Partial Cost Information and Empirical Contingency in Building Retrofit Cost Prediction

Abstract

This study retrospectively evaluated partial cost information and empirical contingency in an archived extract of public-building retrofits. The primary reporting sample comprised 246 records, with all 250 retained for sensitivity analysis. Adding four recorded component costs reduced total-cost mean absolute percentage error (MAPE) from 23.35% to 17.30% for genetic-algorithm-weighted case-based reasoning and from 23.05% to 14.68% for Extra Trees. The primary comparison did not establish a larger improvement for Extra Trees. Predicting the remaining cost and adding the observed subtotal produced 12.72% total-cost MAPE, but remaining-cost-weighted absolute percentage error was 19.28% and remaining-cost MAPE was 29.42%. The paired target-route difference also remained uncertain. Additional nested selection across 14 family-target routes yielded 12.64% total-cost MAPE within the same archive. The historical project-level 90th-percentile (P90) allowance was 35.47%; separate training/calibration/evaluation splits achieved 76–98% coverage with empirical P90 allowances calibrated on disjoint records. For the largest-area holdout, remaining-cost weighted error reached 46.74%, and the 35.47% historical allowance covered only 62% of cases. The selected extract differed from the other records in our 419-record research archive. Field timing and project dates were unavailable. The results support an evaluation framework, not demonstrated early-stage forecasting accuracy or a transferable contingency rate.

1. Introduction

Building owners need cost estimates to decide which retrofit projects can be completed within a limited budget. These estimates are often prepared before the scope of work and the costs of individual items are fully known. An estimate may therefore change as more information becomes available. Cost estimate classifications recognize this relationship between project definition and estimate accuracy [1,2,3]. For retrofit projects, it is useful to determine how much additional information improves an estimate and whether the improvement depends on the prediction method.

Case-based reasoning (CBR) estimates the cost of a new project by retrieving similar historical projects. The retrieved cases can help an estimator explain how a prediction was obtained [4]. Machine learning methods, such as Extra Trees, provide another way to learn relationships between project characteristics and costs. However, a comparison becomes difficult when the methods use different inputs or different test projects. The same inputs and test partitions are needed to determine whether additional information helps one method more than another. Another issue arises when an input is part of the cost being predicted. For example, recorded window and heating costs may explain a large share of total retrofit cost. A model can then produce a small percentage error for total cost even when its error for the remaining amount is substantial. These inputs are useful only if they are available when the estimate is prepared. Otherwise, their use may give an unrealistic picture of prediction performance [5,6]. Prediction accuracy also does not directly indicate how much contingency should be added to a budget. An average error summarizes prediction performance, whereas a contingency allowance is intended to cover a chosen proportion of possible cost outcomes. The allowance may change when a new project differs from the historical projects or when several projects are considered together [7,8]. These differences need to be examined before model results are used for budgeting.

This study examines whether the same added cost information changes two prediction procedures differently, how observed cost components affect the interpretation of error, and whether an empirical allowance survives the separation of calibration and evaluation and changes in project composition. Its contribution is an auditable evaluation of these linked questions on common projects. Paired comparisons, errors for the predicted remainder and separate allowance evaluation together show which claims the available information can support. The analysis concerns the archive derived from the Korea Land and Housing Corporation (LH) and motivates validation on future building projects.

2. Literature Review

Table 1 summarizes eleven studies that used historical data to estimate construction or retrofit costs. The studies differ in their applications, sample sizes, prediction methods, and evaluation procedures.

2.1. Methods for Construction Cost Estimation

Early cost estimates use regression, similarity, neural and ensemble models. CBR research addresses weighting, retention and robustness [9,10,11,12,13,14,15]. Across samples of 24 to 1978 cases, however, tuning is not always nested, local support is rarely quantified and added dimensions can weaken distance contrast. Recent work also compares smoothed CBR with neural and support-vector methods, reinforcing that analogue construction and estimator choice must be assessed together [16]. Ensemble methods capture nonlinearity [17,18] but seldom hold input boundaries constant while testing shift and calibration. Reviews identify inconsistent variables, proprietary samples and limited external assessment [19,20,21,22,23]. Other studies examine limited-data ensembles [24], prediction linked to construction operations optimization [25], and the need for explicit attribute availability and public datasets [26].

Park et al. [27], co-authored by members of the present team, developed genetic algorithm (GA)-weighted CBR models for preliminary public-building green remodeling costs using 401 cases retained from 456 records, with 305 cases for training and 96 for validation; their reported experiment used 15 selected validation cases. Section 4.1 of that paper describes “preliminary construction cost-related details established during project application” and field-survey-based estimates. Both studies use LH-derived retrofit records and overlapping building and cost attributes. The present study evaluates the effect of partial cost information across prediction methods, distinguishes total-cost from remaining-cost errors, and examines empirical contingency under different validation and project-composition conditions. Its contribution therefore lies in these research questions and the evaluation design, rather than in an independently collected project population.

Recent construction cost research also extends beyond conventional tree ensembles. Wang et al. [28] combine graph convolution, graph attention and a multilayer perceptron with a fused loss, while Wang et al. [29] examine TabPFN-based stacking with SHAP interpretation. These studies broaden the architecture choices and reinforce the need to state the target and validation design. In particular, the latter predicts permit-declared pre-commencement estimated cost, which is distinct from verified final expenditure. Neither its error magnitude nor a graph model’s performance can be transferred to a different archive with undocumented field maturity. The present gap concerns a matched evaluation of information boundaries, remaining-cost error and allowance validation, rather than a claim that CBR and Extra Trees exhaust recent prediction methods.

Table 1. Previous cost estimation studies.

Study	Application and Sample	Method	Target	Validation
Kim et al. [30]	Building construction; 530 (40 test)	MLR, ANN and CBR	Total cost	Single holdout
Kim and Kim [9]	PSC beam bridges; 216	GA-weighted CBR	Total bridge cost	Case comparison
Ahn et al. [10]	Early construction; 99 plus simulations	Covariance-aware CBR	Total cost	Simulation/applicability
Ji et al. [11]	Public apartments; 164	CBR with retention	Total cost	Matched comparison
Kwon et al. [13]	Housing maintenance; 90	GA-weighted CBR	Maintenance cost	Holdout
Fung et al. [17]	Seismic retrofit; 1978	Linear, ensemble, neural	Total cost	Tenfold CV
Alshboul et al. [18]	Green buildings; 283	XGBoost, DNN, RF	Total cost	Split plus CV
Uysal and Sonmez [14]	Conceptual cost; 24, 144, 30	Bagged CBR	Total cost	Fivefold CV
Xiao et al. [15]	Early construction; 1610 plus simulations	CBR robustness	Total cost	CV/perturbation
Shen et al. [16]	Residential cost; 55	Smoothed CBR, FNN, SVR	Unit/component index	Test comparison
Park et al. [27]	Public green remodeling; 401 (305 training, 96 validation)	GA-weighted CBR	Preliminary construction cost	15 selected validation cases
This study	Public retrofit; 246 primary (250 sensitivity)	k-NN CBR, ET, RF, Ridge, OLS, HGB	Total/remaining	Repeated nested CV

CBR = case-based reasoning; GA = genetic algorithm; ET = Extra Trees; MLR = multiple linear regression; ANN = artificial neural network; DNN = deep neural network; RF = random forest; FNN = fuzzy neural network; SVR = support vector regression; HGB = histogram gradient boosting; CV = cross-validation; OLS = ordinary least squares; k-NN = k-nearest neighbors; MAPE = mean absolute percentage error. The table summarizes selected studies and is not a systematic review.

Table 1. Previous cost estimation studies.

Study	Application and Sample	Method	Target	Validation
Kim et al. [30]	Building construction; 530 (40 test)	MLR, ANN and CBR	Total cost	Single holdout
Kim and Kim [9]	PSC beam bridges; 216	GA-weighted CBR	Total bridge cost	Case comparison
Ahn et al. [10]	Early construction; 99 plus simulations	Covariance-aware CBR	Total cost	Simulation/applicability
Ji et al. [11]	Public apartments; 164	CBR with retention	Total cost	Matched comparison
Kwon et al. [13]	Housing maintenance; 90	GA-weighted CBR	Maintenance cost	Holdout
Fung et al. [17]	Seismic retrofit; 1978	Linear, ensemble, neural	Total cost	Tenfold CV
Alshboul et al. [18]	Green buildings; 283	XGBoost, DNN, RF	Total cost	Split plus CV
Uysal and Sonmez [14]	Conceptual cost; 24, 144, 30	Bagged CBR	Total cost	Fivefold CV
Xiao et al. [15]	Early construction; 1610 plus simulations	CBR robustness	Total cost	CV/perturbation
Shen et al. [16]	Residential cost; 55	Smoothed CBR, FNN, SVR	Unit/component index	Test comparison
Park et al. [27]	Public green remodeling; 401 (305 training, 96 validation)	GA-weighted CBR	Preliminary construction cost	15 selected validation cases
This study	Public retrofit; 246 primary (250 sensitivity)	k-NN CBR, ET, RF, Ridge, OLS, HGB	Total/remaining	Repeated nested CV

CBR = case-based reasoning; GA = genetic algorithm; ET = Extra Trees; MLR = multiple linear regression; ANN = artificial neural network; DNN = deep neural network; RF = random forest; FNN = fuzzy neural network; SVR = support vector regression; HGB = histogram gradient boosting; CV = cross-validation; OLS = ordinary least squares; k-NN = k-nearest neighbors; MAPE = mean absolute percentage error. The table summarizes selected studies and is not a systematic review.

