# RECORD 0726a6cc581fee39cc268e4d32d8292b296bebc9 # TITLE: THE COMPARISON OF HEDONIC REGRESSION AND ARTIFICIAL NEURAL NETWORK IN THE DEVELOPMENT OF MASS APPRAISAL MODEL # YEAR: 2024.0 VENUE: Jurnal Riset dan Aplikasi Matematika (JRAM) DOI: 10.26740/jram.v8n2.p94-104 # AUTHORS: Mukti Ratna Dewi; B. S. S. Ulama; D. Susilaningrum # PAGES: 11 CANDIDATE TABLE PAGES (1-based): [5, 7] # 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. ===== PAGE 1 (score 4, numeric-paren 0, table-words 0, var-words 4) ===== J. Ris. & Ap. Mat. Vol. 08 No. 02 (2024) pp. 94-104 Jurnal Riset dan Aplikasi Matematika (JRAM) e-ISSN: 2581-0154 URL: journal.unesa.ac.id/index.php/jram 2020 Mathematics Subject Classification: 62M45 Diterima: 24-09-24; direvisi: 17-10-24; diterima: 21-10-24 94 THE COMPARISON OF HEDONIC REGRESSION AND ARTIFICIAL NEURAL NETWORK IN THE DEVELOPMENT OF MASS APPRAISAL MODEL Case Study: Residential Property in Surabaya City MUKTI RATNA DEWI1*, BRODJOL SUTIJO SUPRIH ULAMA2, DESTRI SUSILANINGRUM3 1, 2, 3 Institut Teknologi Sepuluh Nopember *mukti_ratna@its.ac.id 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. Keywords: Artificial Neural Network, Multiple Regression Analysis, Mass Appraisal. 1. Introduction Tax in Indonesia is the primary source of state revenue besides non-tax and grants, which are divided into seven sectors, one of which is the Land and Building Tax (PBB). PBB included in property tax uses Taxable Object Sales Value (NJOP) as the basis for taxation. PBB tax objects can be assessed using several approaches, one of which is the market comparison approach. In this approach, the market value of a property is based on the selling price of other comparable properties [1]. In practice, a property to be assessed will only be compared with two or three properties with the same characteristics in the vicinity. For tax assessment purposes involving many properties, this manual assessment process is time-consuming, costly, inefficient, and prone to bias and human error. Therefore, it is necessary to develop a mass assessment method that is under the structure of the real estate market and is adaptive to changes over time. Based on KEPI & SPI issued by the Indonesian Appraisers Professional Society (MAPPI), a mass appraisal is defined as a systematic appraisal system for a group of individual properties/assets based on existing data and using standard procedures and statistically tested [2]. A model for estimating the property’s value needs to be developed in mass appraisal. This model is usually based on a comparative approach that assumes the property’s market value can be determined based on other properties whose selling and buying prices and influencing factors ===== PAGE 5 (score 18, numeric-paren 0, table-words 3, var-words 10) ===== MUKTI RATNA DEWI, BRODJOL SUTIJO SUPRIH ULAMA, DESTRI SUSILANINGRUM 98 (iii)Determine the number of neurons in each layer. (iv) Run the backpropagation algorithm. (v) Calculate the relative contribution factor. ➢ Step 5: Determine the best mass appraisal model between MRA and ANN by comparing the performance of both models. 4. Results and Discussion 4.1 Data Exploration Based on Table 2, the selling price of residential property in Surabaya City has an average of 1.935 billion rupiah, with the lowest and highest selling prices being 75 million and 7 billion rupiah, respectively. The distribution of this selling price data is skewed to the right, as shown in Figure 2 (a). In line with the selling price data, the distribution of building area and land area data in Figures 2 (b) and (c) is also skewed to the right, with an average of 149.85 m2 and 125.30 m2, respectively. Meanwhile, most of the houses sold have two floors with facilities of three bedrooms and one bathroom, as presented in Table 2. Table 2. Summary Statistics Variable Mean Variance Min. Median Max Modus House price 1,935.80 1,920,533.70 75 1,600 7,000 2,900 Land area 149.85 10,230.72 18 120 500 60 Built-up area 125.30 4,482.82 18 105 375 90 Beds 3.35 1.25 1 3 6 3 Baths 2.52 1.65 1 2 6 1 Story 1.66 0.25 1 2 3 2 (a) (b) (c) Figure 2. The Distribution of (a) House Selling Price, (b) Built-up Area, and (c) Land Area As seen in Figure 3, the house selling price with building area and land area has a positive linear relationship with correlation values of 0.91 and 0.87, respectively. Meanwhile, the average selling price of a house also appears to increase along with the increasing number of bedrooms, bathrooms, and floors, with correlation values of 0.73, 0.79 and 0.54, respectively. On the other hand, from the collected residential property data, 71% have SHM certificate type, 20% have HGB certificate, and 9% have other types of legal certificates (PPJB, Girik, Adat, and others). Based on Figure 4, the house selling price with HGB certificates has the largest median compared to other ownership certificates. ===== PAGE 6 (score 10, numeric-paren 0, table-words 0, var-words 10) ===== 99 THE COMPARISON OF HEDONIC REGRESSION AND ARTIFICIAL NEURAL NETWORK… (a) (b) (c) (d) (e) Figure 3. Relationship Between House Selling Price and (a) Building Area, (b) Land Area, (c) Number of Bedrooms, (d) Number of Bathrooms, and (e) Number of Stories. Figure 4. Comparison of House Selling Prices Between Types of Ownership Certificates 4.2 Hedonic Regression Model The results of the data exploration analysis show that there is a linear relationship between the selling price of a house and the building area, land area, number of