Comparative Study on Housing Defect Repair Cost through Linear Regression Model

Abstract

Despite stiff competition in the construction industry, housing quality remains a problem. From the consumer’s perspective, these quality problems are called defects. Homeowners experience inconvenience and suffering due to home defects, and developers and builders also experience severe damage in time, costs, and reputation due to defect repairs. In Korea, lawsuits are increasing due to the rise in housing defects, and the cost of repairing defects determined by lawsuits is of great concern. Litigation is a burden to consumers and producers, requiring a hefty court fee, as well as attorneys and specialist firms, and takes some years. Suppose it is possible to predict the repair costs based on the outcome of a lawsuit and present it as objective supporting data. In that case, it can be of great help in bringing a settlement between consumers and producers. According to previous studies on housing repair costs, linear regression models were mainly used. Accordingly, in this study, a linear regression model was adopted as a method to predict housing repair costs. We analyzed the defect repair costs in 100 cases in which lawsuits were filed and the verdict was finalized for housing complexes in Korea. Previous studies investigated using the following independent variables: elapsed period, litigation period, claim amount, home warranty deposit, total floor area, households, and main building’s quantity, construction cost, region, and highest floor. Among these, the floor area, elapsed period, and litigation period were determined to be valid independent variables. In addition, the construction period was discovered as a valid independent variable. The present research model, which combines these independent variables, was compared with previous research models. The results showed that the earlier research model was found to have a multicollinearity issue among some independent variables. Also, the coefficients of some independent variables were not statistically significant. This research model did not have a multicollinearity problem; all independent variables’ coefficients were statistically significant, and the coefficient of determination was higher than other linear research models. Our proposed regression model, which accounts for the interaction of each independent variable, is a significant step forward in our research. This model, using the number of households multiplied by the construction period, the construction period multiplied by the litigation period, and the litigation period multiplied by the litigation period as independent variables, has been rigorously tested and found to have no multicollinearity issue. The coefficients of all independent variables are statistically significant, further bolstering the model’s reliability. Additionally, the explanatory power of this model is comparable to the previous model, suggesting its potential to be used in conjunction with the existing model. Therefore, the linear regression model predicting the repair cost of housing defects following litigation in this study was considered the best. Utilizing the model proposed in this study is expected to play a major role in reconciling disputes between consumers and producers over housing defects.

1. Introduction

As competition in the housing construction industry intensifies, the focus has shifted to better cost and time efficiency; in general, however, quality has been compromised [1]. In the design phase and construction phase of a home, quality problems occur due to errors [2,3]. In addition, problems appear in the post-handover phase once the house is completed and delivered to the consumer [4,5]. Preceding studies have named these problems defects, failure, and rework [6,7,8,9]. According to previous studies, it is difficult to distinguish quality problems clearly [7], and there are slight differences depending on the cause of the problem, the time of occurrence, and the phenomenon. Usually, from the producer’s perspective, the terms failure and rework are often used; particularly, these mainly deal with problems that occur during construction. On the other hand, from the consumer’s perspective, housing quality problems are usually expressed as defects, and they mainly refer to problems in the usage phase after the house is completed in terms of time. In this study, housing quality problems are referred to as defects from the consumer’s perspective.

These housing defects cause disputes between producers and consumers, which have become a problem worldwide. In Korea, many apartment complexes are built in high-rise buildings, commonly seen in large cities in developed countries and new towns in developing countries [10,11,12]. Therefore, this study, conducted mainly on Korean housing, can significantly contribute by applying and referencing it in other countries.

Let us look at the adverse effects of disputes from a time perspective and from the producer’s perspective. The producers want the conflict resolved early to improve their image because they need to continue their business. From the consumer’s perspective, they also wish to repair the defects that cause inconvenience in their lives as early as possible. According to previous studies, lawsuits take an average of 809 days, according to Kang et al. [13], meaning it takes more than two years to resolve a dispute. From the above facts, if a dispute surrounding a housing defect can be settled by reaching an appropriate level of agreement early, it will considerably benefit both parties in terms of time.

Let us look at the adverse effects of disputes from a cost perspective since the definitions and scope of defects that producers and consumers think of differ. The proposed defect repair cost will show a significant difference. Producers consider defects to be only those that violate the standards set by law or are constructed differently from the design drawings, resulting in decreased safety or functionality, and those that are visible. On the other hand, consumers consider maintenance difficulties and inconveniences in daily life due to design errors other than those recognized by the producer. Regarding the scope of repair, the producer thinks that only the part where the defect occurred should be repaired, but the consumer wants the entire part or space where the defect occurred to be repaired. When these differences accumulate, the defect repair cost can vary greatly. It is unknown how much of a difference there is between the defect repair cost claimed by producers and consumers in disputes over housing defects. This is because the information on the defect repair cost exchanged between the two parties for the purpose of settlement is confidential and is not disclosed to the public. Generally, the defect repair cost of a house is the lowest claimed by the producer and the highest demanded by the consumer, whereas the cost presented to the court or arbitration agency is somewhere between the two. It could be confirmed from the data disclosed in previous studies that the difference between the defect repair cost claimed by consumers in lawsuits and that one concluded by a judgment was as much as 2.6 times, according to Kang et al. [13]. Therefore, the difference between producers and consumers is expected to be even greater. Although not all disputes over housing defects are resolved through lawsuits, because there is a large number of lawsuits and the outcome of lawsuits has a binding force on both producers and consumers, it is believed that analyzing the results of the lawsuit and having the two parties seek reconciliation at a similar level can help to find a fair resolution in terms of cost.

