1# RECORD 1076844f99e9f35c7768a4e64f2c167ab26b5afd2# TITLE: Predicting Housing Prices in Riyadh: A Comparative Analysis on Machine Learning and Hedonic Regression3# YEAR: 2025.0 VENUE: Innovation in Statistics and Probability DOI: 10.64389/isp.2025.012204# AUTHORS: Mohamed Ezzeldin; Mahmoud Abouagwa5# PAGES: 19 CANDIDATE TABLE PAGES (1-based): [1, 5, 6, 8, 9, 11, 12, 13, 15]6# ABSTRACT: This study investigates the performance of hedonic regression against artificial neural networks and random forest for real estate price prediction in Riyadh, Saudi Arabia. Using data from a major property platform collected in Q3 2024, the analysis spans 2,997 residential units across five major districts. The study is situated within the context of Vision 2030 and addresses the challenges of real estate valuations in a rapidly evolving urban environment. Twelve locational and structural features were analyzed using a 70/30 training-testing split. Random Forest led with test R²=0.9065, RMSE=0.1911, MAE=0.1353, outperforming Artificial Neural Network (R²=0.8968, RMSE=0.2008, MAE=0.1450) and Hedonic Regression (R²=0.8034, RMSE=0.2673, MAE=0.1970). Random Forest feature importance: North of Riyadh (0.768659), West of Riyadh (0.612986), building type (0.180799), entrances (0.171134), size (0.127103). Random Forest and Artificial Neural Network excelled in capturing non-linear and spatial price trends in Riyadh’s housing market. This study supports the incorporation of machine learning models into workflows for predicting property prices, especially in cities like Riyadh that are quickly urbanizing. The research provides a useful foundation for improving real estate valuation procedures in accordance with Saudi Arabia's Vision 2030 goals by demonstrating the predictive benefits of RF over conventional methods.789===== PAGE 1 (score 13, numeric-paren 5, table-words 0, var-words 7) =====1011Innovation in Statistics and Probability 121(2), 26–44 13DOI:10.64389/isp.2025.01220 14https://sphinxsp.org/journal/index.php/isp/ 15 16 17 18 19 20Research article 21Predicting Housing Prices in Riyadh: A Comparative Analysis on Machine Learning 22and Hedonic Regression 23Mohamed R. Ezzeldin11,* and Mahmoud Abouagwa 2,3 241 Deanship of Educational Services, Qassim University, Qassim 51452, Saudi Arabia; m.ezzeldin@qu.edu.sa 252 College of Business, City University Ajman, Ajman 18484, United Arab Emirates, m.abouagwa@cu.ac.ae 263 Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 2712613, Egypt; mahmoud.aboagwa@cu.edu.eg 28 29* Correspondence: m.ezzeldin@qu.edu.sa 30 31ARTICLE INFO 32Keywords: 33Real estate valuation, Riyadh housing 34market, Hedonic regression, Random 35Forest, Neural networks, Machine 36learning in real estate. 37Mathematics Subject Classification: 3862G08, 68T07 39Important Dates: 40Received: 14 August 2025 41Revised: 21 October 2025 42Accepted: 25 November 2025 43Online: 26 November 2025 44 45 46Copyright © 2025 by the authors. Published 47under Creative Commons Attribution (CC BY) 48license. 49ABSTRACT 50This study investigates the performance of hedonic regression against 51artificial neural networks and random forest for real estate price prediction in 52Riyadh, Saudi Arabia. Using data from a major property platform collected in 53Q3 2024, the analysis spans 2,997 residential units across five major districts. 54The study is situated within the context of Vision 2030 and addresses the 55challenges of real estate valuations in a rapidly evolving urban environment. 56Twelve locational and structural features were analyzed using a 70/30 training-57testing split. Random Forest led with test R²=0.9065, RMSE=0.1911, 58MAE=0.1353, outperforming Artificial Neural Network (R²=0.8968, 59RMSE=0.2008, MAE=0.1450) and Hedonic Regression (R²=0.8034, 60RMSE=0.2673, MAE=0.1970). Random Forest feature importance: North of 61Riyadh (0.768659), West of Riyadh (0.612986), building type (0.180799), 62entrances (0.171134), size (0.127103). Random Forest and Artificial Neural 63Network excelled in capturing non-linear and spatial price trends in Riyadh’s 64housing market. This study supports the incorporation of machine learning 65models into workflows for predicting property prices, especially in cities like 66Riyadh that are quickly urbanizing. The research provides a useful foundation 67for improving real estate valuation procedures in accordance with Saudi 68Arabia's Vision 2030 goals by demonstrating the predictive benefits of RF over 69conventional methods.70 71 72 731. Introduction 74Housing constitutes one of the primary human needs, and a substantial portion of household income is typically 75allocated to its purchase. As such, residential real estate is a critical asset class in household portfolios, and fluctuations 76in housing prices can have substantial macroeconomic repercussions [1,2]. Urban congestion and uneven development 777879===== PAGE 2 (score 19, numeric-paren 0, table-words 1, var-words 17) =====808127 82 83 84 85 86 87contribute to regional inflation in property markets, making housing price forecasting a valuable tool for planners and 88investors. This study investigates real estate price prediction in Riyadh, Saudi Arabia, within the context of urban 89growth, market complexity, and data-driven housing policy under Vision 2030. Saudi Arabia’s urban housing market 90is undergoing rapid transformation, driven in part by strategic initiatives encapsulated in Vision 2030 the Kingdom’s 91ambitious plan to diversify its economy and enhance quality of life. Vision 2030’s housing related goals include 92expanding affordable housing supply, promoting private sector engagement, and improving urban infrastructure and 93governance. These reforms have crucial effects on market dynamics and housing prices, making accurate predictive 94modeling essential for policy and investment decisions. 95In Riyadh, the capital of Saudi Arabia, rapid population growth, extensive infrastructure development, and shifting 96housing preferences have resulted in a highly segmented real estate market. The Kingdom's Vision 2030 initiative has 97further intensified housing market dynamics by encouraging private sector participation, modern urban planning, and 98enhanced home ownership [3]. Understanding price formation in such a rapidly evolving environment requires models 99that can handle nonlinearity, spatial diversity, and heterogeneous consumer preferences. The hedonic pricing method 100is a commonly used approach to estimate property values by decomposing price into the implicit value of its 101characteristics [4,5]. These characteristics are typically grouped into structural (e.g., size, age), locational (e.g., 102proximity to metro stations, CBDs), and environmental (e.g., views, air quality) factors. However, one challenge with 103hedonic regression lies in its reliance on linear or semi-log functional forms and pre-specified relationships between 104variables and price [2,6]. In practice, the relationship between housing features and value is often nonlinear and context 105dependent, particularly in complex urban markets like Riyadh. Several efforts have been made to address this limitation 106using advanced statistical techniques such as Box-Cox transformations and geographically weighted regression or 107semi-parametric models [7,8]. More recently, machine learning methods particularly artificial neural networks (ANN) 108and Random Forest (RF) have been deployed in real estate modeling for their ability to handle high dimensional 109nonlinear relationships without strict assumptions on functional form [9,10,11]. To address these challenges, this study 110compares conventional hedonic regression models against modern machine learning approaches Artificial Neural 111Networks (ANN) and Random Forests (RF) for price prediction of residential properties in Riyadh. Using a dataset of 1122,997 residential units collected in Q3 2024 from a widely used real estate platform (Aqar), we apply cross-validation 113to optimize model parameters and assess performance using metrics such as Root Mean Square Error (RMSE), Mean 114Absolute Error (MAE), and R-squared. By focusing on a localized dataset and comparing traditional and machine 115learning techniques. This study aims to provide actionable insights for urban economists, housing policymakers, and 116private sector developers in Saudi Arabia. The study aims to compare the predictive performance of hedonic regression, 117ANN, and RF for housing price prediction in Riyadh, providing insights for urban planners and policymakers under 118Vision 2030. The study was conducted using data collected from Riyadh, Saudi Arabia, in the third quarter of 2024. 