# RECORD c30509d1b7dff13ef9c6d68570be3618b239e0cd # TITLE: An Assessment Methodology for the Evaluation of the Impacts of the COVID-19 Pandemic on the Italian Housing Market Demand # YEAR: 2021.0 VENUE: Buildings DOI: 10.3390/buildings11120592 # AUTHORS: F. Tajani; F. Di Liddo; M. Guarini; Rossana Ranieri; D. Anelli # PAGES: 28 CANDIDATE TABLE PAGES (1-based): [6, 14, 16, 17] # ABSTRACT: Due to the forced changes that the COVID-19 pandemic has had in many aspects of ordinary life (working, social life, training and learning in schools etc.), the characteristics of domestic spaces have significantly modified buying, selling and renting decisions in the real estate market. The aim of this research was to structure a methodology, articulated into four steps, to assess the variation that has occurred in residential market demand as a result of COVID-19 anti-contagion measures, with regard to six metropolitan Italian cities. We considered two samples of properties for each city, the first referencing the pre-COVID-19 pandemic spread and the second collected in the current situation. Consequently, we were able to determine variations in residential market appreciations through the application of a regressive econometric technique. The obtained results highlighted the relevance assumed by indoor acoustic and thermal comfort property factors, compared with the pre-COVID-19 condition. The proposed methodology could be useful to support the public and private entities involved in urban investment decision-making processes, allowing us to identify the most appreciated factors of the residential real estate market demand, in order to improve the conditions of existing and future assets and reduce the related risk levels. ===== PAGE 1 (score 14, numeric-paren 0, table-words 0, var-words 14) ===== Buildings 2021, 11, 592. https://doi.org/10.3390/buildings11120592 www.mdpi.com/journal/buildings Article An Assessment Methodology for the Evaluation of the Impacts of the COVID-19 Pandemic on the Italian Housing Market Demand Francesco Tajani 1,*, Felicia Di Liddo 2, Maria Rosaria Guarini 1, Rossana Ranieri 1 and Debora Anelli 2 1 Department of Architecture and Design, Sapienza University of Rome, Via Flaminia 359, 00196 Rome, Italy; mariarosaria.guarini@uniroma1.it (M.R.G.); rossana.ranieri@uniroma1.it (R.R.) 2 Department of Civil, Environmental, Land, Building Engineering and Chemistry (DICATECh), Polytechnic University of Bari, Via Orabona 4, 70125 Bari, Italy; felicia.diliddo@poliba.it (F.D.L.); debora.anelli@uniroma1.it (D.A.) * Correspondence: francesco.tajani@uniroma1.it Abstract: Due to the forced changes that the COVID-19 pandemic has had in many aspects of or- dinary life (working, social life, training and learning in schools etc.), the characteristics of domestic spaces have significantly modified buying, selling and renting decisions in the real estate market. The aim of this research was to structure a methodology, articulated into four steps, to assess the variation that has occurred in residential market demand as a result of COVID-19 anti-contagion measures, with regard to six metropolitan Italian cities. We considered two samples of properties for each city, the first referencing the pre-COVID-19 pandemic spread and the second collected in the current situation. Consequently, we were able to determine variations in residential market appreciations through the application of a regressive econometric technique. The obtained results highlighted the relevance assumed by indoor acoustic and thermal comfort property factors, compared with the pre-COVID-19 condition. The proposed methodology could be useful to sup- port the public and private entities involved in urban investment decision-making processes, al- lowing us to identify the most appreciated factors of the residential real estate market demand, in order to improve the conditions of existing and future assets and reduce the related risk levels. Keywords: COVID-19 pandemic; housing market; property prices; genetic algorithm; housing demand 1. Introduction Starting in the first half of 2019, the COVID-19 pandemic has spread rapidly worldwide and, in order to minimize contagion, governments have applied many of measures that, most of all, have forced people to stay at home. This has changed the shape of ordinary lives, requiring people to continue some activities in the domestic space [1–3]. In this way, rooms such as the living room, the bedrooms and the kitchen have had to accommodate functions for which they may not have been equipped: in many cases they have been transformed into working spaces, gyms, and meeting rooms. The impossibility of conducting outdoor activities, on