In summary, if a dispute over a housing defect is settled before it escalates to a lawsuit, it can greatly reduce social waste. Two years will not be wasted once the dispute is resolved before a lawsuit. In particular, if the defect repair cost determined due to the lawsuit is predicted and utilized, it will help narrow the perspective gap between producers and consumers. Furthermore, additional court fees, attorney fees, and professional engineering investigation costs can be saved if a lawsuit is not filed.

To consider the method of conducting this study, the research trends on housing defects are briefly reviewed. As discussed in Section 2, basic studies analyze the current status of what types of defects occur in houses and to what extent [14,15,16,17]. In addition, studies have been conducted on the scale of repair costs for housing defects [7,8,12,18,19]. Further, studies have predicted how much it would cost to repair a house [13,20,21,22,23]. All models proposed in these studies used linear regression to predict defect repair costs (linear regression analysis). The prior regression model has been widely used in construction because it explains the simple but straightforward relationship between the influencing and the influenced factors. Research on housing defect repair costs is in its initial stages and has limitations due to the difficulty in obtaining data [7]. Applying machine learning techniques is difficult unless there is a long-term investment in extensive data collection [24]. Therefore, this study adopts the linear regression model used in previous studies to predict housing defect repair costs.

This study was conducted to achieve the following specific detailed objectives, and the order is as shown in Figure 1. First, the contents of previous studies were reviewed to determine what independent variables were used, what level of explanatory power they had, and whether the assumptions for a linear regression model were met. Second, the valid independent variables adopted in previous studies were selected. This was confirmed through scatter plots and correlation analysis. In addition, independent variables that were not used in previous studies were added. The results of the optimal combination of each independent variable were set as the research model. Third, the defect repair lawsuits in Korea were predicted using this and previous research models, and the best-fit model for research cases was compared. Since each model was a linear regression model, it was checked whether there were problems with linearity, autocorrelation, and multicollinearity and whether the significance of each independent variable coefficient was satisfied. If these primary conditions were met, the model with the highest explanatory power was selected.

2. Literature Study

2.1. Housing Defects and Repair Cost

Research on overall building defects consisted of types of defects, cause analysis, and repair costs. Josephson and Hammarlund identified the causes of defects in seven construction projects, including homes [10]. These were client, design, site management, workmanship, subcontractors, materials, machines, and others. Analysis results indicated that design, subcontractors, and materials caused the defects. On the other hand, only a few cases were attributed to such matters as equipment. Rotimi et al. suggested 43 defects occurring in houses [11]. Representative types of defects include uneven painting, poor finish, and nail pops. Seo classified defects that occurred in ultrahigh-rise housing into five categories: structure, wet finish, dry finish, miscellaneous construction, and facilities construction, and then subdivided them into 16 types [12]. According to this classification, the most frequently occurring defects were window construction, furniture and home appliances, and interior finishing work. Park and Seo subdivided defects that occurred in timber construction in homes into 63 categories [13]. In addition, significant defects were classified according to the number of occurrences of each defect and repair cost. According to their classification, ten types of defects, which were wooden floor breakage, opening and closing faults in doors and windows, and non-installation of anti-rotting end pieces on the door, were the chief defects accounting for 85.62% of the total. These studies are meaningful in that they facilitated the identification of the status quo by classifying the types and causes of defects.

The following studies evaluated the repair costs of a home by comparing them with the construction cost. While the study of Love et al. suggested the repair cost ratio to the construction cost as an average of 0.18% [7], Mills et al. suggested an average of 4%, which was different [14]. In addition, the study by Josephson et al. suggested that the average repair cost ratio to the construction cost was 4.4%, with a minimum of 2.3% and a maximum of 9.4% [8]. Liu et al. suggested a mean of 4.95%, a minimum of 2.07%, and a maximum of 10.27% [15]. From the results of these prior studies, the extent of damage caused by defects could be assumed. However, if the average repair cost was only considered, 4.95% suggested by Liu et al. and 0.18% by Love et al. have a difference of up to 27 times or more. Moreover, according to the study by Liu et al., the difference between the minimum and maximum values was five times.

On the other hand, Park and Seo investigated the housing defect repair cost and deposit [16]. According to the analysis of 290 housing complex cases, the average repair cost for defects was 0.538%, the minimum was 0%, and the maximum was 2.22% of the construction cost. In addition, Park and Seo analyzed the defect costs by dividing the housing construction cost into three cases: when the housing construction cost was less than USD 62 million, USD 62 million to USD 125 million, and USD 125 million or more. The results showed that the ratio of defect repair cost to construction cost was 0.67% in the case of less than USD 62 million. In the case of USD 62 million to USD 125 million, it was 0.5%, and in the case of USD 125 million or more, it was 0.39%. This result implied that there were some differences in the cost of repairing defects depending on the scale of the housing construction cost.

These prior studies were helpful to understand the causes and types of housing defects and how much repair cost was required. However, it was not explicitly presented what factors affected the occurrence of defects and how much the factors changed the cost of repairing defects. Therefore, it was necessary to investigate further the studies to predict and control the defect repair cost. In this study, the initial studies were reviewed using a regression model.

2.2. Prediction of Repair Cost

The research models presented in the prior studies that estimated the repair cost of defects in buildings, including homes, with a regression model, and their characteristics are as follows.