Estimate maturity depends on project and scope definition [1,2,3]. The descriptors, quantities and component costs define information sets. A decision-stage interpretation additionally requires that each field be available when the estimate is prepared. The studies summarized in Table 1 did not compare the effect of the same input change across model families on common test partitions. Let Y denote total cost, C the component subtotal and R = Y − C. Reconstructing Y gives the same absolute error as predicting R, but a different percentage error because the denominators differ:

$${\mathrm{APE}}_Y={\displaystyle \frac{|\widehat{R}-R|}{Y}}={\mathrm{APE}}_R{\displaystyle \frac{R}{Y}}$$

(1)

When C is a large share of Y, evaluating Y alone can make the error in the unknown amount appear smaller. The reviewed studies do not report errors for Y and R together.

2.2. Model Evaluation and Contingency

Accuracy depends on preprocessing, selection and assessment. Direct exponentiation targets a conditional median, whereas Duan smearing can improve mean calibration [31,32]. Nested validation separates selection from assessment; repeated overlapping folds require corrected uncertainty [33,34,35,36]. Importance rankings remain associational [37], and new cases require distribution and support checks [38,39]. Valid prediction intervals require exchangeability or correction [40,41,42]. Because mean absolute percentage error (MAPE) is asymmetric and denominator-dependent, weighted absolute percentage error (WAPE), bias and Y/R results are also needed.

Contingency differs from average error [7,8,43,44,45,46]. A reserve targets a required non-overrun probability. For project groups, it also depends on error cancellation and shared bias. Reference-class forecasting is therefore not only a statistical adjustment: it is a governance choice about which completed projects are sufficiently comparable, when that class is frozen and who approves later changes [47,48]. Table 1 contains no model evaluated at both project and portfolio scales after a distribution change.

2.3. Research Gaps

Previous studies have improved cost estimation through advances in similarity measures, feature weighting, and ensemble methods. However, improvements in overall prediction accuracy do not fully resolve three practical issues. First, the value of additional cost information cannot be separated from estimator choice without comparing models using the same information and validation partitions. Second, total-cost accuracy alone does not reveal how accurately the remaining cost is predicted when some components are already known. Third, contingency allowances derived from historical errors may be sensitive to project mix and grouping, limiting their applicability beyond the projects used to calculate them.

3. Materials and Methods

3.1. Study Procedure

Figure 1 summarizes the study procedure. Four retrospectively flagged records were excluded from the 250-record extract for the primary reporting sample. Five repeats of fivefold splitting produced 25 outer partitions shared by matched models within each sample. Inner cross-validation selected hyperparameters by total-cost MAPE; the selected settings were refitted on the outer training set before predicting its held-out fold. Section 3.4 describes an additional experiment that selects model family, target and hyperparameters together.

Figure 1. Study procedure and validation design.

The protocols distinguish fold-level model contrasts, retrospective contingency from five held-out predictions averaged per case, six composition holdouts, and new three-way training/calibration/evaluation splits. Each comparison shares partitions within its stated sample; the 246-case and 250-case protocols are not interchangeable. Only direct total-cost prediction from X1–X6 avoids component costs. Every remaining-cost route requires C when reconstructing Y, even if its fitted inputs contain only X1–X6. The 419-record linkage audit describes selection and does not add training data or external test cases. The additional model-comparison, calibration, and sensitivity analyses were performed using Python 3.11.2 (Python Software Foundation, Beaverton, OR, USA), with NumPy 1.26.4, pandas 2.2.3, SciPy 1.13.1, and scikit-learn 1.5.2. Figures 1–8 were generated using Matplotlib 3.9.3, whereas Figure A1 and Figure A2 were generated using Matplotlib 3.11.1.

3.2. Project Data

We analyzed a retained extract of 250 public-building retrofit records derived from the Korea Land and Housing Corporation (LH), South Korea. A record-level audit linked all 250 records to a 419-record workbook held by our research group: 248 geometric matches were unique, and 2 ambiguous matches were resolved using recorded costs. Table A8 compares the included records with the other 169 using the same workbook values. The descriptive archive comparison reported in Table A8 was implemented using NumPy 2.3.5 and pandas 3.0.1. This verifies a relationship with the retained archive; it does not establish that the workbook is the complete eligible-project population. The 419-record workbook used for this audit should not be equated with the 401-case analytical sample reported in [27]. We could not locate a dated extraction log identifying the preparer, preparation date or original record-level selection rule for the 250-record extract.

The included 250 records had a median gross floor area of 223.64 m² and nominal total cost of 147.54 million South Korean won (KRW), compared with 387.00 m² and KRW 216.26 million in the other 169 records. The descriptive Kolmogorov–Smirnov (KS) distances were 0.318 for floor area and 0.262 for cost. Buildings with at least three recorded floors comprised 8.0% and 17.2%, respectively; recorded scope and component-cost distributions also differed. Both groups were compared using the same 419-record workbook values, because three component entries differed from the preserved 250-record extract. These results do not support the assumption of representativeness. The primary 246-record comparison gave the same qualitative conclusion (Table A8).

The other 169 records had no X2 value above the full primary sample maximum of 2997.24 m² (0/169); their maximum was 1434.89 m². In contrast, 81/169 (47.93%) exceeded the 393.32 m² training maximum used in the deliberately restricted largest-50 holdout. These are different reference ranges. Remaining within the full sample’s univariate range does not establish representative sampling or adequate multivariate support.

All primary prediction analyses use the preserved extract’s nominal KRW values. Neither implementation dates nor defensible cost-base dates are encoded in the extract or linked workbook. An index-based restatement requires the price date of each amount and a common target date. Building completion year, the 2022 age reference and the publication year are not substitutes. We therefore report nominal-cost comparisons and retain price heterogeneity as a limitation; no defensible time window was available for an index-based sensitivity bound. The USD conversion in Appendix A is a display scale only [49].

The six initial inputs were building area (X₁, m²), gross floor area (X₂, m²), building age (X₃, years), number of floors (X₄), external-wall insulation work quantity (X₅, m²), and roof-insulation work quantity (X₆, m²). X₃ equals 2022 minus the recorded completion year; 2022 is the age reference year, not an asserted year of retrofit or data collection. Completion years in this extract range from 1966 to 2015. The four additional inputs were window replacement cost (X₇), door installation cost (X₈), high-efficiency heating, ventilation and air conditioning cost (X₉), and high-efficiency boiler cost (X₁₀). Recorded zeros were retained without imputing absence of work or missingness.

Four flagged records (IDs 7, 13, 142 and 204) were excluded from the primary reporting analysis, leaving 246 projects; all 250 were retained in sensitivity analyses. Table A6, Panel G records the affected fields, values and rules. Three records contained positive component costs below KRW 1000; the corresponding linked source values differed. The fourth had recorded building area greater than gross floor area despite more than one floor. This is a consistency flag requiring source clarification, not proof of an impossible building. The checks were developed retrospectively during reanalysis; no preregistration or dated record demonstrates that the exclusion decision preceded inspection of predictive accuracy. We therefore retain both samples and do not characterize the primary sample as prospectively quality-certified. Case 212 had a small positive remainder but met neither flag and was retained. In the full extract, X1 exceeded X2 in 79 of 104 one-floor records, none of 126 two-floor records and 1 of 15 three-floor records; the inequality alone was not an exclusion rule.

We also examined the three discrepant component entries by substituting the linked workbook values in a separate copy, leaving the preserved data unchanged. With a fixed remaining-cost Extra Trees specification, paired versions used identical partitions at n = 249 (excluding only ID 142) and n = 250. Total-cost MAPE changed from 12.27% to 12.48% and from 12.39% to 12.57%, respectively (Table A12B). This is a source-version sensitivity, not proof of a transcription error or a reversal of the retrospective screening chronology.

Total recorded retrofit cost was denoted by Y, the component subtotal by C = X7 + X8 + X9 + X10, and the remaining cost by R = Y − C; all R values were positive. For this extract, field-level timestamps, estimate versions, contract status and payment status are unavailable, so we cannot verify the maturity of each X7–X10 or Y value. Table A1, Panel D records that boundary. The component-cost experiments condition on the recorded amounts, and their errors describe that information scenario. X1–X6 also presumes access to the recorded insulation quantities. In the primary sample, C/Y had a median of 27.36% and an interquartile range of 21.42–34.94%.

The variables were retained to define comparable information sets, not selected by searching all possible cost drivers. X1, X2 and X4 describe scale and geometry; X3 describes age at a fixed reference; X5 and X6 quantify recorded insulation scope; and X7–X10 represent the observed monetary subtotal. These roles support a controlled comparison with the inherited CBR specification. They do not imply completeness. Building use, detailed condition, accessibility, specification and material quality, region, procurement, contractor, project date and price basis could affect costs but are unavailable consistently. A recorded zero cannot distinguish the absence of work from incomplete recording. The resulting experiment assesses the retained fields rather than their sufficiency for a new project population.

Figure 2a lists the recorded building attributes, work quantities and component costs; panel (b) gives a schematic cost decomposition, and panel (c) crosses the two input sets with direct and remaining-cost targets. The bar is illustrative rather than a sample proportion. Every reconstruction of Y from R requires observed C. Adding the same C preserves absolute error, mean absolute error (MAE) and root mean squared error (RMSE) while changing percentage error denominators (Equation (1)).

Figure 2. Input sets, cost targets and prediction routes.