1191.1. Housing development and data issues 120Cities have quite different housing markets in terms of pricing and geography. For instance, studies conducted in 121Western cities have demonstrated a pronounced pattern of segmentation brought about by economic and racial 122exclusion [12]. Apart from the ethical and political implications of these developments, a single property's value is 123constantly influenced by environmental, structural, and locational factors in its surrounding community [4]. While the 124adage "location, location, location" is crucial for assessing investment possibilities in the housing market [13], 125environmental and locational factors (such as the distance to the central business district [14] are sometimes more 126challenging to measure. 127These foundational insights demonstrate the multifaceted influences shaping housing markets and underscore the 128critical role of location and urban amenities in determining property prices worldwide. However, contrasting dynamics 129emerge when we examine markets in different cultural and regional contexts. 130Riyadh and other Saudi Arabian cities have their own sets of housing markets, more so depending on the area 131within that city and price range; the differences in these markets emanate from the peculiar cultural, economic, and 132social dynamics of the Kingdom. While Western cities may have housing market segmentation based on racial 133segregation and economic exclusion, in Saudi Arabia, the housing market characteristics are heavily based on the 134proximity to religious, commercial, and urban amenities. For example, the value of the property is highly affected by 135its closeness to areas such as mosques, shopping centers, and planned transport facilities. 136Such localized factors, unique to Riyadh, influence spatial urban patterns and real estate valuation distinctly, 137highlighting the need for models sensitive to these socio-cultural and infrastructural determinants. 138In Saudi Arabia, since the introduction of Vision 2030, several governmental reforms have been undertaken to 139tackle the housing problems, and a transition from a government allocated housing system to market forces has been 140provided. Given the Sakani programs, the opportunities for home ownership have opened for its citizens, thus changing 141the dimensions of urban housing. Housing in Saudi Arabia was once characterized by traditional neighborhoods where 142families lived close to essential services, like schools, retail outlets, and healthcare facilities. Development dependent 143144145===== PAGE 5 (score 25, numeric-paren 4, table-words 3, var-words 15) =====14614730 148 149 150 151 152 153price model, every feature of nonhomogeneous items offers a distinct profit or level of usefulness. The fair and realistic 154pricing of an item in its market is often ascertained using this approach. This strategy is based on the consumer theory 155that Lancaster [15] established, and Rosen [5] expanded to the real estate industry. The multiple regression model and 156the hedonic method serve the same functions. Regression analysis may make use of the hedonic idea. The price of a 157property is the dependent variable, while its qualities are the independent variable. In real estate and related markets, 158including the valuation of any item, regression analysis is referred to as the hedonic pricing model [20]. The hedonic 159analysis focuses on the relationship between a product's attributes and its price. Residential properties are rented or 160purchased because they provide utility or satisfaction from the amenities they have. Each home, whether it is an 161apartment, duplex, or house, has its features that affect its desirability. Structural attributes (land size, interior square 162footage, age of the building, layout of rooms, and additional facilities such as garages or air conditioning) are defined 163as structural. Locational aspects such as proximity to employment centers, retail stores, and recreational venues affect 164property values intrinsically. Environment and sociodemographic factors impact values because, through these two, 165the desirability of a neighborhood is defined. Similar forces affect how willing people are to pay for their housing unit. 166The most basic goal of hedonic analysis within real estate is essentially to quantify the relationship of structural and 167locational attributes to property prices. Observable, measurable items number of bedrooms, distance to school is 168certainly there, but not every factor observable through the lens is directly linked with price determination in the market. 169Through dynamics of supply and demand, the prices in the housing market act in their unique way, whereby their action 170on each unit depends upon a particular type of attribute and a more general market behavior, and therefore, the price 171of a housing unit is unique. Hedonic analysis aims to estimate the hedonic function, according to which each input 172attribute would set the market price. The hedonic analysis assumes that each characteristic of a property has its market, 173conditional on its supply and demand. Thus, every characteristic has its "hedonic price," which informs how much it 174contributes value to the property. Understanding this function is significant for three important reasons: 175Property valuation: It facilitates the determination of the market price of a housing unit based on the attributes of 176that unit, thus contributing significantly to decisions in real estate appraisals and investment decisions. 177Housing price indexing: Cost of living comparisons between regions are possible through price indices of constant 178quality. For instance, comparisons of housing prices in Riyadh and Jeddah will demand adjusting for differences across 179properties. 180Policy analysis: Hedonic models provide a means to value certain implicit benefits from specific attributes, such 181as air quality, which improves insight into the social costs and benefits of environmental and infrastructural policies. 