Kang et al. assumed the defect repair cost, which was the dependent variable, by setting the period between the completion of the home and the filing of a lawsuit (elapsed period; EP), the time from filing a lawsuit to the end of the lawsuit (lawsuit period; LP), the value of the subject matter in the litigation (VL), and the home warranty deposit (HWD) as independent variables [13]. The coefficient of determination (R² value) in the regression model by Kang et al. with 31 cases was 0.700, which was high. However, among the proposed independent variables, the lawsuit period can only be known after the lawsuit is completed. Therefore, there was a limitation that the lawsuit period was a variable that was difficult to utilize in the pre-lawsuit stage. In addition, it was unclear at what time was effective since the value of the subject matter in the litigation among the independent variable kept changing during the lawsuit. In a defect lawsuit, the value of the subject matter in the litigation charged at the initial lawsuit is a formal amount. Normally, when an appraiser submits an appraisal report, the value of the subject matter in the litigation is changed to the amount specified in the appraisal report. Afterward, the value would be changed several times through argument about the factual grounds in supplementing the appraisal and pleadings. Therefore, in the model suggested by Kang et al., there was a limitation that using the value of the subject matter in the litigation as an independent variable was inaccurate.

On the other hand, in the model of Kang et al., the Dubin–Waston value, which was a criterion for determining the independence of residuals, was 1.913, within the range of independence. However, a P-P plot and a scatter plot between the residuals and the predicted values were presented for the residuals. In the study of Kang et al., since the number of samples was more than 30, it seemed that normality could be assumed. Nonetheless, in some zones in the P-P plot, the normality of the residuals was suspicious to some extent. Therefore, it was not easy to ascertain that the residuals and predicted values were within the scatter plot and that there was a unique pattern.

Seo and Lee estimated the dependent variable defect repair cost using the total floor area (TFA), the number of households (HH), and the number of main buildings (MB) as independent variables [20]. In the model by Seo and Lee, the coefficient of determination R² was analyzed as 0.691 for 49 cases. Although this value was slightly lower than that of Kang et al. [13], it was still a high value. However, Seo and Lee’s study did not present the analysis results on residuals and multicollinearity.

In the study of Choi, the dependent variable defect repair cost was estimated using home warranty deposit, total floor area, and the number of households as independent variables [21]. Choi’s model targeted 48 cases, and the coefficient of determination R² was 0.719, which was a high value. Although Choi stated that multicollinearity and independence of residuals were reviewed in his model, the levels could not be confirmed because specific analysis results were not mentioned.

In the study of Forcada et al., unlike other studies, the dependent variable was not the repair cost but a value obtained by taking the natural logarithm of the defect repair cost [22]. For independent variables, a value obtained by taking the natural logarithm of the construction cost (CC) and a nominal variable that classified the locational difference between the headquarters of the construction company and the subjected planned building into four grades were adopted. Forcada et al. [22], in their model, analyzed the coefficient of determination R² as 0.561 for 40 cases, and this was the lowest value among the models in the initial research. Since studies other than Forcada et al. [22] did not mention the coefficient of determination in detail, it was impossible to know precisely what kind of distribution the original data constituted. However, it was presumed that the data were converted to natural logarithms considering normality. On the other hand, the study of Forcada et al. [22] did not include the analysis results for judging residuals and multicollinearity.

In Kim’s study, the dependent variable defect repair cost was estimated using total floor area, number of households, location, and the number of floors in the tallest buildings (NFTB) as independent variables. Among the independent variables used in the model by Kim, the location differed from that of Forcada et al., and the housing location was divided into a metropolitan area and a non-metropolitan area [21]. Kim analyzed the model for 20 cases, and the coefficient of determination R² was found to be 0.865. However, in the significance probabilities for each coefficient of the independent variable used in Kim’s model, only one household fell within 0.05, and the remaining variables were not significant. Among the independent variables reflected in Kim’s model, the three remaining variables, except for the number of households, were invalid. As for the number of households, which was an independent variable, the tolerance limit was 0.109 and the VIF was 9.198, while the tolerance limit for the total floor area was 0.107 and the VIF was 9.384. Kim’s study stated that there was no concern about multicollinearity, but according to the review examined earlier, the issue was that multicollinearity was of concern. Moreover, because there were two independent variables related to multicollinearity in Kim’s model, Kim’s model might have lacked validity. In this model, the Dubin–Waston value, which determined whether the residuals were independent, was 2.588. As mentioned earlier, the Dubin–Waston value of Kim’s model had limitations in that it centered on the independence of the residuals. In addition, normality is assumed if the number of samples is more than 30, whereas Kim’s model had only 20 samples. Forcada et al [22]. analyzed data more rigorously by using variables converted to natural logarithms considering normality, despite having 40 samples, which was twice the size of Kim’s model. Therefore, Kim’s model was lacking in applying statistical analysis methods.

The dependent and independent variables of the regression model presented in the prior studies and the R² value of the coefficient of determination of the regression model derived from each study are summarized and compared, as shown in

Table 1. Independent variable and R² of preceding studies.

