.01777 3.62 0.0004 Lev_of_Flr_M Dummy Variable
for Level of Floor
(Middle) 1 0.02667 0.01847 1.44 0.1500 1 0.00018193 0.02032 0.01 0.9929 Direction_S Dummy Variable
for Direction
(South) 1 0.03346 0.02073 1.61 0.1079 Direction_W Dummy Variable
for Direction
(West) 1 0.02268 0.01984 1.14 0.2541 Sea_View Dummy Variable
for Sea View 1 0.07968 0.02437 3.27 0.0012 MTR_KCR Dummy Variable
for MTR/KCR
Station (within
0.12 Sq. Km.) 1 0.14344 0.02352 6.10 <.0001 dummy_Bus Dummy Variable
for No. of
Bus/Minibus
Route (within 0.12
Sq. Km.) 1 0.07962 0.01696 4.70 <.0001 dummy_Band1 Dummy Variable 1 0.04435 0.03849 1.15 0.2504 Direction_E Dummy Variable
for Direction
(East) 20 Parameter Estimates Variable Label DF Parameter
Estimate Standard
Error t
Value Pr >
t 1 0.02453 0.01889 1.30 0.1954 for No. of Band 1
Primary/Secondary
School (Data of
2003 from EMB) dummy_Recreation Dummy Variable
for No. of
Recreation Venue
(within 0.48 Sq.
Km.) Generated by the SAS System (Local, WIN_PRO) on 01DEC2004 at 5:54 PM 21 Linear Regression (Sales)
Results
The REG Procedure
Model: Linear_Regression_Model
Dependent Variable: ln_Sales
Test of First and Second
Moment Specification
DF ChiSquare Pr > ChiSq 89 94.47 0.3259 Generated by the SAS System (Local, WIN_PRO) on 01DEC2004 at 5:54 PM 22 4) SUMMARY STATISTICS (RENT)
Summary Statistics (Rent)
Results
The MEANS Procedure
Variable Maximum Mean Minimum Std Dev ln_Rent
ln_Gross_Area
ln_Building_Age
dummy_Flats
Lev_of_Flr_H
Lev_of_Flr_M
Direction_E
Direction_S
Direction_W
Sea_View
MTR_KCR
dummy_Bus
dummy_Band1
dummy_Recreation 5.7683210
7.2071189
3.2580965
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000
1.0000000 4.5447832
6.5061415
2.3783464
0.5520000
0.4200000
0.2120000
0.2520000
0.3040000
0.2000000
0.2000000
0.2280000
0.4800000
0.6000000
0.4320000 3.6375862
5.9788858
0
0
0
0
0
0
0
0
0
0
0
0 0.4370788
0.3097479
0.9521093
0.4982862
0.4945486
0.4095448
0.4350322
0.4609053
0.4008024
0.4008024
0.4203842
0.5006020
0.4908807
0.4963481 Generated by the SAS System (Local, WIN_PRO) on 01DEC2004 at 5:55 PM 23 5) LINEAR REGRESSION RESULTS (RENT)
Linear Regression (Rent)
Results
The REG Procedure
Model: Linear_Regression_Model
Dependent Variable: ln_Rent
Analysis of Variance Source DF Sum of
Squares Mean
Square F Value Pr > F Model 13 43.57951 3.35227 198.33 <.0001 Error 236 3.98892 0.01690 Corrected Total 249 47.56843 Root MSE 0.13001 RSquare 0.9161 Dependent Mean 4.54478 Adj RSq 0.9115 Coeff Var 2.86061 24 Parameter Estimates DF Parameter
Estimate Standard
Error t
Value Pr >
t 1 3.50656 0.25998 13.49 <.0001 ln_Gross_Area 1 1.26143 0.03867 32.62 <.0001 ln_Building_Age 1 0.12864 0.01670 7.70 <.0001 dummy_Flats Dummy Variable
for No. of Flats in
the Building 1 0.09277 0.02877 3.23 0.0014 Lev_of_Flr_H Dummy Variable
for Level of Floor
(High) 1 0.01561 0.01980 0.79 0.4311 Lev_of_Flr_M Dummy Variable
for Level of Floor
(Middle) 1 0.00808 0.02284 0.35 0.7237 Direction_E Dummy Variable
for Direction
(East) 1 0.00518 0.02385 0.22 0.8282 1 0.04591 0.02288 2.01 0.0459 Direction_W Dummy Variable
for Direction
(West) 1 0.02158 0.02569 0.84 0.4018 Sea_View Dummy Variable
for Sea View 1 0.08896 0.02978 2.99 0.0031 MTR_KCR Dummy Variable
for MTR/KCR 1 0.16188 0.02403 6.74 <.0001 Variable Label Intercept Intercept Dummy Variable
Direction_S for Direction
(South) 25 Parameter Estimates Variable Label DF Parameter
Estimate Standard
Error t
Value Pr >
t 1 0.04418 0.01848 2.39 0.0176 1 0.24860 0.04134 6.01 <.0001 1 0.00698 0.02189 0.32 0.7500 Station (within
0.12 Sq. Km.) dummy_Bus Dummy Variable
for No. of
Bus/Minibus
Route (within 0.12
Sq. Km.)
Dummy Variable dummy_Band1 dummy_Recreation for No. of Band 1
Primary/Secondary
School (Data of
2003 from EMB)
Dummy Variable
for No. of
Recreation Venue
(within 0.48 Sq.
Km.) Generated by the SAS System (Local, WIN_PRO) on 01DEC2004 at 5:57 PM 26 Linear Regression (Rent)
Results
The REG Procedure
Model: Linear_Regression_Model
Dependent Variable: ln_Rent
Test of First and Second
Moment Specification
DF ChiSquare Pr > ChiSq 87 92.59 0.3208 Generated by the SAS System (Local, WIN_PRO) on 01DEC2004 at 5:57 PM 27 XI REFERENCES
1) LITERATURES Humavindu, M. & Stage, J. (2003). Hedonic pricing in Windhoek township. Environment
and Development Economics, 8, 391 – 404.
White, H. (1980). A heteroscedasticityconsistent covariance matrix estimator and a direct
test for heteroscedasticity. Econometrica, 48, 817 – 838.
2) WEBSITES Centaline Property Agency Limited (www.centanet.com)
Midland Realty Group (www.midland.com.hk)
Centamap (www.centamap.com)
Education and Manpower Bureau (www.emb.gov.hk) 28 ...
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This note was uploaded on 12/13/2010 for the course EE 5070 taught by Professor Fredkwan during the Spring '10 term at City University of Hong Kong.
 Spring '10
 FredKwan

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