182By using hedonic analysis, the construction of house price indices, which allow analysis for changes in market 183conditions while removing effects due to particular property attributes, is possible. In this study, hedonic regression is 184applied to estimate the implicit prices of housing attributes in Riyadh, identifying how structural and locational factors 185influence property values. To conduct the analysis, categorical variables were transformed into numerical variables, 186including Building Type (e.g., apartment, villa) and Location (North, South, West, East, Central Riyadh). In the hedonic 187regression analysis, dummy variable coding was employed, wherein East Riyadh served as the reference category for 188Location, while for Building Type, villas were set as the reference category. All categorical variables were one-hot 189encoded for binary input to the ANN, thereby ensuring compatibility with the input layer of the neural network. A 190product is sold as a collection of characteristics, which may be expressed in a matrix f(x1, x2, x3, … , xn) [34]. This is 191the basic tenet of the hedonic pricing model. As a result, the product's market price may be represented as a function 192of these attributes, or 𝑦= 𝑓(𝑥1, 𝑥2, 𝑥3, … , 𝑥𝑛). Equation (1) illustrates the hedonic pricing model's generic form: 193y = α + β𝐗 + e, 194(2.1) 195where y is the price vector, e is the random error vector, α, β are the coefficient vectors, and X is the matrix of 196independent variables. Scholars have observed that heteroscedasticity can arise from a skewed distribution of both Y 197and xn [30, 33]. Therefore, as the model was being implemented, we used the semi-log model.: 198𝑉𝐴𝐿𝑈𝐸 = 𝑒𝑥𝛽𝜀. 199(2.2) 200Thus 201 𝑙𝑛𝑉𝐴𝐿𝑈𝐸= 𝑥𝛽+ 𝜀. 202(2.3) 203 204In this case, the log of an item’s expected price is the sum of its characteristics X times 𝛃, and the marginal price 205of each attribute x is: 206𝑃𝑅𝐼𝐶𝐸 (𝒙) = 𝑒𝑥𝑏. 207(2.4) 208 209Where x is the current level of the characteristic and b is the regression coefficient. The marginal effect of an 210attribute in a semi-log model can be approximated as (𝑒𝑏−1 ) × 100%, representing the percentage change in price 211associated with a one-unit change in the characteristic. Notice that the semi-log form implies that the price of a given 212213214===== PAGE 6 (score 12, numeric-paren 3, table-words 2, var-words 5) =====21521631 217 218 219 220 221 222characteristic varies with its level, i.e., the prices are nonlinear. Compared to its linear version, the semi-log structural 223hedonic pricing model offers several benefits. It allows the value of one feature (like the number of bathrooms) to 224change proportionally with the value of other qualities (like the number of beds), which is its main advantage. A second 225bathroom offers the same value to a one-bedroom home as it does to a five-bedroom home, but this is not the case with 226a linear model. Also, given the skewed nature of housing prices, we apply a semi-log transformation to stabilize 227variance and improve interpretability. 2282.2.ANN methodology 229The computational and nonlinear statistical modeling technique known as ANN is based on human biological 230neurons [45,46]. Aerospace, automotive, banking, defense, electronics, entertainment, finance, insurance, 231manufacturing, medical, oil & gas, robots, speech, securities, telecommunications, and transportation are just a few of 232the industries that have made extensive use of it. In the context of regression, ANN may also produce precise 233predictions. One may think of it as a nonlinear regression technique [5]. Numerous sub-components, including weights, 234nodes, layers, and activation functions, make up a neural network structure. The input layer, which contains the values 235of the independent variables, the hidden layer, which has a specific number of processing units and nodes, and the 236output layer, which provides the estimated values of the dependent variable, are the three primary layers. Typically, 237weights are selected at random from a distribution of values within a predetermined range, such as [-1,1]. Utilizing 238total net, which is defined as the sum of weighted inputs and bias values, the last component, the activation function, 239generates values. There are connections between each of these elements. Similar to traditional regression models, it 240uses the same independent variables as inputs and the dependent variable as an output. 241 242Figure 1: A sample structure of a multilayer neural network 243To minimize the discrepancy between estimated and real dependent values, ANN essentially learns by analyzing 244the dataset itself and updating weights. Figure 1 illustrates a multilayer perception with one hidden layer, depicting the 245connections between input, hidden, and output layers. The input-hidden layer connection may be stated as follows and 246represented in linear form: 247ht(X) = g (W0 + ∑Xi Wit248P249i=1250), 251(2.5) 252 253where g(.) is the sigmoid activation function, 254𝑔 ( 𝑧 ) =25512561 + 𝑒−𝑧. 257(2.6) 258The weight by 𝑤𝑖𝑡, and the bias value between each variable and the associated hidden node (t) by W0. This value, 259ℎ𝑡(𝑋), is only the result of the hidden node t. The result value may be similarly described as a linear combination of 260these nodes after the number of hidden nodes in the hidden layer has been determined [46]: 261f(X) = η0 + ∑ηt ht262M263t=1264. 265(2.7) 266In this case, the estimated result values are represented by 𝑓(𝑥). The sum of the squared residuals is minimized or 267reduced by updating the parameters of an ANN model. Several learning algorithms, including the popular 268backpropagation method put out by Kim and Nelson, are employed to carry out this updating process. Note that 269reaching the global optimal solution is not guaranteed [47]. In this study, ANN is used to complement hedonic 270regression by capturing nonlinear relationships and interactions between housing attributes in Riyadh. The ANN model 271employs a multilayer perceptron with one or two hidden layers, where the number of nodes per layer was optimized 272273274===== PAGE 7 (score 16, numeric-paren 1, table-words 2, var-words 10) =====27527632 277 278 279 280 281 282through 5-fold cross-validation. A sigmoid activation function is applied, and the model is trained using 283backpropagation with a learning rate of 0.01 for 500 epochs. Regularization techniques, including L2 regularization (λ 284= 0.01) and 20% dropout, were applied to the hidden layers to mitigate overfitting. Early stopping was implemented 285after 10 epochs without improvement in validation loss. Optimization of ANN architecture was carried out using 5 286folds of cross-validation applied to a grid of one or two hidden layers with node counts {5, 10, 15, 20}. The smallest 287RMSE (0.2581) on the validation set was obtained with one hidden layer with 5 nodes and the second with 15 nodes. 288Alternative deeper architectures (ex., 3 layers) increased the complexity in computations (training time escalated from 2892.3 to 4.1 min) but did little to enhance accuracy (RMSE=0.2592). To minimize the overfitting issue, L2 regularization 290(λ = 0.01) and 20% dropout rates have been used on hidden layers. From sensitivity tests with λ = {0.001, 0.1}, the 291decrease in RMSE was minimal (<0.002), while increasing dropout to 30% raised test RMSE to 0.2051. Hence, 20% 292became the optimal dropout rate. Early stoppage occurred after 10 epochs, where validation loss ceased to improve. 293This brought a gap in train and test R² that were previously 0.015 apart to just 0.0074. 2942.3.RF methodology 295A Random Forest is defined formally as follows: it is a classifier consisting of a collection of tree structured 296classifiers {hk(x, Tk)}, k = 1, 2, . . . , L, Where Tk are independent identically distributed random samples, and each tree 297casts a unit vote for the most popular class at input x. As mentioned, RF employs the same method of bagging to 298produce random samples of training sets (bootstrap samples) for each random tree. Each new training set is built, with 299replacement, from the original training set. Thus, the tree is built using the new subset and a random attribute selection. 