Researcher	Independent Variable										R2
	EP	LP	VL	HWD	TFA	HH	MB	CC	Lo	NFTB
Kang et al. [13]	●	●	●	●							0.700
Seo and Lee [20]					●	●	●				0.691
Choi [21]				●	●	●					0.719
Focarda et al. [22]								●	●		0.561
Kim [23]					●	●			●	●	0.865

●: used variable

. Previous research studies established the models by combining various independent variables like elapsed period (EP), lawsuit period (LP), the value of the subject matter in the litigation (VL), home warranty deposit (HWD), total floor area (TFA), number of households (HH), number of main buildings (MB), construction cost (CC), location (Lo), and highest floor number of main buildings (HF). However, it was found that the review of residuals and multicollinearity, which were the most essential prerequisites in the regression model, was missed or inappropriate. In addition, it was confirmed that some independent variables remained even though they should have been excluded from the final regression model because the coefficients were insignificant. Therefore, the regression model for estimating housing defect repair costs should select one that meets these requirements and has an excellent coefficient of determination.

3. Materials and Methods

3.1. Scope

In this study, all quality problems raised for homes were defined as defects, and the cause or liability of the defect was not discussed. The housing for the study was apartment complexes in Korea. Therefore, not only the inside of the house occupied by each owner individually but also the outside of the house owned and used jointly, as well as the parking lot, landscaping, electricity, water, sewage, etc., were included.

As in other countries, disputes between construction companies and homeowners over housing defects frequently occur in Korea, becoming a social issue [25,26,27,28]. The construction company proposes the repair cost for defects using their calculation and procurement methods. In general, construction companies either hire professionals all the time or have affiliates with specialized subcontractors. In the case of construction materials, it is possible to purchase them in bulk or to secure them through regular vendors. Therefore, construction companies can secure laborers and materials for repairs at a lower price than the market. However, homeowners believe that the repair cost quoted by the construction company is too low compared to the actual repair cost. Therefore, homeowners claim that the maintenance cost is calculated through the contractors they hire separately, and the construction company should bear this cost. Vendors hired by homeowners are companies that conduct surveys and estimates instead of repairs, and they used to inflate repair costs because they receive service fees from homeowners.

Because of this, when a housing defect lawsuit occurs, it is difficult to settle due to the extreme difference in the cost of repairs claimed by construction companies and homeowners. Therefore, in a housing defect lawsuit, a professional appraiser appointed by the court inspects the home to confirm the defect, calculates the repair cost, and submits it to the court as a report [29]. The court will determine the defect repair costs based on the contents of this report and by referring to the opinions of both parties to the lawsuit. The method by which a professional appraiser calculates the repair cost borrows the standard for calculating the construction cost of public construction works in Korea. The case data of this study were the repair costs in which a professional appraiser in a housing defect lawsuit investigated the case and calculated the costs, which the court finally judged and confirmed.

3.2. Data Collection

This study used the lawsuit cases filed for housing defects in Korea. Therefore, data necessary for analysis were collected from judgments with litigation results, appraisal reports accompanying them, and building ledgers. The cost of repairs confirmed from the lawsuit and the housing overview were specified in the judicial decision. More specific information could be found through the appraisal report, which contained the results of the investigation by the court appraiser. In addition, basic information such as the year of construction and the house size was based on the building ledger. The building register of each house could be viewed on the Internet information system provided by the Korean Ministry of Land, Infrastructure and Transport [30].

To explain more specifically about the data collection, the verdict was provided free of charge by a professional company that offers specialized technical advice in defect disputes while carrying out a policy service project for the Korean government. These cases are the first trial verdicts that are handed down. The research team did not select them; instead, the company provided 100 randomly selected data points. The research team requested data from other companies besides the professional company to collect more data. Still, no additional data have been provided as of the time of conducting this study. As mentioned in previous studies, the parties to the dispute are reluctant to provide such information. In Korea, the court, which is the organization for housing dispute resolution, provides limited information for reasons of privacy policy, and even this cannot be requested without prior knowledge of the basic information about the case. In the case of another organization, the Defective Dispute Mediation Committee, it is not disclosed because of the Personal Information Protection Act. Therefore, to conduct this study, we did not have a choice but to rely on data provided by related professional companies. The appraisal report is printed on paper and can be viewed by visiting the appraiser.

On the other hand, the cost of repairing defects for the litigation case was determined when the lawsuit was finalized, and the time was different by case. Therefore, organizing these items based on a consistent time point was necessary. In this study, the repair cost for each case was converted according to its future value (FV) by the end of June 2024. The future value method was calculated by considering the present value (PV), the discount rate (interest: i), and the difference from the base point (year: n), as shown in Equation (1). The discount rate of 3.5%, the 3-year KTB rate announced by the Central Bank of Korea, was applied [31].

FV = PV × (1 + i)ⁿ

(1)

3.3. Linear Regression Analysis

Dependent and independent variables were derived by examining the regression model presented in the prior studies. The abbreviation, definition, and unit of each variable are shown in

Table 2. Variable definition.