the other hand, has meant that balconies, terraces or condominium green outdoor spaces have become the only way out of the house, and they too have been transformed into gyms, places of leisure, relaxation or work, and meeting areas. In other words, domestic spaces that previously performed a certain number of functions, strictly related to the ordinary daily activities of people be- fore the restrictive measures of COVID-19, had to welcome new ones, often proving to be inadequate. Moreover, spaces such as balconies or terraces, not always present in all types of residential buildings, have been found to be essential for many reasons—from Citation: Tajani, F.; Di Liddo, F.; Guarini, M.R.; Ranieri, R.; Anelli, D. An Assessment Methodology for the Evaluation of the Impacts of the COVID-19 Pandemic on the Italian Housing Market Demand. Buildings 2021, 11, 592. https://doi.org/10.3390/ buildings11120592 Academic Editor: Dirk H. R. Spennemann Received: 25 October 2021 Accepted: 24 November 2021 Published: 28 November 2021 Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional claims in published maps and insti- tutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses /by/4.0/). ===== PAGE 6 (score 11, numeric-paren 0, table-words 2, var-words 5) ===== Buildings 2021, 11, 592 6 of 28 In the second step (Step II) a study sample related to residential properties sold in the period prior to the anomalous event was collected for the investigation of the “ordi- nary” market mechanism. Therefore, with reference to the present analysis, a sample of 165 housing properties for each city sold in the second half of 2019 (Phase I: “pre-COVID-19 pandemic”) was detected. For each data set, some preliminary correla- tion analysis and descriptive statistic examinations were carried out for the monitoring of data samples statistical robustness. (Tables S1–S24 in the Supplementary files, respec- tively). Then, an econometric technique was implemented in order to obtain a function for each city able to identify the main relationships between the factor selected and the selling prices. The third step (Step III) refers to the same logical approach carried out in the second step with reference to the Phase I, by detecting data related to the period following the occurrence of the phenomenon. In the specific case, the study samples were related to the six Italian cities selected for the analysis, with reference to the first half of 2021 (Phase II: “COVID-19 pandemic in progress”). In the fourth step (Step IV) the comparison of the outputs obtained in the two stages (Phases I and II) is performed. Thus, the synthesis of the results was developed in order to (i) identify the variations in the residential market demand deriving from the COVID-19 pandemic arising and (ii) to provide a framework for orienting the planning and design decisions. In Figure 1, a summary of the main steps for the implementation of the methodology proposed is reported. Figure 1. Summary of the main steps of the methodology for the assessment of the effects of anomalous events on hous- ing market. 4. Case Study 4.1. Implementing Step I of the Methodology 4.1.1. The Study Samples In order to assess the changes occurred in the Italian residential market, the six largest Italian metropolitan cities were selected: Milan and Turin for Northern Italy, Rome and Florence for Central Italy, and Naples and Catania for Southern Italy and the Islands. For each city, the main social, urban, economic and demographic factors were investigated in order to understand the context of reference for each city. In Table 1, a summary of the distinctive features for each city is reported [67]. Table 1. Main distinctive features for each Italian city considered in the analysis. Factor Turin Milan Florence Rome Naples Catania Number of inhabitants (n.) 870,952 1,396,059 372,038 2,837,332 962,589 311,402 Surface (km2) 130.01 181.67 102.32 1,287.36 119.02 182.90 Population density (inhabitant/km2) 6,699.12 7,684.59 3,636.02 2,203.99 8,087.62 1,702.58 Old age index 204.10 196.30 220.40 162.60 114.40 139.60 Square meters per occupant in occupied 41.00 41.50 41.40 29.40 31.70 37.10 ===== PAGE 7 (score 5, numeric-paren 0, table-words 0, var-words 5) ===== Buildings 2021, 11, 592 7 of 28 residential units (m2) Number of residential buildings (n.) 36,158 42,980 31,070 137,021 40,755 28,988 Empty residential properties (n.) 36,779 37,073 5164 118,531 14,140 28,567 Per capita income (€) 25,015 34,046 26,503 28,241 22,434 20,179 Source: elaborations of the authors on ISTAT database. As can be seen in Figures 2 and 3, for each city two study samples consisting of 165 housing properties were detected. The first concerned 