bedrooms, number of bathrooms, and number of floors, so these six variables will be included as predictors in the multiple linear regression analysis. Meanwhile, the ownership status variable is also included in the regression model estimation even though the results of the data exploration analysis show that the type of ownership certificate tends not to affect the selling price of a house. ===== PAGE 7 (score 34, numeric-paren 0, table-words 9, var-words 12) ===== MUKTI RATNA DEWI, BRODJOL SUTIJO SUPRIH ULAMA, DESTRI SUSILANINGRUM 100 Before running the regression analysis, the data was partitioned into two parts, namely training and testing, with a ratio of 80:20. The training data was then used to estimate the multiple linear regression model parameter. The results are presented in Table 3. Table 3. Model Estimation of Residential House Selling Price Variable Coef. SE Coef. t-value p-value VIF Intercept -554.09 94.47 -5.86 <0.05 7.11 Built-up area 6.32 0.52 12.22 <0.05 5.36 Land area 8.36 0.67 12.37 <0.05 3.30 Beds -110.12 31.15 -3.54 <0.05 3.55 Baths 218.43 27.89 7.83 <0.05 1.84 Story 188.99 51.79 3.65 <0.05 1.84 Rights – HGB 54.72 49.92 1.09 0.27 1.11 Rights – other than HGB -16.39 70.56 -0.23 0.82 RSE: 411.60 with df: 461. R-sq: 0.91 and Adj. R-Sq: 0.91. F-stat: 655.7 (df1: 7; df2: 471) and p-value: <0.05. A mass appraisal estimation model for residential properties based on the estimation results in Table 3 is as follows: House price = -554,09 + 6,32 built-up area + 8,36 land area -110,12 beds + 218,43 baths +188,99 story + 54,72 HGB right –16,39 other rights + ε (7) The regression model in equation (7) has an adjusted R2 of 91%, and all predictors are significant at the 5% level except for the type of ownership certificate. However, this variable is maintained in the model considering that in the process of buying and selling a house, the legality aspect is one of the factors affecting the buyer’s decision. The estimation results in Table 3 show that the building area, land area, the number of bathrooms and stories, as well as HGB ownership certificate positively affect a house’s selling price. In contrast, the number of bedrooms and ownership certificates other than HGB and SHM can reduce the value of a house. In practice, the number of bedrooms does not always increase the house’s selling price because too many bedrooms can reduce the availability of space that can be used for other things. It can also indicate a nonlinear relationship between the selling price of a house and the number of bedrooms that cannot be captured by multiple linear regression. (a) (b) Figure 5. Residual Assumptions of (a) Equal Variance and (b) Normality In general, houses with larger land and buildings and more bathrooms and floors carry more value. The average selling price of a house with an HGB certificate is 54.72 million higher ===== PAGE 8 (score 6, numeric-paren 0, table-words 1, var-words 4) ===== 101 THE COMPARISON OF HEDONIC REGRESSION AND ARTIFICIAL NEURAL NETWORK… than a house with an SHM certificate. In contrast, houses with other certificates have an average selling price of 16.39 million lower than houses with an SHM certificate. When checking the residual assumption, a fairly high VIF value was obtained for the building area and land area variables, as presented in Table 3. However, multicollinearity between these predictors can still be tolerated because VIF <10. The identical assumption can be evaluated through Figure 5 (a), where the regression model residuals do not form a particular pattern and are evenly spread on both sides of the zero line. Figure 5 (b) shows the model meets the normality residual assumption. 4.3 Back Propagation ANN ANN is one of the techniques in machine learning that requires input variables (predictors) and output (responses) in the form of numbers (numeric), so dummy variables need to be created for the ownership variables first. Afterward, the data is rescaled so all variables are on a scale of 0 to 1. Theoretically, this stage is not mandatory since the activation function will naturally carry out the rescaling process. However, in practice, non-rescaled data can cause the ANN algorithm to fail to converge before reaching maximum iteration. The rescaled data is then divided into training and testing data with the same composition as multiple linear regression analysis. Figure 6. Graphical Representation of ANN House Selling Price In general, ANN is represented as a collection of layers, namely the input, hidden, and output layers, where each network must have one input layer and one output layer. In this study, the number of neurons in the input layer is the same as the number of predictor variables, and the output layer only has one neuron because the model formed is regression. Meanwhile, in this problem, one hidden layer is considered feasible, with the number of neurons in the layer equal to the average number of neurons in the input and output layers, which is five. After the number of layers and neurons in each layer is determined, ANN will be run on the training data using the backpropagation algorithm. The graphical representation of the ANN results that have been run can be seen in Figure 6. The black line represents the weight vector between neurons, while the blue line represents the added bias. The backpropagation algorithm training process is always considered a black box in ANN. Hence, the internal characteristics of the network built are a set of weight values