300The best split on the random attributes selected is used to split the node. The trees grown are not pruned. The use of 301the bagging method is justified for two reasons [47]: the use of bagging seems to enhance performance when random 302attributes are used; and bagging can be used to give ongoing estimates of the generalization error of the combined 303ensemble of trees, as well as estimates for strength and correlation. These estimates are performed out-of-bag. In a 304Random Forest, the out-of-bag method works as follows: given a specific training set T, generate bootstrap training 305sets Tk, construct classifiers {hk(x, Tk)} and let them vote to create the bagged classifier. For each (x, y) in the training 306set, aggregate the votes only over those classifiers for which Tk does not contain (x, y). This is the out-of-bag classifier. 307Then the out-of-bag estimate for the generalization error is the error rate of the out-of-bag classifier on the training set. 308The error of a forest depends on the strength of the individual trees in the forest and the correlation between any two 309trees in the forest. Strength can be interpreted as a measure of performance for each tree. Increasing the correlation 310increases the forest error rate, and increasing the strength of the individual trees decreases the forest error rate since a 311tree with a low error rate is a strong classifier. Reducing the number of random attributes selected reduces both the 312correlation and the strength [48]. The RF model used 500 trees having max depth=10, min samples split=5, min samples 313leaf=3 selected using the grid search over {100, 300, 500} trees and depth {5, 10, 15}. This setup was a tradeoff sweet 314in terms of accuracy (test RMSE = 0.1911) and overfitting (test-train RMSE gap = 0.0334 vs. 0.0451 for depth=15). 315ANN and RF techniques are selected among other models of Machine Learning for their capability of forecasting the 316nonlinear relationships and complex interactions due to the Vision 2030 project housing factors, which would include 317behavioral factors that influence the housing market of Riyadh. Unlike linear methods such as Lasso Regression, or 318simpler machine learning methods such as k-NN, ANN constructs feature hierarchies through the neural network 319multilayer perceptron and the RF, which is composed of 500 decision trees that smoothen the nonlinear thresholds 320using heterogeneous records (e.g., Size: 56-930 m²). These two have good robustness against mixed attribute datasets, 321but not SVM, which has multiple kernel tuning requirements. Their established effectiveness in real estate [11] and 322balance of predictive power (RF: test R² = 0.9065) with interpretability (RF feature importance) align with the study's 323benchmark goal using hedonic regression against Machine Learning (ML). Also, do not require much of the resource 324intensive alternatives (for example, deep learning), making them a perfect fit for this analysis. 3252.4.Case study and data 326The very highly renowned Riyadh, the capital city of Saudi Arabia, has long been recognized as the cultural, 327financial, and political hub of the country. The capital city has a population greater than 7 million people and is 328surrounded by the King Khalid Road, which outlines an urban area of about 1,500 square kilometers. Areas beyond 329this road were not included in the research as they are largely peripheral with limited support for urban functions. The 330main data has been retrieved from a well-known real estate website, Aqar (https://sa.aqar.fm/), during the third quarter 331of 2024 and georeferenced by property addresses. We collected 2,997 units and 12 variables, which are given with 332some descriptive statistics in Table 1. The dependent variable is listing price rather than transaction price, as actual 333transaction data are not publicly available in Saudi Arabia. Listing prices reflect seller expectations but remain highly 334correlated with transaction prices in this market, as noted in prior empirical work. The dataset belongs to five districts, 335including the North, South, West, East, and Center of Riyadh. The variables used are Building Type, Bedroom, Living 336Room, Bathroom, Kitchen, Size, Street Width, Floor, Age, Entrance Number, Elevator, and Location. The 2,997 units 337338339===== PAGE 8 (score 36, numeric-paren 0, table-words 9, var-words 16) =====34034133 342 343 344 345 346 347represent all available residential listings within Riyadh’s urban boundaries during the data collection period, with only 348properties having complete data for all 12 variables included. The variable “Location” is operationalized as a dummy 349variable for each of the five districts to account for spatial price variations. Key variables include Building Type 350(categorical, e.g., apartment, villa), Size (continuous, square meters), and Age (continuous, years), each expected to 351influence property prices based on their contribution to utility or desirability. 352While actual transaction prices are preferable, they remain inaccessible in Saudi Arabia due to privacy regulations 353and limited public disclosure requirements. We rely on listing prices, which represent seller expectations and are 354publicly available through the Aqar platform. Research from comparable emerging markets suggests listing prices are 355highly correlated with transaction prices, particularly in regulated markets with standardized listing practices. In Saudi 356Arabia's context, the Aqar platform is the most widely used real estate marketplace, and listings undergo verification 357processes that reduce the likelihood of inflated expectations. Moreover, Vision 2030 initiatives have introduced greater 358transparency in the housing sector, narrowing the gap between listing and final transaction prices. 359 3603. Results and findings 3613.1.Data set and preprocessing 362The issue of multicollinearity is significant due to the reference to near-linear dependences among 363independent variables. According to Montgomery [49], the presence of multicollinearity can result in unstable 364regression coefficients with high variances/covariances and absolute values. The condition index and variance 365inflation factor are used to assess the presence or absence of multicollinearity. The thresholds are set at 10 for 366the Variance Inflation Factor (VIF). These criteria show that there is no multicollinearity between independent 367variables. The outcome is shown in the hedonic result table. The dataset has been split into train and test data. 368Between them, with 70% for training and 30% for testing, respectively. Training data was used to fit the models, 369while testing data was used to evaluate them. RMSE, R-squared, and MAE have been computed and provided 370as performance metrics. The outcomes of hedonic regression analysis and artificial neural networks have been 371analyzed using Python 3.12 software. Which are presented in Table 1. 372Table 1: Descriptive Statistics of Property Characteristics. 373Variable 374Min 375Max 376Mean 377Std. Deviation 378Bedrooms 3791 38026 3814.19 3821.78 383Living Rooms 3841 3856 3861.50 3870.82 388Bathrooms 3891 3908 3913.32 3921.11 393Kitchens 3941 3956 3961.04 3970.29 398Size (m²) 39956 400930 401199.44 402114.05 403Floor Number 4040 40510 4061.57 4070.88 408Age (years) 4090 41020 4112.48 4123.99 413Number of Entrances 4141 4152 4161.02 4170.32 418 419In Table 1, the dataset's descriptive statistics are compiled. The figures show that most of the residences are 420apartments, which are typically smaller than villas and feature fewer bedrooms, living rooms, and bathrooms. 