3.3. Cost Prediction Models

CBR was used because its predictions can be related to similar historical projects. Extra Trees was used to examine whether a tree ensemble responded differently to the same additional information. The comparison focused on the effect of the input set rather than identifying a universally best estimator. Equal-weight CBR, Dirichlet-weighted CBR, Ridge, and histogram gradient boosting were included in the additional comparisons. In the unfiltered sample, total-cost MAPE changed from 38.86% to 29.03% for median-scaled Ridge and from 25.89% to 20.48% for histogram gradient boosting when X₇–X₁₀ were added (Table A2A).

For CBR, each input was scaled using only the training data. Min-max scaling was the main specification. Logarithmic and rank-based transformations were examined as sensitivity checks. Ridge used a logarithm scaled by the nonzero training median, followed by standardization:

$$z_{\mathrm{ij},\mathrm{CBR}}={\displaystyle \frac{x_{\mathrm{ij}}-a_j}{b_j-a_j}};z_{\mathrm{ij},\mathrm{Ridge}}={\displaystyle \frac{\log (1+x_{\mathrm{ij}}/s_j)-{\mu }_j}{{\sigma }_j}}$$

(2)

Here a_j and b_j are the training minimum and maximum of input j, s_j is its nonzero training median, and μ_j and σ_j are the training mean and standard deviation after the logarithmic transformation. All scaling statistics are estimated within the relevant training fold. Median scaling is invariant to a positive change of measurement unit; log1p was retained as a separate, unit-dependent sensitivity.

CBR first calculated the distance between a test project and the training projects. The number of retrieved cases, distance measure, and case weighting were selected within the training data. Distance and prediction were calculated as follows:

$$d_{p,\alpha }(q,i)={\left({\sum }_{j=1}^m{\alpha }_j{|z_{\mathrm{qj}}-z_{\mathrm{ij}}|}^p\right)}^{1/p},p=1,2$$

(3)

$$\widehat{Y}(q)=\exp [{\displaystyle \frac{{\sum }_{i\in N_k\left(q\right)}{w}_i·\log \left(Y_i\right)}{{\sum }_{i\in N_k\left(q\right)}{w}_i}}]$$

(4)

Feature weights α_j are nonnegative and sum to one. Case weights w_i are uniform or proportional to inverse distance and normalized over the k retrieved cases; exact matches use their mean log cost. The distance power p is 1 or 2, and k is selected from 3, 5, 7, 10 and 15.

The primary CBR comparison used a genetic algorithm (GA) to select feature weights. The search used 50 individuals and 30 generations. A separate Dirichlet search assessed 512 combinations of feature weights and settings for each input set and outer split. All weight selection used the outer training sample. The held-out projects were not used to choose the weights. Table A2 provides the search settings and selection frequencies.

Extra Trees combined 250 randomized regression trees. The fraction of candidate features, the minimum leaf size, and the maximum tree depth were selected within the training data. Its prediction was the average of the tree predictions:

$$f_{\mathrm{ET}}(x)={\displaystyle \frac{1}{250}}{\sum }_{t=1}^{250}{h}_t(x)$$

(5)

The direct models predicted log(Y), which was converted back to cost by exponentiation. The remaining-cost models predicted log(R), converted it back to cost, and added C. The compared CBR and Extra Trees models used the same target, inputs, and outer test projects. A separate sensitivity check prevented a direct total cost prediction from falling below the known subtotal C:

$$\begin{array}{c}{\widehat{Y}}_{\mathrm{direct}}=\mathit{exp}(f_Y(x))\\ {\widehat{Y}}_{\mathrm{floor}}=\mathit{max}(C,\mathit{exp}(f_Y(x)))\\ {\widehat{Y}}_{\mathrm{residual}}=C+\mathit{exp}(f_R(x))\\ S={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\mathit{exp}({\widehat{e}}_i)\\ {\widehat{Y}}_{\mathrm{smear}}=C+\mathit{Sexp}(f_R(x))\end{array}$$

(6)

The floor at C was examined separately from changing the target to R. For the back-transformation sensitivity of the selected route, the n = 246 remaining-cost Extra Trees settings were retained within each of the original 25 outer splits. Their unsmeared predictions were reproduced before applying Duan smearing [31,32]. Fivefold out-of-fold (OOF) predictions within the outer training sample supplied log residuals; the factor S was the mean of exp(observed log(R) minus its training-held-out prediction). The same fitted model and factor were then applied to the outer test records. Outer test outcomes never entered the factor. This evaluates back-transformation conditional on the selected settings; it does not independently select a smearing rule. The earlier fixed-model n = 250 sensitivity is retained as a separate historical specification in Table A10.

3.4. Model Evaluation

The primary evaluation used five repeats of nested fivefold cross-validation. Each outer split divided the 246 projects into training and test samples. Inner validation selected the settings using total cost mean absolute percentage error (MAPE). The selected settings were then applied to the outer test projects. CBR and Extra Trees used the same 25 outer partitions. The analysis of all 250 records used separately generated partitions.

The original procedure kept hyperparameter selection separate from outer testing [33], but did not enclose family and target choice in the same selection process. Its lowest error is consequently a descriptive minimum among evaluated configurations [34]. We additionally report MAE and RMSE in million nominal KRW (KRW m), alongside MAPE, median absolute percentage error (MdAPE), WAPE, R squared and the descriptive ±15% tolerance. Remaining-cost metrics receive equal emphasis. For a reconstructed route, Y and R have identical absolute errors and therefore identical MAE and RMSE, while percentage errors and R squared differ. For a direct Y route, an implied remainder can be assessed as Ŷ − C; it need not be positive and is labeled as an implied remainder. Aggregate bias uses actual cost as the denominator:

$$\begin{array}{cc}\mathrm{MAPE}={\displaystyle \frac{100}{n}}{\sum }_{i=1}^n{\displaystyle \frac{\left|e_i\right|}{Y_i}}& \mathrm{WAPE}=100{\displaystyle \frac{{\sum }_{i=1}^n\left|e_i\right|}{{\sum }_{i=1}^n{Y}_i}}\\ \mathrm{Bias}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{e}_i& {\mathrm{Bias}}_{\mathrm{agg}}=100{\displaystyle \frac{{\sum }_{i=1}^n\widehat{Y_i}-{\sum }_{i=1}^n{Y}_i}{{\sum }_{i=1}^n{Y}_i}}\end{array}$$

(7)

The signed error is e_i = Ŷ_i − Y_i; negative aggregate bias therefore denotes underprediction.

For each outer split, the change in MAPE after adding X7–X10 was calculated for each method. The two changes were then compared. Changes in percentage errors are expressed in percentage points (pp). Because the training samples overlapped, the 25 estimates were not independent. The Nadeau–Bengio correction was used to calculate the standard error and confidence interval [35]:

$${\mathrm{SE}}_{\mathrm{corr}}=\sqrt{({\displaystyle \frac{1}{K}}+{\displaystyle \frac{n_{\mathrm{test}}}{n_{\mathrm{train}}}})s_{\delta }^2};t={\displaystyle \frac{\overline{\delta }}{{\mathrm{SE}}_{\mathrm{corr}}}},K=25$$

(8)

Small samples can still give wide intervals even when cross-validation is repeated [36]. Case bootstrap intervals and additional attribution checks were therefore reported separately from the corrected split comparisons. Feature importance describes predictive associations rather than causal effects. Permuting dependent inputs can also force extrapolation and distort importance estimates [50].

The additional n = 246 benchmark used the same 25 outer test partitions and a common fivefold inner partition within each training sample. Its candidate pool comprised Extra Trees, random forest, histogram gradient boosting, ordinary least squares, Ridge, and k-nearest neighbors with equal feature weights each predicting log(Y) or log(R), with C added for the latter. Training-median Y and R baselines complete the 14-route pool; these medians are calculated on the original cost scale, with C added for the R baseline. Family, target and hyperparameters were selected jointly using inner total-cost MAPE. The outer fold was untouched until the selected procedure was refitted. Division by positive training medians, log1p transformation and training-only standardization for linear models and min-max scaling for k-nearest neighbors were fitted inside each inner training partition. Table A9 gives grids and all 14 route results. Original GA-CBR was retained as its separate archived information-change comparison and was not re-optimized inside the expanded candidate pool. This is an exploratory internal validation of a stated selection rule; the candidate set itself was developed after examining the archive. The original selected-route result and the new joint-selection result retain separate labels because they estimate different procedures.

For component-cost sensitivity, the original selected Extra Trees models were refitted on their recorded outer-training data, then X7–X10 were perturbed only for held-out prediction. The same perturbed components formed C in the remaining-cost reconstruction. We used common multipliers of 0.8, 0.9, 1.1 and 1.2, and 100 Monte Carlo replicates of independent mean-one lognormal multipliers exp(σZ − σ²/2), Z standard normal, for σ = 0.05, 0.10, 0.20 and 0.30. An additional uniform multiplier on [0.7, 1.3] imposed a genuine ±30% bound. Recorded zeros remained zero and held-out Y stayed unchanged. The seed schedule and complete metrics accompany Table A13B.

3.5. Tests Using Different Project Groups

The originally selected remaining-cost model was tested on six groups that differed from the training projects. Five tests held out successive ID blocks: 1–50, 51–100, 101–150, 151–200, and 201–250. The sixth held out the 50 projects with the largest gross floor areas. The four retrospectively flagged records were excluded before each test. Model settings were selected again using only the remaining projects.

These tests examined sensitivity to project composition. The ID blocks index archive order rather than calendar time, and all groups came from the same LH extract. The tests were therefore neither temporal nor external validation. The six results were also not independent replications. A separate nearest-neighbor check compared the distance of the 201–250 group with the distances found within cases 1–200. This check used all 250 records and did not remove projects or change predictions. It provided a descriptive indication of whether the held-out projects were well represented in the training data [38,39].