Acronym	Variable	Definition	Unit	Variable Type
DRC	Defect repair cost	Defect repair cost to the housing complex	USD	Continuous variable
CP	Construction period	The period from construction start to completion	Month	Continuous variable
EP	Elapsed period	The period from building completion to initiation of a lawsuit	Month	Continuous variable
LP	Lawsuit period	The period from initiating a lawsuit to the end of the lawsuit	Month	Continuous variable
TFA	Total floor area	Sum of floor area to public space and private space	Thousand m2	Continuous variable
HH	Households	Households living in a housing complex	Household	Continuous variable
MB	Main buildings’ quantity	Main building’s quantity in a housing complex	Building	Continuous variable
NFTB	Number of floors in the tallest building	Number of floors in the tallest building in a housing complex	Floor	Continuous variable
Lo1	Distance from the developer’s headquarters to the housing complex	Distance from the developer’s headquarters to the housing complex, whether in the same municipality, in the same metropolitan region, or between other metropolitan regions		Nominal variable
Lo1-1	Dummy 1 of Lo1	Same local municipality or not		Nominal variable
Lo1-2	Dummy 2 of Lo1	Same metropolitan region or not		Nominal variable
Lo1-3	Dummy 3 of Lo1	Between other metropolitan regions or not		Nominal variable
Lo2	Location from builder’s headquarters to housing complex	Location of builder’s headquarters and housing complex, whether in the same basic local municipality, in the same metropolitan region, or between other metropolitan regions		Nominal variable
Lo2-1	Dummy 1 of Lo2	Same basic local municipality or not		Nominal variable
Lo2-2	Dummy 2 of Lo2	Same metropolitan region or not		Nominal variable
Lo2-3	Dummy 3 of Lo2	Between other metropolitan regions or not		Nominal variable
Lo3	Location of the housing complex	Capital area or non-capital area		Nominal variable
Lo3-1	Dummy 1 of Lo3	Capital area or not		Nominal variable
Lo3-2	Dummy 2 of Lo3	Non-capital area or not		Nominal variable

. Since the dependent variable was based on the defect repair cost in most studies, the dependent variable was also set as the defect repair cost in this study. As mentioned in Section 3.1, the cost of repairs for defects shall be based on the judgment and final decision in the litigation.

All independent variables of the initial studies identified in Section 2.2 were, in principle, considered for independent variables, and related information was collected from the case data. However, among the major independent variables suggested in the preceding studies, lawsuit costs, home warranty deposits, and construction costs were often impossible to extract from the data. Since the cost of litigation was the amount charged at the time of filing the first lawsuit, it was tentative, and it was impossible to obtain accurate information because it constantly changed during the lawsuit. In addition, according to the housing law of Korea, the home warranty deposit is set at 3% of the construction cost, so the deposit and construction cost are the same variables. However, since Korean public developers were exempted from home warranty deposits, confirming the deposit or construction cost from the judgments or appraisal reports was impossible. Therefore, these three variables were excluded from the independent variables in this study because a standard analysis was inapplicable in only some cases.

Among the independent variables, Forcada et al. divided the distance between the headquarters of a construction company and the construction site into overseas projects, domestic projects, and intra- and inter-regional projects rather than a numerical distance [20]. However, whether a construction company means a developer or a builder is unclear. In addition, for all cases in this study, only domestic projects were executed in Korea. Therefore, in this study, three types of locational divisions were classified: the construction site (Lo1) and the developer’s head office were within the same primary local municipality, both existed within the same regional municipality, and both existed in another regional municipality outside of the regional municipality. Similarly, the builder (Lo2) was classified in the same way. In addition, the location (Lo3) proposed in Kim’s study was divided into the capital and non-capital regions.

Meanwhile, the construction period was added as an independent variable, although it was not considered in previous studies. This was added based on similar elapsed and litigation periods adopted in previous studies.

Since the dependent variable was continuous and many independent variables were present, multiple regression analysis was selected. In addition, nominal variables among independent variables were reflected in the model through dummy transformation. The statistical program IBM SPSS ver. 21 was used for analysis.

4. Results

4.1. Outline

The statistical status of the entire homes, which was the case of this study, is as follows. Each case consists of one or more complexes. A statistical summary of all cases is shown in

Table 3. Statistics of Case.

Variable (Unit)	Minimum	Mean	Maximum	Standard Deviation	Variance
DRC (USD)	84,455	886,415	4,271,102	752,318.93	5.660 × 1011
CP (Month)	19.63	32.0930	100.33	10.84	117.51
EP (Month)	14.67	157.13	73.18	34.41	1184.00
LP (Month)	10.43	23.85	55.83	7.20	51.88
TFA (Thousand m2)	11.53	100.10	297.84	59.37	3,524,566.98
HH (Households)	96	814.31	3129	473.50	224,206.64
MB (Buildings)	1	9.91	39	5.69	32.35
NFTB (Floors)	12	19.80	40	5.51	30.38

, and the average repair cost is USD 886,415 (an exchange rate of KRW 1323.57 per American dollar, as of June 2024, was applied) [32]. The average construction period was 32.09 months, the elapsed period was 157.13 months, and the average lawsuit period was 23.85 months. The average total floor area was 100.10 thousand m², the average number of households was 814.31, the average number of main buildings was 9.91, and the average number of the highest floors was 19.8 stories.

The correlation analysis was conducted in this study because it was possible to know the relationship between variables [33]. The results of the correlation analysis between the variables listed in Table 3 are shown in Figure 2. All variables, including the dependent variable, repair cost (DRC), construction period (CP), and number of floors in the tallest building (NFTM), were found to be correlated. Among them, the total floor area (TFA) was the highest at 0.620, and the remaining variables were all found to have a positive correlation. On the other hand, the elapsed period (EP) was found to have a negative correlation of −0.201. Therefore, each independent variable was considered related to the dependent variable, the defect repair cost, and could be regarded as an influential factor. Meanwhile, the correlation between each independent variable, the total floor area (TFA), households (HH), and number of main buildings (MB) showed a strong positive correlation, and the households (HH) and number of main buildings (MB) also showed a similar level of positive correlation. Therefore, since these variables are interrelated, the possibility of autocorrelation problems cannot be ruled out if all variables are used in a regression model. Thus, in this case, interactions that reflect new variables through combinations of highly interrelated variables must be considered.