421Typically, apartments are 152.74 square feet in size, with 1–7 bedrooms, 1-3 living spaces, and 1–5 baths. On 422the other hand, villas are more expensive and diverse, with an average size of 347.13 square units, ranging from 4232 to 26 bedrooms, 1-6 living rooms, and 1 to 8 bathrooms. The average size of a property is 199.44 square units, 424with 4.19 bedrooms, 1.50 living rooms, and 3.32 bathrooms, according to the total figures. 425The dataset underwent rigorous quality control during data collection from the Aqar platform. Only 426properties with complete information for all 12 variables were included in the analysis, resulting in the final 427sample of 2,997 residential units. Properties with missing values in any field were excluded during the initial 428data cleaning phase. 429Regarding outliers, descriptive statistics reveal property sizes ranging from 56 to 930 square meters, which 430represent legitimate market variations rather than data errors. The semi-log transformation applied to the 431dependent variable (housing prices) helped stabilize variance and mitigate the influence of extreme values 432without requiring arbitrary outlier removal. Additionally, the Variance Inflation Factor (VIF) analysis confirmed 433no multicollinearity issues (all VIF values below 4), and the Breusch-Pagan test (p = 0.13) confirmed 434homoscedasticity, indicating that the data structure was appropriate for modeling 435 4363.2.Hedonic Regression Results 437The hedonic regression results are given in Table 2. Which includes the hedonic coefficient, standard error, 438439440===== PAGE 9 (score 35, numeric-paren 1, table-words 5, var-words 12) =====44144234 443 444 445 446 447 448t-statistics, P-value, and VIF calculated below. 449 450Table 2: Hedonic regression model result. 451 452B 453Std. Error 454t 455Sig. 456Tolerance 457VIF 458Building Type 459-0.473 4600.022 461-21.673 4620.000 4630.275 4643.642 465Bed Room 4660.012 4670.004 4682.837 4690.005 4700.447 4712.24 472Living Room 4730.045 4740.008 4755.349 4760.000 4770.491 4782.036 479Bathroom 4800.03 4810.006 4825.007 4830.000 4840.533 4851.877 486Kitchen 487-0.005 4880.019 489-0.259 4900.795 4910.751 4921.331 493Size 4940.002 4950 49627.336 4970.000 4980.36 4992.775 500Street Wide 5010.001 5020.001 5031.468 5040.142 5050.821 5061.217 507Floor 508-0.022 5090.006 510-3.599 5110.000 5120.815 5131.228 514Age 515-0.007 5160.001 517-5.051 5180.000 5190.842 5201.188 521Entrance Number 5220.047 5230.016 5242.972 5250.003 5260.942 5271.062 528Elevator 5290.065 5300.011 5315.861 5320.000 5330.796 5341.256 535North of Riyadh 5360.333 5370.013 53824.641 5390.000 5400.653 5411.532 542South of Riyadh 543-0.686 5440.016 545-41.622 5460.000 5470.747 5481.338 549West of Riyadh 550-0.298 5510.013 552-22.715 5530.000 5540.684 5551.462 556Central Riyadh 557-0.169 5580.045 559-3.797 5600.000 5610.938 5621.066 563(Constant) 56414.211 5650.06 566238.054 5670.000 568 569 570F (P-Value) 571840.452 572(0.000) 573 574 575 576 577 578Categorical variables of hedonic regression results indicate a few key trends in the housing market of Riyadh. 579Deciding on physical characteristics and types of buildings is important, with apartments showing very low 580prices compared to villas (-0.473; p < 0.001). The number of bedrooms shows a mild positive effect on house 581prices, with each bedroom adding 1.2% to the price (p = 0.005). Where living spaces are concerned, the effect 582is larger, with each additional living space contributing 4.5% (p < 0.001) to the house price. Bathrooms are also 583positively affecting pricing; an additional bathroom will increase the value by 3% (p <0.001). Interestingly, 584despite its practical significance, the number of kitchens had an insignificant effect on pricing (p = 0.795). This 585may be because of the dataset's low variance (mean = 1.04, SD = 0.29) or Riyadh culture's preference for other 586features, such as location or size, over more kitchens. A more positive coefficient for property size is determined 587at least from the numerical values as one of significance (0.002, p < 0.001) - thus, higher prices are commanded 588for bigger properties. Street width has a positive trend but is statistically insignificant (p=0.142). Higher units 589would be less well priced, as their floor level adversely affects the price (-0.022, p < 0.001). Conversely, older 590units will expect a lower price because of the same negative parameter of the age (-0.007, p < 0.001) of the 591building. The number of entrances influences a positive price valuation on properties (0.047, p = 0.003), with 592the presence of an elevator increasing property values by 6.5% (p < 0.001). The location is thus a significant 593price driving factor for housing in Riyadh, with substantial distances between neighborhoods and East Riyadh 594(reference category). The properties in North Riyadh command a hefty premium, being priced 33.3% higher than 595East Riyadh (p <0.001). On the other hand, South Riyadh has the most negative effect, with the pricing 68.6% 596lower than the reference area (p < 0.001). Properties in West Riyadh are priced 29.8% lower (p <0.001), while 597Central Riyadh prices are 16.9% lower (p <0.001) in comparison with East Riyadh. Diagnostic tests for the 598model yielded strong results, with VIF values for all low predictor variables being below 4, implying that serious 599multicollinearity can be ruled out, while significance levels for most variables indicate the robustness of the 600model in explaining price variation in the Riyadh housing market. A Breusch-Pagan test (p = 0.13) confirmed 601no significant heteroscedasticity. VIF ranged from 1.062 to 3.642, with a condition index of 8.2, ruling out 602multicollinearity (Montgomery et al., 2012). The regression model demonstrates strong statistical significance, 603with an F-statistic of 840.452 (p < 0.001), indicating that the predictors collectively explain a significant portion 604of the dependent variable's variance. Due to the absence of precise geographic coordinates (latitude and 605longitude) in the dataset, it was not possible to conduct explicit spatial autocorrelation tests such as Moran’s I. 606Therefore, the study incorporates location dummy variables at the district level to partially account for spatial 607608609===== PAGE 10 (score 26, numeric-paren 4, table-words 10, var-words 1) =====61061135 612 613 614 615 616 617dependencies. This limitation suggests caution in interpreting results near district boundaries, where unmodeled 618spatial interactions may persist [22]. This constraint advises using caution when interpreting findings close to 619district boundaries, where unmodeled spatial effects may persist. To partially account for spatial heterogeneity, 620we employed district-level dummy variables (North, South, East, West, and Central Riyadh) in all three models. 621This approach captures broad locational premiums/discounts but has limitations at district boundaries where 622properties may share similar spatial characteristics despite being assigned to different administrative zones. 623 624 625Figure 2: Observed and predicted house prices by hedonic regression 626 627Figure 2 Observed vs. Predicted House Prices by Hedonic Regression. The plot shows a strong linear 628relationship, with predictions closely aligning with actual prices. However, there is a clear underestimation of 629larger price points, suggesting that the model's effective pricing struggles with nonlinear in the Riyadh housing 630market. Strong linearity can be seen in the plot, which indicates a broad capture of price trends by the hedonic 631regression model. However, there is a clear underestimation of larger price points, suggesting that the model's 632effective pricing is nonlinear in the Riyadh housing market. 