165 residential units sold in the second half of 2019 (Phase I), whereas the second related to 165 residential units sold in the first of 2021 (Phase II). In Figure 2, the locations of the properties (green points) col- lected for the cities in the pre-COVID-19 spread are represented, and it is possible to note their heterogeneous distribution throughout the urbanized territory. The entire sample was detected in order to take into account all municipal trade areas provided by the Real Estate Market Observatory (OMI) of the Italian Revenue Agency, i.e., the “portion of the territorial band that reflects a homogeneous part of the local real estate market, in which there is a substantial uniformity of appreciation for economic and socio-environmental conditions is observed” [68] or, the central, semi-central, peripheral and suburban por- tion of urbanized territory that synthetized the features of the neighborhood. The same considerations were carried out for Figure 3, pertaining to the locations of the properties (red points) that refer to the sample of Phase II. City of Turin City of Milan City of Florence City of Rome ===== PAGE 14 (score 23, numeric-paren 0, table-words 4, var-words 7) ===== Buildings 2021, 11, 592 14 of 28 Iteration 4 2.329 3.120 2.789 2.789 2.329 2.329 2.329 2.329 2.015 2.015 2.997 3.102 Iteration 5 2.279 3.089 3.256 3.256 2.279 2.279 3.345 3.345 2.058 2.058 2.279 2.279 Iteration 6 2.228 3.310 3.658 3.658 2.228 2.228 2.228 2.228 2.987 2.987 2.228 2.228 Iteration 7 3.123 3.531 3.987 3.987 3.123 3.123 3.004 3.004 2.753 2.753 3.123 3.123 Iteration 8 2.127 2.178 3.854 3.854 2.127 2.127 2.127 2.127 2.861 2.861 2.127 2.127 Iteration 9 3.404 3.650 3.145 3.145 3.404 3.404 2.767 2.767 2.001 2.001 3.404 3.404 Iteration 10 2.026 2.077 3.521 3.521 2.026 2.026 2.026 2.198 3.021 3.021 2.026 2.026 In Table 5 a summary of the variables selected in each model is shown to conven- iently compare the most influencing factors among those analyzed. Table 5. Variables selected by the models generated by EPR-MOGA for each study sample of Phase I. No. City N. Variables Si Sg Sb Se L B Yc C Sc P Mg Me Vm 1 Turin 9 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 2 Milan 7 ✓ ✓ ✓ ✓ ✓ ✓ ✓ 3 Florence 9 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 4 Rome 10 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 5 Naples 9 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 6 Catania 10 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ It should be noted that the variables referring to the internal area (Si), the number of bathrooms in the property (B), the building construction year (Yc) and the average mar- ket value (Vm) were present in all six equations, with a non-zero multiplicative coeffi- cient. Furthermore, no variable was excluded by the models and all factors analyzed were included in at least two models. For all the equations obtained for Phase I, their algebraic structure did not allow an immediate interpretation of the functional relationships among the variables, as each additive term was a combination of different variables that occurred several times in the same model. Therefore, in order to verify the empirical consistence of the functional links between the independent explanatory variables selected by each model, and the values of the dependent variable of total selling prices, a simplified exogenous approach that con- sidered the other variable values equal to the average values of the starting database (value “1” or “0” if the factor was a dummy variable) was used. This approach deter- mined the marginal price of the generic variable through the changes in value of the as- sessed variations of selling prices, in correspondence with each i-th variable in the ad- missible range of its corresponding sample collected. In particular, for each Italian city, with reference to the Phase I (second half of 2019 “pre-COVID-19 pandemic”) Figures S1–S6 in the Supplementary Materials show the functional correlations detected for each explanatory variable selected by the six models. The marginal influence on selling prices, in terms of the average percentage varia- tion obtained in correspondence with the passage from one level to the next, or from the absence to the presence of a specific factor, was reported for each variable. The analysis of the functional correlations between independent explanatory variables, selected by the models and housing prices, verified the empirical evidence of the coefficient signs for all the cities, as the consistency of the links with the expected phenomena was confirmed. According to the aim of the research, some interest can be accomplished for the in- trinsic factors