4.2. Comparison

The results of analyzing the case data in Section 4.1 with the regression model of each preceding study are shown in

Table 4. Regression analysis result 1.

Model	R2	Adjusted R2	Durbin–Watson	Independent Variable	Standardized Coefficient (Beta)	t	p-Value	Multicollinearity Statistics
								Tolerance	VIF
Kang et al. [13]	0.150	0.133	2.162	EP	−0.244	−2.583	0.011	0.983	1.017
				LP	0.334	3.540	0.001	0.983	1.017
Seo and Lee [20]	0.385	0.365	1.993	TFA	0.611	3.608	0.000	0.223	4.481
				HH	0.038	0.166	0.869	0.124	8.047
				MB	−0.191	−0.191	0.849	0.226	4.418
Choi [21]	0.384	0.372	1.996	HH	0.009	0.052	0.958	0.223	4.479
				TFA	0.612	3.631	0.000	0.223	4.479
Forcada et al. [22]	0.021	−0.020	1.867	Lo 1-1	−0.085	−0.788	0.433	0.884	1.131
				Lo 1-2	−0.023	−0.197	0.844	0.765	1.307
				Lo 2-1	0.084	0.825	0.411	0.993	1.007
				Lo 2-2	0.110	0.959	0.340	0.790	1.266
Kim [23]	0.387	0.361	1.978	TFA	0.588	3.205	0.003	0.171	5.857
				HH	0.027	0.147	0.884	0.196	5.100
				Lo 3	−0.044	−0.535	0.594	0.975	1.025
				NFTB	0.037	0.396	0.693	0.745	1.342
This Study 1	0.523	0.503	2.285	TFA	0.559	7.385	0.000	0.877	1.140
				CP	0.202	2.718	0.008	0.907	1.103
				EP	−0.248	−3.380	0.001	0.934	1.070
				LP	0.161	2.168	0.033	0.911	1.097

. All models were analyzed as having linearity.

The model by Kang et al. [13] was a model for estimating the repair cost when the elapsed period and the lawsuit period were used as independent variables. The coefficient of determination of the regression model was analyzed to be 0.150. The Dubin–Watson value was 2.162, so there was no problem with the independence of the residuals and multicollinearity.

The model by Seo and Lee [20] estimated the repair cost of defects with the total floor area, the number of households, and the number of main buildings as independent variables. The coefficient of determination of the regression model was analyzed as 0.365. The Dubin–Watson value was 1.993, so there was no problem with the independence of the residuals. However, it was found that the coefficients of the number of households and the number of households among the independent variables were insignificant. In the case of the number of households, multicollinearity became a concern.

The model by Choi [21] estimated the repair cost using the number of households and the total floor area as independent variables. The coefficient of determination of the regression model was analyzed to be 0.384. The Dubin–Watson value was 1.996, which confirms that there was no problem with the independence of the residuals and the problem of multicollinearity. However, it was found that the coefficient of the number of households among the independent variables was insignificant.

In the model by Forcada et al. [22], the distance between the developer and buyer’s head office and the construction site was divided into projects within the basic local municipality, projects within the regional municipalities, and projects outside the regional municipalities, respectively, as independent variables. Since these are nominal variables, a binary dummy variable was additionally applied. Among the eight total independent variables in the model, the cases where the business operation status of developer was within the basic local municipality (Lo1-1), the developer was in the regional metropolitan municipality (Lo1-2), the builder was in the basic local municipality (Lo2-1), and the developer was in the metropolitan municipality (Lo2-2) were included. In the regression model, the coefficient of determination of the regression model was 0.021. There was no residual independence or multicollinearity problem, but the coefficients of all independent variables were insignificant. This was because all independent variables were nominal variables.

The application results of Kim’s model [23] estimated the repair cost of defects when the total floor area, number of households, location (Lo3), and number of floors in the tallest building were used as independent variables. Unlike Forcada et al. [22], the location (Lo3) of Kim’s model was a nominal variable divided into metropolitan and non-metropolitan areas. Therefore, the location (Lo 3) was also applied by adding a variable dummy in binary form. The analysis results indicated that only the original non-dummy variables were applied to the local variables, and the rest of the binary variables were excluded. The coefficient of determination of the regression model was 0.387. The Dubin–Watson value was 1.978, which confirmed no problem with the independence of the residuals and multicollinearity. However, the coefficients of all independent variables except for the total floor area among the independent variables were insignificant.

4.3. Suggested Model

In summary, the case analysis results for the preceding research model in Section 4.2 showed that the effective independent variables in estimating the defect repair cost and dependent variables were assumed to be total floor area, elapsed period, and lawsuit period. In addition, since the construction period is assumed to be a valid independent variable, regression analysis was conducted using these, and for convenience, it is referred to as this study’s model 1. As shown in Table 4, the coefficient of determination of the regression model was 0.523, and the Dubin–Watson value was 2.285, which was slightly increased compared to other models, but there was no problem with the independence of the residuals. In addition, the coefficients of all independent variables were significant, and there was no multicollinearity problem.

This study’s model 1 is as shown in

Table 5. Coefficients of this study’s model 1.

