1# RECORD 0726a6cc581fee39cc268e4d32d8292b296bebc92# TITLE: THE COMPARISON OF HEDONIC REGRESSION AND ARTIFICIAL NEURAL NETWORK IN THE DEVELOPMENT OF MASS APPRAISAL MODEL3# YEAR: 2024.0 VENUE: Jurnal Riset dan Aplikasi Matematika (JRAM) DOI: 10.26740/jram.v8n2.p94-1044# AUTHORS: Mukti Ratna Dewi; B. S. S. Ulama; D. Susilaningrum5# PAGES: 11 CANDIDATE TABLE PAGES (1-based): [5, 7]6# ABSTRACT: The appraisal of land and building tax objects in Surabaya City has been carried out manually, so it is prone to bias, human error, and inefficiency in terms of time and energy. Therefore, it is necessary to develop a mass appraisal system based on a property price prediction model in accordance with the real estate market structure. The traditional approach to mass appraisal is based on multiple regression analysis, which, despite having a long history in the appraisal world, cannot address interactions between variables such as nonlinearity. This deficiency was then overcome by introducing an Artificial Intelligence approach based on an artificial neural network (ANN), which has the ability to learn on its own and generalize solutions. Specifically, this study aims to build a mass appraisal model for residential property using (i) multiple regression analysis and (ii) artificial neural network, as well as (iii) determining the best mass appraisal model. The result of the study shows that ANN performs better than multiple regression analysis in predicting the value of residential property in Surabaya City.789===== PAGE 1 (score 4, numeric-paren 0, table-words 0, var-words 4) =====1011J. Ris. & Ap. Mat. Vol. 08 No. 02 (2024) pp. 94-104 12Jurnal Riset dan Aplikasi Matematika (JRAM) 13e-ISSN: 2581-0154 14URL: journal.unesa.ac.id/index.php/jram 15 16 17 2020 Mathematics Subject Classification: 62M45 18Diterima: 24-09-24; direvisi: 17-10-24; diterima: 21-10-24 19 2094 21 22THE COMPARISON OF HEDONIC REGRESSION AND 23ARTIFICIAL NEURAL NETWORK IN THE DEVELOPMENT 24OF MASS APPRAISAL MODEL 25 26Case Study: Residential Property in Surabaya City 27 28MUKTI RATNA DEWI1*, BRODJOL SUTIJO SUPRIH ULAMA2, DESTRI SUSILANINGRUM3 29 301, 2, 3 Institut Teknologi Sepuluh Nopember 31 32*mukti_ratna@its.ac.id 33 34ABSTRACT 35 36The appraisal of land and building tax objects in Surabaya City has been carried out manually, so 37it is prone to bias, human error, and inefficiency in terms of time and energy. Therefore, it is necessary 38to develop a mass appraisal system based on a property price prediction model in accordance with the 39real estate market structure. The traditional approach to mass appraisal is based on multiple regression 40analysis, which, despite having a long history in the appraisal world, cannot address interactions between 41variables such as nonlinearity. This deficiency was then overcome by introducing an Artificial 42Intelligence approach based on an artificial neural network (ANN), which has the ability to learn on its 43own and generalize solutions. Specifically, this study aims to build a mass appraisal model for residential 44property using (i) multiple regression analysis and (ii) artificial neural network, as well as (iii) 45determining the best mass appraisal model. The result of the study shows that ANN performs better than 46multiple regression analysis in predicting the value of residential property in Surabaya City. 47 48Keywords: Artificial Neural Network, Multiple Regression Analysis, Mass Appraisal. 49 501. Introduction 51Tax in Indonesia is the primary source of state revenue besides non-tax and grants, which 52are divided into seven sectors, one of which is the Land and Building Tax (PBB). PBB included 53in property tax uses Taxable Object Sales Value (NJOP) as the basis for taxation. PBB tax 54objects can be assessed using several approaches, one of which is the market comparison 55approach. In this approach, the market value of a property is based on the selling price of other 56comparable properties [1]. In practice, a property to be assessed will only be compared with 57two or three properties with the same characteristics in the vicinity. For tax assessment purposes 58involving many properties, this manual assessment process is time-consuming, costly, 59inefficient, and prone to bias and human error. Therefore, it is necessary to develop a mass 60assessment method that is under the structure of the real estate market and is adaptive to changes 61over time. 62Based on KEPI & SPI issued by the Indonesian Appraisers Professional Society (MAPPI), 63a mass appraisal is defined as a systematic appraisal system for a group of individual 64properties/assets based on existing data and using standard procedures and statistically tested 65[2]. A model for estimating the property’s value needs to be developed in mass appraisal. This 66model is usually based on a comparative approach that assumes the property’s market value can 67be determined based on other properties whose selling and buying prices and influencing factors 686970===== PAGE 5 (score 18, numeric-paren 0, table-words 3, var-words 10) =====7172MUKTI RATNA DEWI, BRODJOL SUTIJO SUPRIH ULAMA, DESTRI SUSILANINGRUM 98 73 74(iii)Determine the number of neurons in each layer. 