3.6. Empirical Contingency

Each project received five held-out predictions from repeated cross-validation. These predictions were averaged before calculating project-level contingency diagnostics. A metric calculated from case-mean predictions differs from a mean of the 25 outer-fold metrics. We checked the effect of aggregation by calculating P90 separately within each repetition and after pooling all 1230 predictions, retaining the dependence between repeated predictions of a case. This check evaluates aggregation sensitivity; a single final fitted model remains a different deployment procedure.

An empirical contingency allowance was calculated from the ratio of actual cost to predicted cost. The allowance was set to zero if the selected quantile was negative. P80, P90, and P95 denoted allowances corresponding to the 80th, 90th, and 95th percentiles of this ratio. Coverage at the 12.72% fold-mean MAPE allowance was also calculated to illustrate what happens when MAPE is used as contingency:

$$\begin{array}{cc}{c}_q=\max [0,Q_q({\displaystyle \frac{Y_i}{{\widehat{Y}}_i}}-1)]& c_A=\max [0,{\displaystyle \frac{{\sum }_{i\in A}{Y}_i}{{\sum }_{i\in A}{\widehat{Y}}_i}}-1]\end{array}$$

(9)

For project groups, the same calculation used the sum of actual costs and the sum of predictions. For each group size of 5, 10, 25, 50 and 100, 10,000 subsets were sampled without replacement within each draw (NumPy seed 20292807). A group of 246 contained the full primary dataset. Sensitivity analyses examined replacement sampling and shared shocks. The main calculations used the same historical records for calibration and description. They did not provide a prospective coverage guarantee for new projects. Such guarantees require additional assumptions and validation [40,41,42]. Pointwise project-quantile intervals used 10,000 case-bootstrap resamples (seed 20291807). Composition-test P90 intervals used 10,000 resamples per test (seed 20293807 plus the test index, numbered 1–6); further sampling details are reported in Appendix A.2, and the archived analysis code is available from the corresponding author on reasonable request.

An additional calibration/evaluation experiment used ten seeded partitions, each with 146 proper training, 50 calibration and 50 evaluation records. The remaining-cost Extra Trees family and target were fixed from the original study. Only the 146 training records were used for hyperparameter selection and training-out-of-fold smearing. A single frozen fit then predicted both disjoint calibration and evaluation sets. The empirical P90 allowance was the nonnegative linear 90th percentile of calibration Y/Ŷ − 1 and was applied unchanged to the evaluation set. A finite-rank sensitivity used the 46th of 50 ordered ratios, ceil(51 × 0.90). Coverage is reported as covered/evaluated with exact binomial intervals separately by split; overlapping repetitions are not pooled as independent observations. This internal experiment does not independently validate the original 35.47% allowance or establish coverage under future price or project-mix changes.

A supplementary training-OOF allowance check reused the original 25 outer partitions and each route’s selected settings. Within outer training, fivefold out-of-fold predictions supplied the allowance, which was then applied to the outer-test predictions. We examined both the original selection folds and separately seeded OOF folds. Selection had already used the full outer-training sample, so these residuals retain selection dependence; OOF fits also use fewer records than the refitted prediction model. This conditional check complements the disjoint training/calibration/evaluation design and carries no split-conformal coverage guarantee (Table A13A).

4. Results

4.1. Effect of Additional Cost Information

In the n = 246 primary reporting analysis, direct log(Y) MAPE decreased from 23.35% to 17.30% for GA-weighted CBR and from 23.05% to 14.68% for Extra Trees (Table 2). The improvements were 6.05 and 8.36 percentage points. The Extra-Trees-minus-CBR change was −2.31 points (corrected 95% interval −5.20 to 0.58; p = 0.112), so the primary analysis did not establish a larger benefit for Extra Trees. Its direction favored Extra Trees in 21 of 25 splits, but those overlapping splits are not independent replications. Negative changes in Table 3 indicate lower MAPE. All component-cost results remain retrospective experiments conditional on observed X7–X10.

Table 2. Prediction performance. (A). Primary model comparisons. (B). Total and remaining cost errors. (C). Internal project composition tests.

(A)
Model/Target	Inputs	Y-MAPE, %	MAE, KRW m	RMSE, KRW m	Y-WAPE, %	R-WAPE, %
GA-weighted CBR	X1–X6	23.35 ± 4.06	43.83	87.65	22.61	—
GA-weighted CBR	X1–X10	17.30 ± 2.39	36.04	70.32	18.72	—
Extra Trees log(Y)	X1–X6	23.05 ± 4.79	39.98	80.93	20.68	—
Extra Trees log(Y)	X1–X10	14.68 ± 2.42	30.23	61.40	15.69	—
Extra Trees log(R) + C	X1–X10	12.72 ± 1.60	25.67	49.28	13.41	19.28
(B)
Metric	Total Cost Y			Remaining Cost R
WAPE, %	13.41			19.28
MdAPE, %	7.93			12.03
MAPE, %	12.72			29.42
R squared	0.873			0.730
Aggregate bias, % (case-means)	−6.11			−8.78
MAE, KRW million	25.67			25.67
RMSE, KRW million	49.28			49.28
(C)
Held-Out Reference Class	Test n	Median X2, m2	Test MAPE, %	Aggregate Bias, %	Coverage at 12.72%, %	Historical P90 Uplift, %
ID block 1–50	48	172.75	11.50	+0.13	83.33	28.17
ID block 51–100	50	163.15	14.25	−5.38	78.00	41.85
ID block 101–150	49	221.29	10.96	−5.75	87.76	18.00
ID block 151–200	50	171.01	10.97	−1.42	82.00	20.77
ID block 201–250	49	418.89	18.88	−17.93	57.14	55.33
Largest 50 projects by X2	50	622.24	23.84	−29.53	30.00	98.07

(A) Primary reporting sample n = 246 after four retrospective flags. MAPE is mean ± standard deviation (SD) over 25 outer folds; MAE, RMSE and WAPE are means of the corresponding fold metrics. KRW m = million nominal KRW. X1–X10 and all log(R) + C predictions are retrospective known-component-cost experiments. R-WAPE is shown here for the directly modeled remainder; Table A9 also gives implied-remainder metrics for direct routes. X1–X6 still requires recorded quantities. All five rows retain the original validation protocol. (B) MAPE, MdAPE, WAPE and R squared are means across 25 flag-excluded outer folds. The aggregate-bias row instead uses the 246 case-mean predictions. R-squared values for Y and R are calculated separately on each original-scale outer test fold. R-squared for Y in a reconstructed model is partly attributable to observed C; R-squared for R is the model-attributable figure. Y-MdAPE and R-MdAPE are median absolute percentage errors for Y and R. The row is the best-performing configuration in this comparison, not a nested family-selection estimate, and it requires C at the estimation point. (C) Each model was tuned within the complementary training records after the four retrospective exclusions. Aggregate bias uses actual cost as the denominator; negative values denote underprediction. P90 is the 90th percentile of observed cost divided by predicted cost minus one, truncated below at zero. These are internal composition tests, not temporal or external validation. Bootstrap intervals for P90 are reported in Table A7.

Table 3. Changes in prediction error. (A). Primary and full-sample analyses. (B). Alternative specifications and target sensitivity.

(A)
Estimator or Contrast	Mean Delta, pp	Corrected 95% Interval	t(24)	p
Primary n = 246: GA-weighted CBR, 23.35% to 17.30%	−6.05	−9.64 to −2.47	−3.48	0.002
Primary n = 246: Extra Trees, 23.05% to 14.68%	−8.36	−12.06 to −4.66	−4.67	<0.001
Primary n = 246: Extra Trees minus GA-weighted CBR	−2.31	−5.20 to 0.58	−1.65	0.112
Sensitivity n = 250: GA-weighted CBR, 24.62% to 17.41%	−7.21	−11.65 to −2.78	—	—
Sensitivity n = 250: Extra Trees, 25.74% to 14.59%	−11.15	−16.32 to −5.99	—	—
Sensitivity n = 250: Extra Trees minus GA-weighted CBR	−3.94	−7.80 to −0.07	−2.10	0.046
Primary n = 246: remaining ET minus direct ET, X1–X10	−1.97	−3.97 to 0.04	−2.02	0.055
(B)
Estimator or Contrast	Mean Delta, pp	Corrected 95% Interval	t(24)	p
Equal-weight CBR, direct log(Y), 26.61% to 24.00%	−2.61	−7.44 to 2.22	—	—
Dirichlet-search CBR, direct log(Y), 24.28% to 20.09%	−4.19	−10.06 to 1.69	—	—
Extra Trees minus Dirichlet-search CBR, direct log(Y)	−6.96	−11.94 to −1.99	−2.89	0.008
Extra Trees minus equal-weight CBR, direct log(Y)	−8.54	−14.57 to −2.51	−2.92	0.007
Extra Trees minus CBR with inner-selected preprocessing, direct log(Y)	−6.96	−12.32 to −1.60	−2.68	0.013
Sensitivity log(R) + C: equal-weight CBR, X1–X6 to X1–X10	+1.43	−1.09 to 3.95	—	—
Sensitivity log(R) + C: Extra Trees, X1–X6 to X1–X10	−2.57	−4.97 to −0.17	—	—
Extra Trees minus equal-weight CBR, log(R) + C	−4.01	−6.48 to −1.53	−3.34	0.003

(A) pp = percentage points. Each change is X1–X10 MAPE minus X1–X6 MAPE; a negative difference in changes means a larger Extra Trees improvement. Primary rows exclude cases 7, 13, 142 and 204, regenerate folds at n = 246 and refit both procedures. Full-sample rows use n = 250. GA weighting and the complete distance specification were selected inside each outer-training sample. Intervals use the conservative Nadeau–Bengio correction across 25 overlapping outer estimates. Values use unrounded fold results. Em dashes denote within-method sensitivity changes for which only intervals are reported; they do not denote zero effects. The final row is a separate paired target-route contrast (log(R) + C minus direct log(Y)) on identical original outer predictions, not an input-change interaction. Its corrected interval conditions on the compared routes and does not remove historical route selection. (B) All rows in Panel B use n = 250 and common outer partitions and are sensitivity analyses. The five full-sample Extra Trees-minus-CBR specifications, including the GA result in Panel (A), form a dependent robustness family; no joint multiplicity-adjusted claim is made. The two displayed −6.96-point estimates arise from different CBR specifications and are numerically equal only after rounding. Dirichlet search evaluated 512 joint candidates per input set and split. The log(R) + C rows predict R and reconstruct Y by adding observed C; they are conditional on C being observed. Values use unrounded fold results. Em dashes denote interval-only reporting for within-method sensitivity changes.