633 634 635Table 3: Comparison of training & testing results 636 637Splitting Ratio 638N 639R-squared 640RMSE 641MAE 642Training Results 64370% 6442097 6450.8178 6460.2668 6470.1969 648Testing Results 64930% 650900 6510.8034 6520.2673 6530.1970 654 655The hedonic regression model is performant and stable, exhibiting this quality in both the training and testing 656datasets. The model was developed from a 70-30 split of data, with 2,097 observations in the training set and 657900 observations in the testing set, thus giving a respectable number of observations for analysis. The 658measurement metrics shown in Table 3 also support the model's prediction ability. RMSE shows good agreement 659on both training (0.2668) and testing (0.2673) datasets, while the MAE remains stable across training (0.1969) 660and testing (0.1970) phases. The near-match of the error statistics between training and testing indicates that the 661model generalized well, without overfitting, making it a reliable tool for price prediction. Regarding R-squared, 662there are little decrease values for the model when measured on the testing set (with R-squared moving from 6630.8178 to 0.8034), indicating that the model's power didn’t have a significant decrease when confronted with 664new observations property which is highly desirable in any real estate valuation model. 6653.3.ANN results 666In this study, it must be researched how to tune the number of hidden layers and the number of nodes in each 667layer. The cross-validation process has been performed to determine them effectively. One or two hidden layer 668options have been considered. The number of nodes for each of the hidden layers is {5,10,15,20}. The literature 669has described several activation functions. The sigmoid activation function is the most commonly used one and 670is used in the present study as well. RMSE, R-squared, and MAE performance measures for each combination: 671one hidden layer or two hidden layers, four possible hidden layer node numbers based on training and testing 672673674===== PAGE 11 (score 29, numeric-paren 0, table-words 10, var-words 3) =====67567636 677 678 679 680 681 682data sets. By these criteria, the best configuration was found using a sigmoid activation function, hidden nodes. 683The five and fifteen hidden nodes are hidden layer 1 and hidden layer 2, respectively. The lowest testing RMSE 684value was calculated using this configuration. The output is given in Table 5 for each combination. The model 685has been fitted using these options against the entire training data set. Testing results were thus achieved via this 686model using the testing dataset. To mitigate overfitting in the ANN model, we implemented L2 regularization 687(λ = 0.01) and applied a dropout rate of 20% in the hidden layers. Additionally, early stopping was used to halt 688training when validation loss did not improve for 10 consecutive epochs. Predictive neural network architectures 689for house price prediction analyses have been concluded to unveil fascinating structures in various 690configurations. The results comprise arguments around combinations of hidden layers and node configurations 691short among one-layer and two-layer networks that each have sigmoid function activation. Performance metrics 692RMSE, R-squared, and MAE illustrate noticeable variations across different architectures. As shown in Table 4, 693layer 1 is for single layer configurations, in which case 20 hidden nodes in its architecture gave the best 694performance compared to others in a one-layer fashion with an RMSE of 0.260158562 and R-squared of 6950.826944395, and an MAE of 0.193798218. Presumably, investigation indicates that increasing the number of 696nodes in a single layer generally improves model performance to a certain limit. Layer 2 is for two-layer 697configurations; optimal performance was obtained with the first hidden layer, having 20 nodes, and the second 698hidden layer with 5 nodes. Results were the best overall: RMSE of 0.258084424, R-squared of 0.829692798, 699and MAE of 0.190277261, making it the strongest performance among all applications. There are ranges of 700improvements over single-layer architectures; differences are small, and hence they indicate that using a second 701layer with a proper configuration of nodes may enhance the model's capability of prediction. Interestingly, more 702nodes in the second layer did not always lead to better performance, as found by the fact that larger second-layer 703configurations had slightly worse performance for single-layer architectures. This suggests that a more compact 704second layer might be better at capturing the underlying patterns in housing prices without overfitting. All 705configurations have high R-squared values (consistently above 0.82); hence, both single- and two-layer 706architectures explain a considerable portion of the variance in housing prices, while the two-layer structure is 707slightly ahead in terms of predictive accuracy, see Table 4. 708 709Table 4: ANN results 710Layer 711Act. Function 712#Hidden 713Nodes 1 714#Hidden 715Nodes 2 716RMSE 717R-squared 718MAE 719 720 7215 722- 7230.261197515 7240.825559427 7250.192662644 7261 727sigmoid 72810 729- 7300.260923272 7310.825925541 7320.191840764 733 734 73515 736- 7370.263006816 7380.823134376 7390.194910972 740 741 74220 743- 7440.260158562 7450.826944395 7460.193798218 747 748 749 7505 7510.266138597 7520.818897206 7530.199709806 754 755 7565 75710 7580.265614815 7590.819609354 7600.196885088 761 762 763 76415 7650.265299801 7660.82003698 7670.19616688 768 769 770 77120 7720.261160046 7730.825609471 7740.192564723 775 776 777 7785 7790.264051023 7800.821727181 7810.196315661 782 783 78410 78510 7860.262675799 7870.823579297 7880.194912253 789 790 791 79215 7930.260063996 7940.827070181 7950.192583763 7962 797sigmoid 798 79920 8000.26194096 8010.824564996 8020.192689893 803 804 805 8065 8070.259715786 8080.827532956 8090.193317165 810 811 81215 81310 8140.258833053 8150.828703341 8160.19196207 817 818 819 82015 8210.258158948 8220.82959443 8230.190836668 824 825 826 82720 8280.264755273 8290.820774971 8300.197949421 831 832 833 8345 8350.258084424 8360.829692798 8370.190277261 838 839 84020 84110 8420.261053266 8430.825752046 8440.193597329 845 846 847 84815 8490.261140706 8500.825635298 8510.195061518 852 853 854 85520 8560.263808809 8570.82205409 8580.195502868 859 860The neural network model demonstrated exceptional performance with extraordinary levels of predictive 861power for both training and testing datasets. The model was trained with 2,097 observations, while 900 862863864===== PAGE 12 (score 21, numeric-paren 0, table-words 8, var-words 3) =====86586637 867 868 869 870 871 872observations were subjected to testing, using a 70%-30% split ratio, allowing for evaluation on more solid 873ground. From the training, the model's performance shows that the R-squared value was 0.9042. In effect, it 874explains 90.4% of the variance in housing prices in the training data. Together with this finding are very low 875error measures of RMSE: 0.1546 and MAE: 0.111, thereby confirming a high degree of accuracy for the 876predicted value during training, see Table 5. 