analyzed, connected with the domestic spaces and their related accessory surfaces: i. A direct link between the internal surface and housing prices was detected for the six cities considered (+26% for the city of Turin, +37% for the city of Milan, +20% for the city of Florence, +38% for the city of Naples, +25% for the city of Rome, and + 6% for the city of Catania, considering an average variation of 40 m2). ===== PAGE 15 (score 13, numeric-paren 0, table-words 0, var-words 13) ===== Buildings 2021, 11, 592 15 of 28 ii. Variables related to direct and private accessory surfaces, i.e., balconies or terraces and gardens, had different influences; for example, for the city of Turin the presence of balconies was strongly appreciated up to a surface of 9.50 m2 (+22%), beyond which the contribution on the prices progressively decreased (an average +5%). The marginal contribution on selling prices provided by the biggest balconies or terraces and gar- dens surfaces was confirmed by the microeconomics principle, for which the rele- vance of a good was strongly associated with the need of it (known as law of de- creasing marginal utility). Moreover, the variable was also directly linked to the sell- ing prices in the city of Milan, for which the variation between the absence and the presence of balconies was higher (+14%), compared with the subsequent balconies area (+4%). The model selected for the city of Florence proved a growth of the resi- dential values in correspondence with the presence of balconies (+31% compared with its absence), and a progressive attenuation in prices increase for larger balcony surface areas (+17%). Similarly, for the city of Catania, a direct correlation between the varia- ble related to the surface of balconies Sb and housing prices was found, with a relevant initial variation equal to +19% between the properties without balconies and those characterized by the balcony presence. Then, the percentage variation decreased, and was equal on average to +4%. The presence of private gardens was not included in the models of the city of Turin, Naples, Catania and Milan, due to the most common res- idential typology sold in those markets, i.e., residential units located in apartment buildings. A decrease in housing prices was found for the city of Florence model (−11%), in correspondence with properties with private gardens. With reference to the study sample collected, only 6% of the total individuals included were characterized by this domestic space, and all were localized in the higher hydrogeological risk areas of the city. Furthermore, a significant influence of private green area was detected for the city of Rome, especially due to the position of the sample residential units, in par- ticular, valued urban zones (in the proximity of the Appia Antica Regional Park). iii. The models selected showed a lack of appreciation for the presence of condominium areas, in the second half of 2019, in the cites of Naples, Turin, Florence and Rome. On the other hand, the price functions generated by the EPR-MOGA technique for the cities of Catania and Milan denoted a relevant contribution—positive for the first city, negative for the second—deriving from the presence of these spaces on selling prices. In particular, for the city of Catania, it should be outlined that most properties col- lected in the study sample were located in prestigious residential complexes, in which the shared gardens were in excellent conservative conditions, and were for the exclu- sive use of inhabitants. On the other hand, for the city of Milan, most residential units in the study samples considered for the external condominium area (41% of the total sample individuals) were constituted by economic buildings, for which other factors could negatively influence the selling prices. iv. The floor level on which each residential property was located influenced the housing dynamics in the cities of Florence, Rome, Naples and Catania. The model selected for the city of Naples indicated an average variation on selling prices equal to +7%, and a higher significance in correspondence with the passage from the ground floor to the first floor (+25%), and an attenuation for the highest floors, from level eight upward (+5%). For the city of Catania, a direct functional correlation was found on average equal to +2%, and a relevant appreciation for the ground floor was detected, if the properties were characterized by condominium areas, compared with the higher floors. The same positive link typology was revealed with regards to the study sample collected for the city of Rome, for which the highest floor levels were those most ap- preciated, compared with the lowest