75(iv) Run the backpropagation algorithm. 76(v) Calculate the relative contribution factor. 77➢ Step 5: Determine the best mass appraisal model between MRA and ANN by comparing 78the performance of both models. 794. Results and Discussion 804.1 Data Exploration 81Based on Table 2, the selling price of residential property in Surabaya City has an average 82of 1.935 billion rupiah, with the lowest and highest selling prices being 75 million and 7 billion 83rupiah, respectively. The distribution of this selling price data is skewed to the right, as shown 84in Figure 2 (a). In line with the selling price data, the distribution of building area and land area 85data in Figures 2 (b) and (c) is also skewed to the right, with an average of 149.85 m2 and 125.30 86m2, respectively. Meanwhile, most of the houses sold have two floors with facilities of three 87bedrooms and one bathroom, as presented in Table 2. 88 89Table 2. Summary Statistics 90Variable 91Mean 92Variance 93Min. Median Max 94Modus 95House price 961,935.80 1,920,533.70 9775 981,600 7,000 992,900 100Land area 101149.85 10210,230.72 10318 104120 105500 10660 107Built-up area 108125.30 1094,482.82 11018 111105 112375 11390 114Beds 1153.35 1161.25 1171 1183 1196 1203 121Baths 1222.52 1231.65 1241 1252 1266 1271 128Story 1291.66 1300.25 1311 1322 1333 1342 135 136 137 138 139 140(a) 141 142 143 144(b) 145 146 147 148(c) 149Figure 2. The Distribution of (a) House Selling Price, (b) Built-up Area, and (c) Land Area 150 151As seen in Figure 3, the house selling price with building area and land area has a positive 152linear relationship with correlation values of 0.91 and 0.87, respectively. Meanwhile, the 153average selling price of a house also appears to increase along with the increasing number of 154bedrooms, bathrooms, and floors, with correlation values of 0.73, 0.79 and 0.54, respectively. 155On the other hand, from the collected residential property data, 71% have SHM certificate type, 15620% have HGB certificate, and 9% have other types of legal certificates (PPJB, Girik, Adat, 157and others). Based on Figure 4, the house selling price with HGB certificates has the largest 158median compared to other ownership certificates. 159160161===== PAGE 6 (score 10, numeric-paren 0, table-words 0, var-words 10) =====16216399 164 THE COMPARISON OF HEDONIC REGRESSION AND ARTIFICIAL NEURAL NETWORK… 165 166 (a) 167(b) 168 (c) 169 (d) 170 (e) 171Figure 3. Relationship Between House Selling Price and (a) Building Area, (b) Land Area, (c) 172Number of Bedrooms, (d) Number of Bathrooms, and (e) Number of Stories. 173 174 175Figure 4. Comparison of House Selling Prices Between Types of Ownership Certificates 1764.2 Hedonic Regression Model 177The results of the data exploration analysis show that there is a linear relationship between 178the selling price of a house and the building area, land area, number of bedrooms, number of 179bathrooms, and number of floors, so these six variables will be included as predictors in the 180multiple linear regression analysis. Meanwhile, the ownership status variable is also included 181in the regression model estimation even though the results of the data exploration analysis show 182that the type of ownership certificate tends not to affect the selling price of a house. 183184185===== PAGE 7 (score 34, numeric-paren 0, table-words 9, var-words 12) =====186187MUKTI RATNA DEWI, BRODJOL SUTIJO SUPRIH ULAMA, DESTRI SUSILANINGRUM 100 188 189Before running the regression analysis, the data was partitioned into two parts, namely 190training and testing, with a ratio of 80:20. The training data was then used to estimate the 191multiple linear regression model parameter. The results are presented in Table 3. 192 193Table 3. Model Estimation of Residential House Selling Price 194Variable 195Coef. 196SE Coef. 197t-value 198p-value 199VIF 200Intercept 201-554.09 20294.47 203-5.86 204<0.05 2057.11 206Built-up area 2076.32 2080.52 20912.22 210<0.05 2115.36 212Land area 2138.36 2140.67 21512.37 216<0.05 2173.30 218Beds 219-110.12 22031.15 221-3.54 222<0.05 2233.55 224Baths 225218.43 22627.89 2277.83 228<0.05 2291.84 230Story 231188.99 23251.79 2333.65 234<0.05 2351.84 236Rights – HGB 23754.72 23849.92 2391.09 2400.27 2411.11 242Rights – other than HGB 243-16.39 24470.56 245-0.23 2460.82 247RSE: 411.60 with df: 461. 