In the full n = 250 sensitivity, the Extra-Trees-minus-CBR change was −3.94 points (−7.80 to −0.07; p = 0.046). Screening reduced component-cost-free errors more than component-cost-conditional errors. However, the 1.63-point change in the between-method contrast reflects both the sample change and refitting on regenerated partitions; it does not isolate the effect of individual excluded records. The dependent full-sample and alternative-specification comparisons qualify the primary result and do not supply independent confirmation of a between-method advantage.

Figure 3a compares mean MAPE and descriptive standard deviations across the 25 outer partitions; panels (b) and (c) use the same change convention as Table 3: X1–X10 minus X1–X6, with a negative Extra-Trees-minus-CBR contrast indicating a larger Extra Trees improvement. The corrected interval includes zero. In the unfiltered support sensitivity, 50% of the 201–250 holdout exceeded the X1–X6 development threshold and 48% exceeded the X1–X10 threshold (Table A3D).

Figure 3. MAPE and error changes for CBR and Extra Trees with and without component-cost inputs. (a) mean MAPE ± SD for CBR and Extra Trees; (b) cumulative distributions of MAPE changes; (c) paired differences in changes (Extra Trees minus CBR), with the mean and corrected 95% confidence interval.

4.2. Total and Remaining Cost Errors

For the amount genuinely predicted, the original remaining-cost Extra Trees route had R-WAPE of 19.28%, R-MAPE of 29.42% and R squared of 0.730 (Table 2B). Its MAE was KRW 25.67 million and RMSE was KRW 49.28 million. Adding observed C preserved those absolute errors but yielded Y-MAPE of 12.72%, Y-WAPE of 13.41% and Y R squared of 0.873. The higher total-cost fit is partly attributable to known C. On identical outer test records, remaining-route minus direct-route Y-MAPE was −1.97 percentage points (dependence-corrected 95% interval −3.97 to 0.04; p = 0.055). Thus, the lower point estimate does not establish route superiority at the 5% level. Case 212 accounted for 24.47% of summed case-mean R percentage error; removing it reduced case-mean R-MAPE from 29.08% to 22.05%, but R-WAPE only from 19.11% to 18.88%. We retain it and report the denominator sensitivity rather than removing the difficult observation.

The matched log(R) + C full-sample sensitivity is conditional on C. Equal-weight CBR changed from 17.02% to 18.45%, Extra Trees from 15.14% to 12.56%, and their difference was −4.01 points (−6.48 to −1.53; Table 3).

The component-cost-free X1–X6 Extra Trees route achieved 23.05% MAPE. Its quantities still require verification at the intended decision point. The lower known-component-cost errors do not demonstrate performance under that information boundary. In the n = 250 sensitivity, flooring direct X1–X10 predictions at C changed MAPE only from 14.59% to 14.52%.

Prediction-time component perturbations increased the remaining-route MAPE to 13.11%, 14.00% and 15.22% for lognormal σ of 0.10, 0.20 and 0.30; multiplying all components by 0.8 or 1.2 gave 14.25% and 15.99% (Table A13B). A genuinely bounded ±30% uniform perturbation gave 13.73%. These values remain below the component-cost-free benchmark under the specified assumptions. They do not establish observed early-estimate performance: lognormal σ = 0.30 is not a ±30% bound, and its multiplier’s central 95% interval is approximately 0.531–1.721.

Errors were grouped by predicted-cost decile because grouping by the observed outcome couples error comparisons to the percentage error denominator. Primary-sample decile MAPE ranged from 7.44% to 18.80%. Aggregate bias was most negative in deciles 6 and 10 (−12.45% and −13.93%) but was close to zero in deciles 1 and 8 (+0.80% and +0.09%). The pattern is non-monotonic and does not support a blanket high-cost adjustment. WAPE, bias and original-scale residuals therefore complement project-level APE.

In the unfiltered n = 250 analysis, the X₅ = 0 versus X₅ > 0 MAPE ratio was 2.24 for repeated-validation case-mean predictions and 1.30 for the separate 201–250 holdout (Table A3A). This ratio comparison has no reported confidence interval. A distinct support diagnostic compared outside- with inside-support holdout errors; its MAPE difference was 4.98 points with a bootstrap interval of −2.83 to 12.49 (Table A3B). The primary X₅ groups had case-mean MAPE of 8.9% for positive values (n = 163) and 19.7% for zero values (n = 83). A recorded zero is not a verified absence of work, so these descriptive contrasts do not establish a deployment rule.

Figure 4a compares observed Y and R with case-mean held-out predictions, (b) shows their cumulative percentage-error distributions, and (c) ranks projects by remaining-cost error. Each mean uses five predictions. Panel (b) medians of 7.76% for Y and 13.08% for R differ from fold-mean MdAPE values of 7.93% and 12.03% because aggregation differs. Component costs are known, and family selection was not nested. The extreme R error is retained because a small denominator alone did not justify exclusion.

Figure 4. Prediction performance for total and remaining costs: (a) observed versus predicted costs; (b) cumulative percentage-error distributions; (c) project-level errors ranked by remaining-cost error.

In the additional common-partition benchmark, inner selection chose Extra Trees with log(R) in all 25 outer splits. The resulting Y-MAPE was 12.64% ± 1.54%, MAE KRW 25.47 million, RMSE KRW 48.67 million and R-WAPE 19.14% (Table A9; Figure 5a). Random forest with log(R) gave 13.90% Y-MAPE; the paired Extra-Trees-minus-random-forest difference was −1.26 points (corrected 95% interval −2.98 to 0.47; p = 0.146). Thus, the expanded comparison does not establish general Extra Trees superiority. All candidates use the same component-cost information and original-scale metrics, and the full table retains weaker baselines rather than reporting only the minimum.

Figure 5. Additional internal validation of selection and calibration: (a) model comparison using mean total-cost MAPE ± SD; (b) calibration-set contingency allowances; (c) evaluation coverage with exact 95% binomial confidence intervals for empirical-quantile coverage. The dashed line in (c) indicates the nominal 90% coverage target.

Panel (a) shows mean ± SD of outer-fold Y-MAPE, not confidence intervals. All routes use X1–X10; the inner selector chose ET log(R) in 25/25 folds. The two median baselines included in selection are omitted from the panel for readability. Panels (b) and (c) show separately calibrated P90 allowances and evaluation coverage; panel (c) includes exact 95% binomial intervals for the empirical-quantile coverage. Each split has 146 training, 50 calibration and 50 evaluation records with no within-split overlap. Repetitions reuse records. Calibration results are discussed in Section 4.4.

4.3. Performance for Different Project Groups

Figure 6 compares the six composition tests. The primary ID block MAPE ranged from 10.96% to 18.88%, and P90 ranged from 18.00% to 55.33%. The largest floor area group had a median X2 of 622.24 m² and a median total cost of KRW 279.88 million. Its MAPE was 23.84%, aggregate bias was −29.53%, and P90 was 98.07% (bootstrap interval 52.18–118.33%; Table A7A; point estimate in Table 2C). These results show a substantial loss of coverage for the larger projects.

Figure 6. Performance across project groups: (a) inner-validation and held-out total-cost MAPE; (b) aggregate signed error; (c) budget coverage using a 12.72% contingency allowance.

The unfiltered comparison between cases 1–200 and 201–250 also found differences in project composition. X₂ had the largest difference (KS D = 0.480; Holm-adjusted p < 0.001). Total cost, C, R, X₉, and X₇ differed, whereas C/Y and X₅ did not (Table A5). These findings describe project composition because ID order was not a documented time sequence.

Table A3, Table A5 and Table A7 together distinguish three associated characteristics: larger building and cost scale, weaker similarity to the development cases, and an ambiguous recorded insulation state. In the primary 201–250 block, median floor area was 418.89 m², compared with 163.15–221.29 m² across the other four ID blocks; aggregate bias was −17.93% and P90 was 55.33% (Table A7A). The supporting unfiltered 200/50 comparison in Table A5 had median floor areas of 180.75 and 413.44 m², respectively. The holdout differences in floor area and in total, component and remaining costs were supported by Holm-adjusted p values below 0.05 for X2, Y, C, R, X7 and X9. The component share C/Y did not differ detectably (adjusted p = 0.727). Thus, a larger known subtotal did not eliminate the larger amount still to be predicted. These composition contrasts identify a relevant change in the prediction task; they do not isolate the effect of any one variable.