ones. In addition, in the central trade area, the location on the highest floors allowed panoramic views that implied a strong influ- ence on housing values. A moderate contribution on selling prices was observed for the city of Florence, with a marginal price equal to 4%. ===== PAGE 16 (score 16, numeric-paren 0, table-words 4, var-words 3) ===== Buildings 2021, 11, 592 16 of 28 v. The central municipal trade area variable was included in the models selected for the cities of Rome and Catania; the semi-central areas appeared in the models of the cities of Turin, Catania and Naples, and the peripheral area factor was also present in the price functions of Turin, Florence and Naples. It should be outlined that the semi-central municipal trade area was particularly appreciated in the context of the city of Naples (+25%) and in the city of Catania (+52%), whereas a negative influence was given by the position of housing properties in the semi-central trade area and pe- ripheral area of the city of Turin (−33% and −38%, respectively). In the city of Florence, the selling price variation determined by the localization of the property in the pe- ripheral area was equal to –18%, whereas for the city of Naples a decrease in housing prices equal to –20% was recorded for the peripheral trade area. The location of properties in the central municipal trade area of the city of Rome determined an in- crease in selling price equal to +13%, whereas this was equal to +5% in the central area of Catania. 4.3. Implementating Step III of the Methodology Application of the Technique to Phase II: “COVID-19 Pandemic in Progress” By recalling the aim of the present research, the identification of the changes in res- idential market demand caused by the COVID-19 pandemic in six Italian metropolitan cities, Step III of the analysis concerns the same operative logic carried out as in the pre- vious Step II. Therefore, six study samples, each consisting of 165 housing properties sold in the first half of 2021 (one for each city) were collected. For each residential unit, the same factors detected for Phase I were investigated in order to determine the most in- fluential factors on selling prices, and to study the functional correlation between the explanatory independent variables and price. Thus, the same stages developed in Phase I (second half of 2019) were replicated in Phase II (first half of 2021). The implementation of the EPR-MOGA technique was iteratively carried out for all the samples. The dependent variable of total selling price was constituted by its natural logarithm (Y = ln(Q)). The application of EPR-MOGA generated several models able to describe the residential market dynamics, and those chosen for the analysis of the func- tional link between influential factors and housing prices are reported in Table 6. Table 6. Models generated by the EPR-MOGA implementation for each Italian city analyzed for the Phase II. City Model CoD (%) Turin Y = + 2.434  Vm0.5 + 0.3733  Me0.5 + 0.99371  Sb0.5  B0.5  Vm0.5 – + 4.4136  Sb0.5  B0.5  Yc0.5  P0.5  Me0.5 + 7.617  Si0.5 − 4.1752  Si  Vm0.5 + + 7.4833 85.53 Milan Y = + 0.49351  C0.5  Vm − 0.88769  Yc0.5  P − 0.56312  L0.5  B0.5  Mg + + 24.1533  Sg0.5  Se2  L + 1.2286  Sg  Vm + 8.1673  Si0.5 − 4.1711  Si + + 2.8284  Si  L  B0.5 + 10.7489 96.04 Florence Y = + 23.2683  Vm0.5 − 13.2187  Vm + 0.61728  B0.5  Me 0.5  Vm2 + + 1.8377  Sb2 + 5.8364  Si0.5 + 170.3596  Si0.5  Sb2  L  Yc – + 2.2608  Si + 0.18337 93.00 Rome Y = + 2.3773  Vm0.5 + 0.27166  Me – 0.66914  Yc0.5  Me2 + + 9.5008  Se  Yc2  P2 + 1.7449  Sb  L0.5  B + 3.0846  Si0.5 + + 2.5818  Si0.5  L0.5  Yc2  Me2 + 9.402 89.84 Naples Y = + 4.3382  Vm − 2.0486  Vm2 + 0.98283  L  Yc0.5  Me2 + 0.75291  Sb0.5  B0.5   Me0.5 + 9.3479  Si0.5 − 4.2403  Si + 7.4542 93.72 Catania Y = + 1.9795  Vm0.5 + 0.38123  Me2 + 1.0016  B0.5 + 13.2376  L0.5  B2  Yc2  Mg + + 2.5865  Sb0.5  Se2  B  Yc  C  Me2 + 2.1141  Sg2  Yc0.5  Vm2 + 2.762  Si0.5 + + 8.1768 84.73 For each polynomial equation, the CoD was specified; in particular, a high statistical accuracy level was associated with them (+85.53% for the city of Turin, +96.04% for Milan, ===== PAGE 17 (score 31, numeric-paren 0, table-words 5, var-words 8) ===== Buildings 2021, 11, 592 17 of 28 +93.00% for Florence, +89.84% for the city of Rome, +93.72% for Naples, +84.73% for Ca- tania). Moreover, in this analysis the main statistical indicators (RMSE, MAPE and MaxAPE) were calculated, and a ten-fold cross-validation was carried out. With reference to the statistical indicator the lowest RMSE was concerned with the city of Milan (3.21%) and the highest referred to the city Turin (3.98%). Furthermore, the lowest MAPE was calculated