877 878Table 5: Multilayer perceptron results 879 880Splitting Ratio 881N 882R-squared 883RMSE 884MAE 885Training Results 88670% 8872097 8880.9042 8890.1546 8900.1111 891Testing Results 89230% 893900 8940.8968 8950.2008 8960.1450 897 898Some potential decrease in performance was anticipated when the model was applied to the testing dataset; 899however, its performance remains strong. The testing R-squared of 0.8968 states that the model explains almost 90090% of the price variance in the unseen data. There is a moderate increase in error metrics during the testing 901phase, with RMSE currently at 0.2008 and MAE at 0.1450. Therefore, the variances in training and testing 902metrics indicate some given degree of overfitting, but otherwise, the model is successful in its predictive power 903applied to new data. The relatively small gap difference between training and testing performance indicates that 904the model has reached a good trade-off between fitting the training data while generalizing to new observations, 905thereby qualifying as a trustworthy housing price prediction tool. Regularization and early stopping help to offset 906the small overfitting shown by the train-test R2 gap (0.9042 vs. 0.8968), guaranteeing robust generalization. To 907minimize the overfitting issue, L2 regularization (λ = 0.01) and 20% dropout rates have been used on hidden 908layers. From sensitivity tests with λ = {0.001, 0.1}, the decrease in RMSE was minimal (<0.002), while 909increasing dropout to 30% raised test RMSE to 0.2051. Hence, 20% became the optimal dropout rate. Early 910stoppage occurred after 10 epochs, where validation loss ceased to improve. This brought the train and test R² 911that were previously 0.015 apart to just 0.0074. 912 913Figure 3. Observed and predicted house prices by multilayer perceptron. 914 915Figure 3 Compared with hedonic regression, ANN predictions come much closer to the actual, particularly 916in terms of midrange and higher properties. 9173.4.RF Result 918This machine learning method, which is very popular in the applications of ensemble learning, was used to 919fit the data for non-linear capture or non-linear relationships present in the real estate price data. It uses 500 920decision trees to construct an ensemble of trees, with each tree built differently through controlled complexity 921parameters (max depth=10, min samples split=5, min samples leaf=3) to avoid overfitting while still retaining 922the model's prediction power. The model was trained on 70% of the standardized dataset, of which the remaining 92330% was left for validation purposes. Random Forests would also be a better investment for real estate valuation 924because the complex interactions that take place with property and characteristics can be modeled without the 925926927===== PAGE 13 (score 30, numeric-paren 5, table-words 8, var-words 6) =====92892938 930 931 932 933 934 935need for explicit specification. This was unlike traditional hedonic pricing models: the Random Forests method 936for threshold effects and segmentation patterns in the housing market, with certain features bearing different 937impacts at different price points. The built-in feature importance mechanism in the model gives insights into 938which factors cause the highest variations in property values, reinforcing an alternative to the coefficient-based 939way that hedonic regression explains the differences in value and Shapley Additive Explanations (SHAP) values 940from neural networks. The strong performance of the random forest model which trained as the same as Hedonic 941Regression and ANN on a 70/30 split utilizing 2,097 training samples and 900 testing samples is evident from 942R-squared values of 0.9315 (training) and 0.9065 (testing), which means that over 90% of variance in the target 943variable is explained by the model while generalizing well to new unseen observations. The RMSE (0.1577 944training, 0.1911 testing) and MAE (0.1116 training, 0.1353 testing) are low, indicating precise predictions, with 945only small increases in error on the test set, the result shown in Table 6. 946 947Table 6: Performance Metrics for Random Forest Model 948 949Splitting Ratio 950N 951R-squared 952RMSE 953MAE 954Training Results 95570% 9562097 9570.9315 9580.1577 9590.1116 960Testing Results 96130% 962900 9630.9065 9640.1911 9650.1353 966 967The feature importance scores in Table 7, generated by the random forest model, indicate that geographical 968location strongly dominates the prediction of property values in Riyadh. For example, "North of Riyadh" has an 969importance score of 0.768659, substantially higher than other features. This dominance implies that location 970variables heavily influence the model predictions, potentially overshadowing other structural and attribute 971variables, which should be considered when interpreting the model's robustness. 972 973Table 7: Feature importance by random forest 974 975Feature 976Importance 97711 978North of Riyadh 9790.768659 98014 981West of Riyadh 9820.612986 98313 984East of Riyadh 9850.589257 98612 987South of Riyadh 9880.283161 9890 990Building Type 9910.180799 9929 993Entrance Number 9940.171134 9955 996Size 9970.127103 99815 999Central Riyadh 10000.08131 10013 1002Bathroom 10030.079826 100410 1005Elevator 10060.057982 10074 1008Kitchen 10090.049231 10102 1011Living Room 10120.044905 10138 1014Age 10150.038062 10161 1017Bed Room 10180.037562 10197 1020Floor 10210.028789 10226 1023Street Wide 10240.023201 1025 1026Conversely, "Central Riyadh" sits at the other end with a lower importance of 0.08131, further hinting that 1027it may play a less influential role in this regard. Some property-related parameters like "Building Type" 1028(0.180799), "Entrance Number" (0.171134), and "Size" (0.127103) also have a noteworthy contribution, though 1029certainly much less than location. Features such as "Bathroom," "Kitchen," "Living Room," and "Bed Room" 1030have less than this importance (from 0.079826 to 0.037562), while "Street Wide" (0.023201) and "Floor" 1031(0.028789) seem to be the most trivial. This distribution indicates that, in this model, spatial factors take 1032precedence over structural or amenity-based characteristics when it comes to influencing predictions. 1033 103410351036===== PAGE 14 (score 7, numeric-paren 5, table-words 0, var-words 2) =====1037103839 1039 1040 1041 1042 1043 1044 1045Figure 4: Observed and predicted house prices by RF. 1046 1047Figure 4 Most of the values predicted by the RF model closely match the actual housing prices, therefore, 1048evidence of predictive power in this model can be concluded. The results also portray that RF is well suited for 1049modeling nonlinear relationships and spatial effects, which are components that diminish the performance of 1050both hedonic regression and ANN. Figure 5 The SHAP value chart indicates that location related variables (for 1051example, distance from North Riyadh) top the list in affecting property prices, with property size and structural 1052attributes (such as number of entrances) also contributing, and street width and number of kitchens having 1053minimal impact. 1054 1055 1056Figure 5: SHAP plot for feature impact 1057 1058The gradient color indicates the direction of the impact, where higher values for key features lead to 1059increased property prices. The SHAP summary plot shows that location features "North of Riyadh" (0.768659) 1060and "West of Riyadh" (0.612986) had the strongest influence on house price predictions; the higher the value of 1061these features, the more value is added due to the proximity of amenities and infrastructures. "Size" (0.127103) 1062also plays an important role, whereby larger properties increase values, while features like "Kitchen" (0.049231) 1063and "Street Wide" (0.023201) remain irrelevant. The color gradient indicates non-linear effects whereby higher 1064values of key features (location, size, etc.) will induce positive price consequences, in line with what was found 1065in this study concerning location and structural attributes. 