Limited analogue support accompanies that shift. In the unfiltered ordered holdout, 24/50 projects exceeded the development P95 nearest-neighbor-distance threshold for X1–X10 (Table A3B,D). Their aggregate bias was −21.57%, versus −10.34% inside the threshold, and MAPE was 21.12% versus 16.14%. The MAPE-difference interval (−2.83 to 12.49 percentage points) includes zero, so this is a descriptive warning rather than a validated rejection rule. Table A3A also shows larger errors for X5 = 0 than X5 > 0, both in repeated-validation case means (19.34% versus 8.64%) and in the ordered holdout (21.36% versus 16.47%). However, X5 did not differ detectably between development and holdout samples after adjustment (Table A5). Its zero state therefore identifies an error-prone subgroup without explaining the block-level deterioration by itself. These n = 250 diagnostics support the interpretation of, but are not numerically interchangeable with, the n = 246 composition tests.

The example predictions in Table A7B make the remaining-cost limitation concrete. For the largest-cost ordered-holdout case, a recorded subtotal of KRW 615.5 million raised the reconstructed total prediction to KRW 682.8 million, against an observed total cost of KRW 1084.6 million; remaining-cost APE was still 85.7%. Adding known components can therefore improve the total prediction while leaving a large scope-dependent remainder unresolved. This selected example is from the unfiltered sensitivity and is not a population effect estimate. Together with the largest-area support diagnostics below, it motivates checking comparable large projects and the content of the remaining work before using a historical contingency rate.

Figure 6a compares inner validation MAPE with MAPE for each held-out group. Panel (b) shows aggregate signed error; negative values indicate underprediction. Panel (c) shows coverage after the same 12.72% allowance is added to each prediction. The dashed line marks the 79.7% reference coverage, and the dotted line marks the 90% reference target. The six holdouts reuse the same dataset and are not independent external or temporal cohorts. The largest area test indicates limited applicability rather than a recommended reserve.

The largest-area holdout reveals a specific extrapolation problem (Figure 7; Table A11). All 50 test projects exceeded the training maximum X2 of 393.32 m². Eleven had actual R above the training maximum of KRW 318.95 million, and 42% had X9 outside its training range. An unsmeared regression-tree ensemble averages training log-target values and cannot extrapolate R beyond the fitted target range; adding known C does not remove that limit. Reproduced holdout MAE was KRW 106.26 million, RMSE KRW 163.98 million, R-WAPE 46.74% and R squared −0.004. Even the historical 35.47% allowance covered only 31/50 cases (62%). In the ten largest test buildings, mean observed R was KRW 369.36 million versus the mean predicted R of KRW 116.18 million. These diagnostics support limited training support and target-range restriction as plausible contributors; they do not identify a causal effect of size or rule out omitted scope and price factors. This fixed-threshold stress check is not an independent calibration because the historical allowance used all 246 records; the disjoint experiment assesses calibration separately.

Panels (a), (c) and (d) show predictions, absolute errors and fixed-uplift coverage for five ordered area groups, each containing ten held-out projects and labeled by median area. Panel (b) shows out-of-range input frequencies. The fixed allowances in panel (d) were derived from the complete sample; the coverage results are not independent allowance calibration. Full results are shown in Table A11.

4.4. Empirical Contingency for Projects and Groups

For the flag-excluded reference class, single-project contingency was 13.87% at P80, 35.47% at P90 and 47.12% at P95 (Table 4, Panel A). The bootstrap interval for P90 was 23.70–42.89%. Treating the 12.72% fold-mean MAPE as an allowance covered only 79.7% of repeated case-mean predictions, rather than 90%. With grouping without replacement, P90 fell to 20.90% for five projects and 9.00% for 100, while the probability of aggregate underprediction rose from 52.44% to 99.97%. P90 gives reserve size; underprediction probability ignores magnitude. The complete n = 246 reference class required a 6.51% aggregate uplift relative to predicted cost. The MAPE calculated directly from the case-mean predictions was 12.51%.

P90 calculated separately within the five repetitions ranged from 34.19% to 37.01%; pooling all 1230 dependent held-out predictions gave 35.38%, compared with 35.47% from the 246 case-mean predictions (Table A12A). The observed comparison does not indicate a downward P90 effect from averaging predictions.

Figure 7. Training support and remaining-cost errors for the largest-area holdout.

Figure 7. Training support and remaining-cost errors for the largest-area holdout.

For the selected n = 246 route on its original partitions, training-only smearing reduced case-mean aggregate Y bias from −6.11% to −0.03% and retrospective P90 from 35.47% to 27.88% (Table 4B). However, fold-mean Y-MAPE increased from 12.72% to 15.16% and R-WAPE from 19.28% to 21.07%; Y-RMSE decreased from KRW 49.28 million to KRW 47.40 million. A smaller additional uplift therefore partly reflects a higher point prediction and is not evidence that every loss or budget outcome improves. The factors ranged from 1.062 to 1.189. These matched results directly assess the selected route, while the earlier n = 250 fixed-specification sensitivity remains in Table A10.

Table 4. Contingency for project groups. (A). Tuned remaining-cost model. (B). Matched back-transformation sensitivity for the selected n = 246 route.

(A)
Projects in Subset	1	5	10	25	50	100	246
Historical empirical uplift at P80, %	13.87	14.47	12.73	10.33	9.14	8.15	6.51
Historical empirical uplift at P90, %	35.47	20.90	16.60	12.77	10.71	9.00	6.51
Historical empirical uplift at P95, %	47.12	25.50	19.82	14.71	11.89	9.76	6.51
Probability of subset underprediction, %	52.44	67.13	77.01	90.92	98.10	99.97	100.00
(B)
Back-Transformation	Y-MAPE, %	R-WAPE, %	Y-bias, %		P90 uplift, %	Y-RMSE, KRW m
Naive exp(f)	12.72	19.28	−6.11		35.47	49.28
Training-OOF smearing	15.16	21.07	−0.03		27.88	47.40

(A) P80, P90 and P95 are empirical quantiles of subset observed cost divided by subset predicted cost minus one, truncated below at zero. Sizes 5–100 use 10,000 draws without replacement; size 1 uses individual projects and size 246 the entire primary sample. Each subset ratio is a predicted-cost-weighted mean of project ratios. Its quantiles need not decrease monotonically with subset size. The rise in P80 from 13.87% to 14.47% is not caused by truncation at zero; both quantiles are positive. These values describe the finite observed reference class. (B) Panel B uses the selected n = 246 remaining-cost Extra Trees route on identical original outer partitions. Y-MAPE, R-WAPE and RMSE are fold means; aggregate bias and P90 use five held-out predictions averaged per case. Smearing factors are estimated only from training-out-of-fold residuals, conditional on the original selected settings. No outer-test outcome enters a factor. P90 remains a descriptive historical quantile; lower uplift alone does not imply better calibrated final budgets. The earlier fixed n = 250 sensitivity is retained in Table A10, Panel C.

Table 4. Contingency for project groups. (A). Tuned remaining-cost model. (B). Matched back-transformation sensitivity for the selected n = 246 route.

(A)
Projects in Subset	1	5	10	25	50	100	246
Historical empirical uplift at P80, %	13.87	14.47	12.73	10.33	9.14	8.15	6.51
Historical empirical uplift at P90, %	35.47	20.90	16.60	12.77	10.71	9.00	6.51
Historical empirical uplift at P95, %	47.12	25.50	19.82	14.71	11.89	9.76	6.51
Probability of subset underprediction, %	52.44	67.13	77.01	90.92	98.10	99.97	100.00
(B)
Back-Transformation	Y-MAPE, %	R-WAPE, %	Y-bias, %		P90 uplift, %	Y-RMSE, KRW m
Naive exp(f)	12.72	19.28	−6.11		35.47	49.28
Training-OOF smearing	15.16	21.07	−0.03		27.88	47.40

(A) P80, P90 and P95 are empirical quantiles of subset observed cost divided by subset predicted cost minus one, truncated below at zero. Sizes 5–100 use 10,000 draws without replacement; size 1 uses individual projects and size 246 the entire primary sample. Each subset ratio is a predicted-cost-weighted mean of project ratios. Its quantiles need not decrease monotonically with subset size. The rise in P80 from 13.87% to 14.47% is not caused by truncation at zero; both quantiles are positive. These values describe the finite observed reference class. (B) Panel B uses the selected n = 246 remaining-cost Extra Trees route on identical original outer partitions. Y-MAPE, R-WAPE and RMSE are fold means; aggregate bias and P90 use five held-out predictions averaged per case. Smearing factors are estimated only from training-out-of-fold residuals, conditional on the original selected settings. No outer-test outcome enters a factor. P90 remains a descriptive historical quantile; lower uplift alone does not imply better calibrated final budgets. The earlier fixed n = 250 sensitivity is retained in Table A10, Panel C.

Figure 8a ranks project uplift as 100 × (Y/Ŷ − 1); negative values denote overprediction. Panel (b) gives empirical allowances with pointwise 95% bootstrap intervals, and (c) gives quantiles for sampled project groups. Table 4 reports aggregate underprediction probability. At 246 projects, only one aggregate ratio remains, so P80, P90 and P95 coincide. These retrospective estimates use the same records for calibration and description and provide no prospective coverage guarantee.

Figure 8. Historical empirical budget contingency: (a) ranked project-level required cost uplifts; (b) contingency estimates by target non-overrun probability, with 95% bootstrap intervals; (c) P80, P90, and P95 contingency estimates by sampled project-group size.