for the Milan study sample (2.80%), and the highest MAPE was calculated for the city of Catania (3.78%). Moreover, the city of Catania presented the highest MaxAPE (9.21%), and the lowest MaxAPE was verified for the Florence case study (8.12%). Table 7 reports the output of the ten-fold cross-validation. These analyses confirmed that the se- lected samples were stable and statistically performing. Table 7. Average percentage errors (%) obtained through a ten-fold cross-validation for Phase II. No. Itera- tion Turin Milan Florence Rome Naples Catania Training Set Validation Set Training Set Validation Set Training Set Validation Set Training Set Validation Set Training Set Validation Set Training Set Validation Set Iteration 1 2.217 2.351 2.551 2.614 2.292 2.434 2.227 2.237 2.125 2.136 2.660 2.667 Iteration 2 2.872 2.889 2.121 2.179 2.880 2.887 2.917 2.938 2.884 2.894 3.201 3.212 Iteration 3 2.091 2.078 2.889 2.985 3.210 3.221 2.156 2.208 2.485 2.506 2.998 3.008 Iteration 4 2.373 2.348 2.789 2.843 2.384 2.394 2.385 2.448 2.444 2.496 2.581 2.602 Iteration 5 2.299 2.364 3.256 3.258 2.309 2.330 3.345 3.403 2.252 2.315 2.411 2.463 Iteration 6 2.247 2.231 2.543 2.653 2.268 2.320 2.273 2.369 2.987 3.045 3.012 3.075 Iteration 7 3.208 3.138 2.852 2.985 3.260 3.323 3.004 3.058 2.101 2.197 2.589 2.647 Iteration 8 2.130 2.129 2.998 2.895 2.193 2.251 2.184 2.186 2.001 2.055 2.875 2.971 Iteration 9 3.201 3.321 3.145 3.145 3.259 3.355 2.767 2.782 2.589 2.591 3.001 3.055 Iteration 10 2.028 2.080 3.521 3.521 2.124 2.178 2.049 2.198 3.021 3.036 2.498 2.500 In Table 8, a summary of the variables selected in each model is reported. All equa- tions included a large number of influential factors among those considered in the anal- ysis (seven for the cities of Turin, Florence and Naples, ten for Milan, nine for the city of Rome, and eleven for the study sample of Catania). Table 8. Variables selected by the models generated by EPR-MOGA for each study sample for Phase II. No. City N. Variables Si Sg Sb Se L B Yc C Sc P Mg Me Vm 1 Turin 7 ✓ ✓ ✓ ✓ ✓ ✓ ✓ 2 Milan 10 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 3 Florence 7 ✓ ✓ ✓ ✓ ✓ ✓ ✓ 4 Rome 9 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ 5 Naples 7 ✓ ✓ ✓ ✓ ✓ ✓ ✓ 6 Catania 11 ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ First of all, it should be noted that the internal surface (Si), the number of bathrooms (B), the building construction year (Yc) and the average market value (Vm) represented significant factors in selling price formation, as they were in all six models with a multi- plicative coefficient greater than zero. Furthermore, only the variable related to the loca- tion of the properties in the semi-central trade area (Sc) was excluded. For all price functions obtained for Phase II, the polynomial form of the equations did not allow an immediate analysis of the functional correlations among the explanatory variables and selling prices. Therefore, the same simplified exogenous approach imple- mented in Phase I was used for the verification of the empirical coherence of the func- tional links. In Figures S7–S12 in the Supplementary Materials, for each Italian city with reference to Phase II (first half of 2021 “COVID-19 pandemic in progress”), the functional correlations between the independent variables selected by the six models and the ===== PAGE 18 (score 6, numeric-paren 0, table-words 1, var-words 4) ===== Buildings 2021, 11, 592 18 of 28 housing prices are reported. Moreover, the average percentage of selling price variations detected was specified. For all study samples collected and the variables selected, the empirical evidence of the equation’s coefficient signs, i.e., the consistency of the relationships with the expected market phenomena, was verified. For the variables for which a direct functional correlation was detected, their influ- ence (represented by their average marginal contribution) on selling prices is reported in the graphs in Figure 5. In particular, for the quantitative continuous factors related to surfaces (Si), (Sg) and (Sb), the average marginal contribution was analyzed by taking into account specific ranges (<10 m2, 10–30 m2, 31–70 m2, >71 m2 for the surface of a pri- vate garden, < 70 m2, 71–100 m2, 101–130 m2, >131 m2 for the internal surface, < 6 m2, 7–20 m2, 21–50 m2, >51 m2 for the surface of balconies or terraces). For the dummy variables (Se), (Me), (C), the marginal contribution was determined considering the variations that occurred with the absence or the presence of this property characteristic, whereas for the quantitative discrete variables (L) and (B), the marginal price related to each increase of the factor was determined.