Model		Unstandardized Coefficients		Standardized Coefficients (Beta)	t	Sig.
		B	Std. Error
1	(Constant)	−277,561.179	260,242.528		−1.067	0.289
	TFA	7.081	0.959	0.559	7.385	0.000
	CP	14,037.694	5164.691	0.202	2.718	0.008
	EP	−5417.073	1602.755	−0.248	−3.380	0.001
	LP	16,809.405	7752.889	0.161	2.168	0.033

below, this regression model used total floor area (TFA), construction period (CP), elapsed period (EP), and lawsuit period (LP) as independent variables. The coefficients of these four variables were all significant at the 95% level. The coefficient of the total floor area of the regression model was 7.652, the coefficient of the elapsed period was −6331.264, and the coefficient of the lawsuit period was 18,440.671. The housing defect repair cost (DRC) was directly proportional to the total floor area and lawsuit period but inverse to the elapsed period. Equation (2) below provides a summary.

DRC = 7.081 × TFA +14,037.694 × CP − 5417.073 × EP + 16,809.405 × LP − 277,561.179

(2)

Meanwhile, since some independent variables appeared to have autocorrelation, we examined whether there was an interaction effect through combinations of each independent variable. From the independent variables listed in Table 3 to the additionally proposed construction period, each independent variable was multiplied to transform into a new independent variable, which was then reflected in the regression model for analysis. This is referred to as this study’s model 2 to distinguish it. Model 1 and model 2 of this study are examined together, and the regression analysis results are shown in

Table 6. Regression analysis result 2.

Model	R2	Adjusted R2	Durbin–Watson	Independent Variable	Standardized Coefficient (Beta)	t	p-Value	Multicollinearity Statistics
								Tolerance	VIF
This Study 1	0.523	0.503	2.285	TFA	0.559	7.385	0.000	0.877	1.140
				CP	0.202	2.718	0.008	0.907	1.103
				EP	−0.248	−3.380	0.001	0.934	1.070
				LP	0.161	2.168	0.033	0.911	1.097
This Study 2	0.523	0.508	2.287	HH × CP	0.822	9.522	0.000	0.667	1.500
				CP × LP	−0.467	−5.467	0.000	0.682	1.467
				LP × LP	0.169	2.349	0.021	0.965	1.036

using three independent variables: the households multiplied by the construction period, the construction period multiplied by the litigation period, and the litigation period multiplied by the litigation period. According to this, the explanatory power was 0.523, the same as the model of this study presented in Table 4. The revised explanatory power was 0.508, slightly higher than before, but the Durbin-Watson value increased slightly. The coefficients of each independent variable were all significant, and the VIF value was less than 2, confirming no multicollinearity problem. Therefore, both models can be utilized.

As shown in

Table 7. Coefficients of this study’s model 2.

Model		Unstandardized Coefficients		Standardized Coefficients (Beta)	t	Sig.
		B	Std. Error
1	(Constant)	606,179.675	136,035.969		4.456	0.000
	HH × CP	30.554	3.209	0.822	9.522	0.000
	CP × LP	−314.700	57.560	−0.467	−5.467	0.000
	LP × LP	288.129	122.684	0.169	2.349	0.021

, model 2 uses the multiplied value of the households (HH) by the construction period (CP), the value of the construction period (CP) multiplied by the litigation period (LP), and the value of the litigation period (LP) multiplied by the litigation period (LP) as independent variables. The coefficients of these three variables were all significant at a confidence level of 95%. The coefficient of the value multiplied by the households (HH) by the construction period (CP) of the regression model was 30.554, the coefficient of the value multiplied by the construction period (CP) by the litigation period (LP) was −314.700, and the coefficient of the value multiplied by the litigation period (LP) was 288.129. In model 2, the housing defect repair cost (DRC) is proportional to the value multiplied by the households (HH), by the construction period (CP), and by the litigation period (LP) but is inversely proportional to the value multiplied by the construction period (CP) and by the litigation period (LP). This relation is summarized in Equation (3).

DRC = 30.554 × (HH × CP) − 314.7 × (CP × LP) + 288.129 × (LP × LP) + 606,179.675

(3)

5. Discussion

This discussion is based on a summary of the analysis results from previous studies on housing repair costs. These studies, while valuable, were often limited by a small number of cases, leading to less accurate predictions. Our research aims to address these limitations and provide a more effective model for predicting housing repair costs.

When comparing the coefficient of determination of the regression model, the coefficient of determination of the regression model predicted for 100 housing defect lawsuit cases in Korea was 0.021 to 0.387 for the previous research models and both model 1 and model 2 of this study were 0.523. However, compared to the results in previous studies, which were 0.561 to 0.865, the prediction was not up to expectation. This might be because the previous studies were conducted with a limited number of cases, 20 to 49. On the other hand, the model of this study, which was optimized and combined with the leading independent variables used in previous studies, showed a higher coefficient of determination than the model of the last survey. Therefore, this model would be more useful in the case of housing defect lawsuits.

Next, as far as the leading independent variables of the regression model are concerned, previous studies have used various independent variables such as EP, LP, VL, HWD, TFA, HH, MB, CC, Lo, and NFTB. Among them, TFA, HH, HWD, and Lo are the most frequently used independent variables. However, as can be confirmed in Table 4, TA and HH seem to have a mutually affecting relationship among the independent variables. From the results of the Seo and Lee model [20] analysis, HH appear to have a multicollinearity problem as its VIF exceeds 8. At the same time, since the VIF of TFA also exceeds 4, it is presumed that they correlate. The p value for HH in the regression model was also statistically insignificant. Since it commonly appeared in both Choi’s [21] and Kim’s models [23], TFA and HH have a mutually affecting relationship. Although TFA and HH are essential variables in estimating housing repair costs, it would be reasonable to use only one to satisfy the crucial assumptions of the regression model. Considering these points, this study model showed that when only TFA was adopted, excluding HH, the coefficient of determination was the highest, there was no multicollinearity issue, and the p value of each independent variable coefficient was statistically significant.