With disjoint calibration and evaluation records, unsmeared empirical P90 allowances ranged from 16.39% to 43.63% and evaluation coverage ranged from 38/50 to 49/50 (76–98%; Figure 5b,c and Table A10). The descriptive mean coverage across ten overlapping splits was 89.8%; it is not a binomial estimate from 500 independent projects. Split 1 covered 47/50 (94%; exact 95% interval 83.45–98.75%), whereas split 3 covered 38/50 (76%; 61.83–86.94%). The finite-rank sensitivity achieved 82–98% coverage, with a descriptive mean of 91.4%. Table A10 also reports the matched smeared fits. The wide spread demonstrates calibration uncertainty within this archive and prevents the interpretation of the historical 35.47% as a fixed future P90 budget rule.

Conditional training-OOF calibration gave mean P90 allowances of 34.14% for log(R) + C, 34.34% for direct X1–X10 and 49.78% for direct X1–X6, with mean outer-test coverage of 89.36%, 89.93% and 89.36%, respectively (Table A13A). Separately seeded OOF folds gave mean P90 allowances of 33.98%, 33.56% and 51.01%, with mean coverage of 89.85%, 89.85% and 89.68%, respectively, for the same three routes. These estimates suggest how the assumed information boundary affects the required allowance, while retaining the selection and refit-size qualifications described in Section 3.6.

5. Discussion

5.1. Additional Cost Information and Model Performance

The added component costs improved both GA-weighted CBR and Extra Trees within this archive, while their difference in improvement remained uncertain. Previous CBR work emphasizes feature weighting, retention and robustness [9,11,12,14,15]; the smaller contrast after learned weighting is consistent with similarity design affecting the comparison. The additional ensemble comparisons reinforce the need to assess the whole selection procedure. Recent graph-based and TabPFN stacking studies [28,29] address different data structures and prediction targets, so their findings inform method choice rather than a direct accuracy ranking on the LH extract.

The nested benchmark evaluates selection within an explicit candidate pool and complements the original GA-CBR comparison of information changes. It retains weaker baselines and uncertainty around paired contrasts, which makes the consequences of selecting the lowest observed error visible. The candidate pool and screening decisions nevertheless reflect prior work with this archive; Section 5.5 states the resulting validation limits.

An observed cost component has two roles: it can be a predictor and it can be an amount added directly to a predicted remainder. Reporting Y and R together separates this accounting contribution from the learned prediction. A low total-cost percentage error can coexist with substantial error for the unknown amount, especially when R is small. This distinction gives the information comparison a practical interpretation even when the preferred estimator remains uncertain.

The timing of information determines how these comparisons can be used. Cost-estimate classifications relate accuracy to project definition [1,2,3]. For application to a new estimate, both the component costs and the insulation quantities would need a dated snapshot at the intended decision stage, with an independently defined outcome. The present experiments quantify performance conditional on the recorded inputs.

5.2. Errors in Total and Remaining Cost

The remaining-cost errors in Section 4.2 describe the modeling burden when C is known. Reporting those errors alongside common MAE and RMSE prevents the larger total-cost denominator from obscuring prediction uncertainty. The remaining-cost formulation can be chosen for its information boundary and accounting transparency; the paired comparison leaves its accuracy advantage over direct prediction uncertain.

Case 212 illustrates the denominator sensitivity of remaining-cost MAPE: subtracting known components left a small remainder, and removing the case would have improved MAPE much more than WAPE. Retaining it and reporting several error measures therefore gives a more complete view of model performance. Predicted-cost deciles and the comparisons of zero versus positive X5 values also showed heterogeneous error patterns. Field definitions and validation on new projects are needed before these patterns can justify cost adjustments or exclusion rules.

5.3. Using Model Errors to Examine Contingency

The historical MAPE allowance and P90 allowance answer different questions. The former averages absolute percentage errors; the latter summarizes the upper tail of observed-to-predicted cost ratios. Contingency studies and reference-class forecasting similarly distinguish risk allowance from average accuracy [7,8,43,44,45,46,47,48]. The separate calibration and evaluation experiment shows how uncertainty in an estimated quantile translates into variable coverage, even within the same archive.

The loss of coverage in the largest-area holdout calls for a review of comparable projects and model support before increasing a reserve. At portfolio scale, overestimates partly offset underestimates, reducing the required uplift, while negative aggregate bias made some shortfall more frequent. Reserve size and shortfall probability therefore describe different aspects of budget risk. Future common shocks would add dependence that historical grouping alone cannot assess.

An operational evaluation would define a justified comparison population, dated information sets and a common price basis, freeze the prediction procedure, and reserve separate records for allowance calibration and final evaluation. The present three-way experiment demonstrates the last step internally. The remaining data requirements are stated in Section 5.5.

5.4. Cost Uncertainty and Economic Feasibility

Energy-retrofit appraisal connects intervention costs to energy-performance outcomes and measures such as net present value (NPV), return on investment (ROI) and payback [51]. For a point estimate Ŷ and cost uplift q, the stressed initial investment is K(q) = Ŷ(1 + q). NPV equals the discounted sum of annual net savings over the chosen horizon less K(q). Discounted net ROI is NPV divided by K(q); with constant annual net savings S, simple payback is K(q)/S. The allowance is a risk-budget scenario, not expected expenditure. Earmarking an unspent reserve alone does not reduce realized NPV; the calculation assumes that the stressed capital amount is spent.

For illustration only, consider a KRW 100 million capital estimate, annual net savings of KRW 10 million, a 15-year horizon and a 5% discount rate. Discounted savings total KRW 103.80 million. At capital multipliers of 1.0000, 1.1272 and 1.3547, NPV is respectively +3.80, −8.92 and −31.67 million KRW; discounted net ROI is +3.80%, −7.92% and −23.38%; simple payback is 10.00, 11.27 and 13.55 years (Table 5). The 12.72% and 35.47% uplifts illustrate consequences of the historical quantities, not validated probabilities for this hypothetical project. A marginally feasible option can cross an acceptance threshold as cost assumptions change. A uniform multiplier need not reorder simple-payback rankings, whereas intervention-specific uncertainty or funding constraints can alter priorities. The LH archive contains no measured energy savings or intervention-specific cash flows, so actual ROI, NPV or ranking effects cannot be estimated. Those applications require joint uncertainty in costs, savings, tariffs, maintenance, service life and discount assumptions.

Table 5. Illustrative capital-cost stress test for economic feasibility.

Cost Scenario	Capital KRW m	NPV KRW m	Discounted Net ROI %	Simple Payback Years
Point-estimate capital cost	100.00	3.80	3.80	10.00
12.72 percent cost stress	112.72	−8.92	−7.92	11.27
35.47 percent cost stress	135.47	−31.67	−23.38	13.55

Hypothetical assumptions: annual net savings KRW 10 million at each year end, 15 years, discount rate 5%, no residual value or additional cash flows. PV of savings = KRW 103.80 million. The full stressed capital amount is assumed spent at time zero. ROI = NPV/capital; simple payback ignores discounting. These are arithmetic scenarios, not observed energy-performance results or validated project-specific P90 budgets.

5.5. Limitations and Practical Use

The extract is not a probability sample, and the 419-record comparison shows differences in building scale, costs and recorded work content. We could not reconstruct the original extraction decisions, project implementation dates, cost-base dates or field-entry timestamps. Area conventions and recorded zeros remain incompletely documented. The exclusions and candidate development were retrospective. Joint family/target selection is nested within its stated candidate set, but earlier data-informed choices remain. The additional source-version analysis fixes one model setting; the training-OOF allowance analysis conditions on settings selected from the same outer-training data; and component perturbations are assumed error mechanisms. All are sensitivity analyses alongside the disjoint calibration experiment. Independent dated projects, measured energy savings and verified final-outturn records are still needed.

The supported use is to evaluate how a cost model is being interpreted. Information availability, remainder error, selection uncertainty and coverage under changed project composition should be reported together [52]. The largest-area holdout illustrates a concrete failure mode: models trained on smaller buildings substantially underpredicted the remainder. Dated and independently collected data, source-field verification and provider permission for wider access are necessary before extending the framework to actual budgeting or economic prioritization.

5.6. Information Collection and Decision-Time Uncertainty

The results suggest an information-collection sequence, as follows. First, verify the fields already used; distinguish true zero work from an unrecorded quantity, document the extent and specification of insulation and other retrofit work, and attach an estimate date and maturity status to each component amount. The X5 contrasts in Table A3 make scope verification relevant, while Table A11 shows why a new large project also needs comparable training cases. More detailed inputs alone cannot supply missing examples of large remaining costs. Until that support is established, an estimator should obtain a project-specific scope review and itemized estimate, rather than apply the historical 35.47% allowance automatically.

Second, collect information that can be known at the intended estimate date but is not included as a verified predictor here. Building use and occupancy can describe service requirements and constraints on working in an occupied building; region and site-access conditions can describe local procurement and execution conditions. Planned retrofit year, estimate date and component price-base dates can support a common price basis, while verified actual implementation dates are needed later to distinguish scheduling changes from price changes. Planned and actual dates must be stored separately. Detailed work packages, specifications, survey findings and procurement assumptions would help distinguish projects with similar floor areas but different remaining scope. These are candidate explanations for unexplained errors, not demonstrated causes of the observed block or size effects; this study has not estimated the accuracy gain from adding building use, region or retrofit year.

The available quantitative evidence for extra information concerns recorded component costs. On the matched Extra Trees comparison, adding X7–X10 reduced direct total-cost MAPE from 23.05% to 14.68%; predicting R and adding C gave 12.72%, without establishing an advantage over direct prediction. Under assumed prediction-time component error, remaining-route MAPE increased to 15.22% for mean-one lognormal σ = 0.30 and to 13.73% for independent uniform multipliers on [0.7, 1.3] (Table A13B). These sensitivities indicate that information quality matters, but they do not measure the benefit of collecting a particular new field. A future evaluation should add verified descriptor, scope and dated-cost groups incrementally on common partitions, retain only information available at the prediction date, and report changes in Y-MAPE, R-WAPE, bias and independently evaluated coverage. Dated cohorts and sufficiently represented building-use, regional and size groups would permit assessment of where a gain persists.