248R-sq: 0.91 and Adj. R-Sq: 0.91. 249F-stat: 655.7 (df1: 7; df2: 471) and p-value: <0.05. 250 251A mass appraisal estimation model for residential properties based on the estimation 252results in Table 3 is as follows: 253 254House price = -554,09 + 6,32 built-up area + 8,36 land area -110,12 beds + 218,43 255baths +188,99 story + 54,72 HGB right –16,39 other rights + ε 256(7) 257 258The regression model in equation (7) has an adjusted R2 of 91%, and all predictors are 259significant at the 5% level except for the type of ownership certificate. However, this variable 260is maintained in the model considering that in the process of buying and selling a house, the 261legality aspect is one of the factors affecting the buyer’s decision. 262The estimation results in Table 3 show that the building area, land area, the number of 263bathrooms and stories, as well as HGB ownership certificate positively affect a house’s selling 264price. In contrast, the number of bedrooms and ownership certificates other than HGB and SHM 265can reduce the value of a house. In practice, the number of bedrooms does not always increase 266the house’s selling price because too many bedrooms can reduce the availability of space that 267can be used for other things. It can also indicate a nonlinear relationship between the selling 268price of a house and the number of bedrooms that cannot be captured by multiple linear 269regression. 270 271(a) 272(b) 273Figure 5. Residual Assumptions of (a) Equal Variance and (b) Normality 274In general, houses with larger land and buildings and more bathrooms and floors carry 275more value. The average selling price of a house with an HGB certificate is 54.72 million higher 276277278===== PAGE 8 (score 6, numeric-paren 0, table-words 1, var-words 4) =====279280101 281 THE COMPARISON OF HEDONIC REGRESSION AND ARTIFICIAL NEURAL NETWORK… 282 283than a house with an SHM certificate. In contrast, houses with other certificates have an average 284selling price of 16.39 million lower than houses with an SHM certificate. 285When checking the residual assumption, a fairly high VIF value was obtained for the 286building area and land area variables, as presented in Table 3. However, multicollinearity 287between these predictors can still be tolerated because VIF <10. The identical assumption can 288be evaluated through Figure 5 (a), where the regression model residuals do not form a particular 289pattern and are evenly spread on both sides of the zero line. Figure 5 (b) shows the model meets 290the normality residual assumption. 2914.3 Back Propagation ANN 292ANN is one of the techniques in machine learning that requires input variables 293(predictors) and output (responses) in the form of numbers (numeric), so dummy variables need 294to be created for the ownership variables first. Afterward, the data is rescaled so all variables 295are on a scale of 0 to 1. Theoretically, this stage is not mandatory since the activation function 296will naturally carry out the rescaling process. However, in practice, non-rescaled data can cause 297the ANN algorithm to fail to converge before reaching maximum iteration. The rescaled data is 298then divided into training and testing data with the same composition as multiple linear 299regression analysis. 300 301Figure 6. Graphical Representation of ANN House Selling Price 302 303In general, ANN is represented as a collection of layers, namely the input, hidden, and 304output layers, where each network must have one input layer and one output layer. In this study, 305the number of neurons in the input layer is the same as the number of predictor variables, and 306the output layer only has one neuron because the model formed is regression. Meanwhile, in 307this problem, one hidden layer is considered feasible, with the number of neurons in the layer 308equal to the average number of neurons in the input and output layers, which is five. After the 309number of layers and neurons in each layer is determined, ANN will be run on the training data 310using the backpropagation algorithm. 311The graphical representation of the ANN results that have been run can be seen in Figure 3126. The black line represents the weight vector between neurons, while the blue line represents 313the added bias. The backpropagation algorithm training process is always considered a black 314box in ANN. Hence, the internal characteristics of the network built are a set of weight values 315