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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 self-study 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 re-code 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 cut-off values. If the values of the variables are smaller than the cut-off values (below average), they are re-coded into 0, or otherwise re-coded 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 p-value of the ANOVA is smaller than 0.0001, it provides a strong evidence for the overall significance. Besides, the R-Square 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 R-Square 0.9488 Dependent Mean 5.60600 Adj R-Sq 0.9460 Coeff Var 1.98059 Since significant level of 0.05 is considered, the variables that have p-value 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 p-value 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 Chi-Square 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 p-value of the ANOVA is smaller than 0.0001, it indicates the overall significance of the model. Besides, the R-Square 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 R-Square 0.9161 Dependent Mean 4.54478 Adj R-Sq 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 p-value 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 p-value 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 Chi-Square 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 R-Square 0.9488 Dependent Mean 5.60600 Adj R-Sq 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 Chi-Square 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 R-Square 0.9161 Dependent Mean 4.54478 Adj R-Sq 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 Chi-Square 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 heteroscedasticity-consistent 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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