Other independent variables were also examined. EP and LP were first proposed in Kang et al.’s model [13] and adopted in this research model. These two variables did not have multicollinearity issues, and the p values of the coefficients of each independent variable were statistically significant. Therefore, EP and LP are useful as independent variables that support TFA. In addition, this study additionally discovered the construction period (CP) as an independent variable, and CP was also confirmed as a valid variable.

On the other hand, Lo, a variable for regional classification between the address of the builder or general contractor and the address of the house, was used by Forcada et al. [22]. This variable was subdivided into Lo1 and Lo2 in this study. Lo3 was added depending on whether the residential address was in the metropolitan area, which was used in Kim’s study [23]. However, the regression model coefficients were statistically insignificant since these are nominal variables. Further, since they did not affect the coefficient of determination, it might not have a substantial significance.

Since CC and HWD are not disclosed in Korean housing defect lawsuit cases, it was challenging to properly implement the models of Kang et al. [13], Choi [21], and Forcada et al. [22]. These previous research models utilized them as independent variables. Choi’s model adopted TFA and HH in addition to HWD, so the coefficient of determination was higher. At the same time, Kang et al.’s and Forcada et al.’s models [13,22] had extremely low coefficients of determination, probably because they used CC and HWD as the key independent variables.

In summary, among the independent variables suggested in the previous research model, TFA, CP, EP, and LP are considered the most valuable variables. In addition, the research model combining these variables in predicting the cost of repairing defects in Korean housing defect lawsuit cases is regarded as the most helpful model.

In addition, the interactions that consider the relationship between each independent variable are discussed. As confirmed in Section 2.2 and Section 4.1, TFA, HH, MB, etc., have a strong positive correlation, so if a new variable that combines them is used, the explanatory power of the regression model is increased, or it becomes a stable model. Therefore, this was also considered in this study, and the presence of an interaction was confirmed through combinations of key independent variables. However, according to the analysis results, there was no difference in the explanatory power of research models 1 and 2. Therefore, asserting the improvement effect from the interaction is not easy. Despite this, since it is based on the currently collected case data, it cannot be ruled out that it may be effective or more evident for new cases. Furthermore, since the explanatory power of the two models proposed in this study does not differ much, it would be reasonable to utilize them in a complementary manner.

6. Conclusions

Disputes over housing defects are becoming a global issue. Early reconciliation should be conducted at a reasonable level based on specific evidence to resolve conflicts. In Korea, disputes over housing defects are expanding into lawsuits and becoming a social problem. There are hundreds of issues in the dispute, and it is not easy to assert an appropriate repair cost based on the differences in perspectives between producers and consumers. Therefore, since it is challenging to settle in a situation where the claims of both sides are considerably different, no one can deny that the repair costs presented in the judgment are the most realistic alternative to balance the claims of both sides. From this perspective, if the information on the defect repair cost according to the judgment is appropriately predicted and utilized to mediate the dispute between the two parties, it will benefit both parties. The time wastage and the accompanying economic losses due to litigation can also be prevented.

With this in mind, this study sought a model and influencing factors for predicting defect repair costs. Although collecting data on defects was quite tricky, several valid influencing factors have been suggested through the efforts of previous studies, and these have been predicted using linear regression models. However, some problems, such as autocorrelation, multicollinearity, and the significance of independent variable coefficients, were identified in the previous research models. Therefore, this study proposed a new model that addresses these problems. The defect repair cost concluded by a Korean housing defect lawsuit was used as a dependent variable, and the independent variables suggested in previous studies were used to examine which linear regression model was optimal. Among the influential factors indicated in earlier studies, TFA, EP, and LP were confirmed as strong, independent variables because they did not have problems such as autocorrelation. In addition, this study proposed CP as an independent variable, and the linear regression model combining these four independent variables showed the best explanatory power. Our proposed regression model, which accounts for the interaction of each independent variable, is a significant step forward in our research. This model, using the number of households multiplied by the construction period, the construction period multiplied by the litigation period, and the litigation period multiplied by the litigation period as independent variables, has been rigorously tested and found to have no multicollinearity issue. The coefficients of all independent variables are statistically significant, further bolstering the model’s reliability. Additionally, the explanatory power of this model is comparable to the previous model, suggesting its potential to be used in conjunction with the existing model.

On the other hand, this study has limitations due to data collection and influencing factors. Although more data were secured compared to previous studies, they are still insufficient. Since it is challenging to collect housing defect data, it seems that this will not be easy to improve soon. Although most of the litigation materials in Korean courts are electronic documents, the verdicts are not made public for reasons such as privacy protection. Despite this, to improve housing defect problems, such information needs to be shared and utilized for research to solve the problem. In addition, because we relied on prior research and case studies, we examined limited influencing factors. Although this research model met the assumptions of the regression model and had higher explanatory power than previous research models, it did not reach a generally expected high level. However, since various factors differentiate each house, there might be an ample possibility that additional valid factors that can affect the housing defect repair cost can be explored from these. Therefore, in the future, methods such as listening to the opinions of related experts should also be considered.