1066 106710681069===== PAGE 15 (score 38, numeric-paren 7, table-words 14, var-words 1) =====1070107140 1072 1073 1074 1075 1076 10773.5.Comparison of the methods 1078A comparison of the test performances of hedonic regression, ANNs, and RF is shown in Table 8. In terms 1079of measures of performance R-squared, (RMSE), and Mean Absolute Error (MAE) both machine learning 1080techniques generally have performance that ranks far above that of conventional hedonic regression: RF, indeed, 1081has the highest predictive capacity overall. RF achieved the greatest R-squared (0.9065), or 91% explanation of 1082variance in house prices, another side 90% and 82% for ANN and hedonic regression, respectively. And it 1083produced the minimum prediction error, according to RMSE 0.1911 (compared with 0.2008 for ANN and 0.2668 1084for hedonic regression) and MAE 0.1353 (compared with 0.1450 for ANN and 0.1969 for hedonic regression). 1085 1086Table 8: Comparison of test performance of hedonic regression, ANN, and RF 1087 1088Hedonic 1089Regression 1090ANN 1091RF 1092R-squared 10930.8034 10940.8968 10950.9065 1096RMSE 10970.2673 10980.2008 10990.1911 1100MAE 11010.1970 11020.1450 11030.1353 1104 1105Because both machine learning methods used here captured significantly non-linear relationships, they 1106excelled over ordinary hedonic regression. RF, however, on all metrics, gave marginally better performance 1107when compared to ANN. This shows that it's more efficient in modeling the complexity of Riyadh's housing 1108market compared with single tree architectures like those of ANNs, hence, it's at a little higher precision level 1109than ANNs, yet interpretable. In Table 9, a sample of 20 observations is presented of predicted house prices 1110using hedonic regression and artificial neural networks (ANN) in Riyadh, Saudi Arabia, in log form and 1111compared against the actual prices. The results show that among the three models, the RF model gave the best 1112predictive feature, whereas the ANN and Hedonic Regression models were inferior. The higher R-squared value 1113(0.9065) and lower RMSE (0.1911) and MAE (0.1353) values accounted for this and showed that RF could 1114predict house prices more accurately and reliably than others. RF gave the best performance due to its capability 1115to capture complex interactions and nonlinearities in the data. ANN is better in performance than Hedonic 1116Regression since it has an R-squared value of 0.8968, showing that it can identify nonlinear patterns, though it 1117has a higher RMSE and MAE than RF. Hedonic Regression, though the traditional method, is the most apparent 1118of the three, with an R-squared of 0.82, indicating that the model might not capture the full real estate price 1119determinant complexity. 1120 1121Table 9 above shows that among the three models, the RF model gave the best predictive feature, whereas 1122the ANN and Hedonic Regression models were inferior. The higher R-squared value (0.9065) and lower RMSE 1123(0.1911) and MAE (0.1353) values accounted for this and showed that RF could predict house prices more 1124accurately and reliably than others. RF gave the best performance due to its capability to capture complex 1125interactions and nonlinearities in the data. ANN is better in performance than Hedonic Regression since it has 1126an R-squared value of 0.8968, showing that it can identify nonlinear patterns, though it has a higher RMSE and 1127MAE than RF. Hedonic Regression, though the traditional method, is the most apparent of the three, with an R-1128squared of 0.82, indicating that the model might not capture the full real estate price determinant complexity. 1129Figure 6 brings up the fact that RF produces the best prediction as compared to ANN, while hedonic regression 1130significantly underestimates prices. This also indicates that the ML models yield better results owing to the 1131strong influence of nonlinear and spatial effects in the real estate market of Riyadh. The results demonstrate 1132ANN's effectiveness in modeling nonlinear relationships and interactions among features (e.g., Size, Location), 1133likely enhanced by cross-validation during model development. Hedonic regression, although providing a more 1134robust structure, appears less adept at sorting heterogeneous and varying high-valued properties, primarily 1135influenced by unique urban factors of Riyadh, such as congestion and access to amenities. These takeaways from 1136the choice observations reveal that ANN extended improved predictive accuracy throughout the 2,997-property 1137dataset, suggesting it could be a more effective tool for real estate valuation in this regard. 1138 1139 1140 1141 1142 1143 114411451146===== PAGE 16 (score 12, numeric-paren 0, table-words 1, var-words 2) =====1147114841 1149 1150 1151 1152 1153 1154Table 9: Predicted house prices obtained by hedonic regression, ANN, and RF 1155Cases 1156Actual Price 1157Hedonic Regression Price 1158ANN prices 1159RF 11601. 116112.67607627 116212.97913951 116314.02735233 116412.79326833 11652. 116613.44444688 116713.09504317 116813.32105923 116913.39909212 11703. 117113.50079981 117213.50260718 117313.51704311 117413.40802153 11754. 117615.36307307 117715.19602075 117814.73604679 117915.20827409 11805. 118114.15198279 118213.46822121 118313.66140079 118413.92980437 11856. 118614.25376549 118713.58558079 118814.02284718 118914.00800457 11907. 119114.45208739 119214.11736312 119314.19547176 119414.14799829 11958. 119615.36307307 119715.19602075 119814.73604679 119915.20827409 12009. 120115.52025865 120215.25070181 120314.63071537 120415.4457558 120510. 120613.01700286 120712.99152837 120813.32105923 120912.97964453 121011. 121113.54107371 121213.70104505 121313.49339771 121413.76861773 121512. 121613.57978822 121713.41867479 121813.42337124 121913.49201393 122013. 122113.59236701 122213.98696611 122313.73884885 122413.65702343 122514. 122613.61705962 122713.98896421 122813.89270578 122913.60157394 123015. 123113.67394699 123213.76853638 123313.68364811 123413.79487572 123516. 123613.68767719 123714.04977926 123814.08522486 123913.69303799 124017. 124113.76421726 124214.06136506 124313.92757988 124414.05108602 124518. 124613.81551056 124713.96331322 124813.845191 124913.84581778 125019. 125113.99783211 125214.06805398 125313.95209458 125414.00282764 125520. 125614.07787482 125713.65837871 125813.90108395 125913.84240501 1260 1261 1262 1263Figure 6: Actual and predicted prices by hedonic regression, ANN, and RF 1264Figure 6 reveals distinct prediction patterns across models. Hedonic regression systematically 1265underestimates high-value properties, with predictions deviating up to 15-20% below actual prices for properties 1266exceeding SAR 3,000,000. This pattern suggests the linear functional form fails to capture exponential price 1267premiums associated with luxury features and prime North Riyadh locations. 1268ANN predictions show improved performance in the mid-range, reducing underestimation to 8-12%, but 1269still exhibit scatter for properties above SAR 4,000,000 (log price ~15.2). This indicates the neural network 1270captures some nonlinear relationships but may require deeper architectures or additional training for ultra-high-1271value properties. 1272RF demonstrates superior performance across the entire price spectrum, with minimal deviation even for 1273properties exceeding SAR 5,000,000 (log price ~15.4). The ensemble approach effectively models the complex 1274interactions between location (particularly North Riyadh premium), property size, and luxury features that 1275