Finally, some realized information cannot be known with certainty when the estimate is prepared. Concealed deterioration may be discovered only during intrusive inspection or construction; later design changes, contractor outcomes and future price or schedule shocks may remain uncertain. Surveys and documented assumptions can reduce parts of this uncertainty, but realized changes and final expenditure must remain outcomes for later evaluation. At the decision date, their plausible consequences should be represented by explicit scenarios and a separately calibrated allowance, with the estimate updated when new evidence becomes available. This separates missing but collectable descriptors from uncertainty that remains at the chosen decision stage, and prevents future information from being used as if it were already observed.

6. Conclusions

The data support three bounded findings. First, adding four recorded component costs reduced error for both GA-weighted CBR and Extra Trees, while the primary corrected interval did not establish a difference in the magnitude of improvement. Second, the original remaining-cost route had 19.28% R-WAPE and 29.42% R-MAPE despite a reconstructed total-cost MAPE of 12.72%; its paired advantage over direct prediction was uncertain. Third, the model transferred poorly to the largest-area holdout, where R-WAPE reached 46.74% and a 35.47% historical allowance covered only 62% of cases. The extract also differed from the other records in the research archive.

The methodological implication is an evaluation sequence that distinguishes the information observed, the amount predicted and the allowance evaluated. Joint inner selection makes the candidate comparison explicit, while separate calibration and evaluation expose uncertainty in coverage. This sequence connects model assessment to the decisions needed before a contingency rate can be applied.

Smearing reduced the additional historical uplift while worsening relative prediction errors, showing that the point forecast and reserve must be assessed together. The illustrative economic calculation similarly shows how spending a cost allowance can turn a marginally positive NPV negative. Applying that calculation to actual retrofit choices requires independently assessed savings and cost outcomes.

Prospective use requires validation on independently collected, dated projects with documented cost versions, price bases and selection rules.

Future studies should freeze the model and information boundary before assessing separate calibration and evaluation cohorts, including larger buildings. Economic applications also need independently validated energy savings, tariffs, maintenance and service-life assumptions.

Appendix A.1. Data Definitions and Supporting Tables

Table A1. Data definitions (Panel (A)). Descriptive statistics (Panel (B)). Primary descriptive statistics (Panel (C)). Recorded field provenance and decision-time availability (Panel (D)).

(A)
Variable	Description		Input Variable Group		Unit	Interpretation Constraint
X1	Building area		Baseline		m2	Recorded building-area field; not relabeled from area inequalities
X2	Gross floor area		Baseline		m2	Recorded gross-floor-area field; distinct from X1
X3	Building age at reference year 2022		Baseline		years	2022 minus completion year; not age at retrofit
X4	Number of floors		Baseline		count	Recorded floor count
X5	External-wall insulation work quantity		Scope		m2	Zero is a recorded value, not verified absence of work
X6	Roof-insulation work quantity		Scope		m2	Recorded roof work area; retain source units
X7	Window replacement cost		Recorded cost		USD	Conditional input; contains one sub-USD-1 source value
X8	Door installation cost		Recorded cost		USD	Conditional input; contains two sub-USD-1 source values
X9	High-efficiency HVAC cost		Recorded cost		USD	Conditional input; part of Y
X10	High-efficiency boiler cost		Recorded cost		USD	Conditional input; part of Y; strongly quantized
Y	Total recorded retrofit cost		Outcome		USD	Recorded outcome; project dates not encoded in extract
(B)
Variable	Mean	SD	Minimum	Q1	Median	Q3	Maximum	Skewness	Zero, %	VIF
X1, m2	229.02	144.24	73.40	143.38	185.87	271.73	1108.47	2.96	0.0	4.14
X2, m2	369.28	448.61	78.00	149.04	223.64	369.16	2997.24	3.75	0.0	7.67
X3, years	16.42	5.77	7	13	15	17	56	2.61	0.0	1.21
X4, count	1.69	0.69	1	1	2	2	5	1.09	0.0	2.55
X5, m2	247.28	254.93	0	0	247.92	379.34	2100.00	2.21	34.4	1.28
X6, m2	125.58	141.90	0	0	118.48	184.90	750.00	1.40	41.6	1.19
X7, USD (thousands)	23.80	33.59	0	10.28	14.67	27.03	300.49	5.36	8.0	2.14
X8, USD (thousands)	2.42	3.57	0	0	0.73	3.74	24.87	2.34	45.2	1.07
X9, USD (thousands)	13.79	17.00	0	4.61	10.06	18.14	135.95	3.65	17.2	1.30
X10, USD (thousands)	1.55	3.62	0	0	0.60	1.66	31.09	5.75	37.6	1.06
Y, USD (thousands)	136.62	109.44	5.80	82.23	106.63	160.77	798.98	3.18	0.0	-
(C)
Variable	Median		Q1		Q3		Minimum		Maximum	Zero, n
X1	185.87		143.38		271.73		73.40		1108.47	0
X2	227.68		148.71		370.78		78.00		2997.24	0
X3	15.00		13.00		17.00		7.00		56.00	0
X4	2.00		1.00		2.00		1.00		5.00	0
X5	250.00		0.00		386.79		0.00		2100.00	83
X6	118.48		0.00		181.60		0.00		750.00	102
X7	20.43		14.43		37.55		0.00		415.76	19
X8	1.02		0.00		5.17		0.00		34.42	112
X9	13.85		6.38		25.10		0.00		188.10	42
X10	0.87		0.00		2.30		0.00		43.01	91
Y	148.02		114.37		223.48		8.03		1105.47	0
(D)
Field	Recorded Content/Source				Timing and Cost Maturity				Implication
X5, X6	Insulation quantities in the LH-derived extract				Scope/version timestamps unavailable				Component-cost-free does not mean verified early-stage
X7	Window replacement amount; archived monetary field				Preliminary/contract/final status unverified				Retrospective known component
X8	Door installation amount; archived monetary field				Preliminary/contract/final status unverified				Retrospective known component
X9	High-efficiency HVAC amount; archived monetary field				Preliminary/contract/final status unverified				Retrospective known component
X10	High-efficiency boiler amount; archived monetary field				Preliminary/contract/final status unverified				Retrospective known component
Y	Total recorded retrofit cost; archived outcome field				Price date and final-outturn status unverified				Prediction target is recorded cost

(A) Sample basis: unfiltered n = 250. (B) Sample basis: unfiltered n = 250. (C) Primary sample n = 246 after excluding IDs 7, 13, 142 and 204. Units: X₁, X₂, X₅ and X₆ in m²; X₃ in years; X₄ in floors; X₇–X₁₀ and Y in million KRW. C/Y median = 27.36%; Q1 = 21.42%; Q3 = 34.94%. Zero counts describe recorded values without inferring absence of work. Full-sample descriptions remain in Panel (B). (D) Field-level timestamps, estimate versions and contract/payment status were not available for the present extract. No field timing was imputed.

Table A1. Data definitions (Panel (A)). Descriptive statistics (Panel (B)). Primary descriptive statistics (Panel (C)). Recorded field provenance and decision-time availability (Panel (D)).

(A)
Variable	Description		Input Variable Group		Unit	Interpretation Constraint
X1	Building area		Baseline		m2	Recorded building-area field; not relabeled from area inequalities
X2	Gross floor area		Baseline		m2	Recorded gross-floor-area field; distinct from X1
X3	Building age at reference year 2022		Baseline		years	2022 minus completion year; not age at retrofit
X4	Number of floors		Baseline		count	Recorded floor count
X5	External-wall insulation work quantity		Scope		m2	Zero is a recorded value, not verified absence of work
X6	Roof-insulation work quantity		Scope		m2	Recorded roof work area; retain source units
X7	Window replacement cost		Recorded cost		USD	Conditional input; contains one sub-USD-1 source value
X8	Door installation cost		Recorded cost		USD	Conditional input; contains two sub-USD-1 source values
X9	High-efficiency HVAC cost		Recorded cost		USD	Conditional input; part of Y
X10	High-efficiency boiler cost		Recorded cost		USD	Conditional input; part of Y; strongly quantized
Y	Total recorded retrofit cost		Outcome		USD	Recorded outcome; project dates not encoded in extract
(B)
Variable	Mean	SD	Minimum	Q1	Median	Q3	Maximum	Skewness	Zero, %	VIF
X1, m2	229.02	144.24	73.40	143.38	185.87	271.73	1108.47	2.96	0.0	4.14
X2, m2	369.28	448.61	78.00	149.04	223.64	369.16	2997.24	3.75	0.0	7.67
X3, years	16.42	5.77	7	13	15	17	56	2.61	0.0	1.21
X4, count	1.69	0.69	1	1	2	2	5	1.09	0.0	2.55
X5, m2	247.28	254.93	0	0	247.92	379.34	2100.00	2.21	34.4	1.28
X6, m2	125.58	141.90	0	0	118.48	184.90	750.00	1.40	41.6	1.19
X7, USD (thousands)	23.80	33.59	0	10.28	14.67	27.03	300.49	5.36	8.0	2.14
X8, USD (thousands)	2.42	3.57	0	0	0.73	3.74	24.87	2.34	45.2	1.07
X9, USD (thousands)	13.79	17.00	0	4.61	10.06	18.14	135.95	3.65	17.2	1.30
X10, USD (thousands)	1.55	3.62	0	0	0.60	1.66	31.09	5.75	37.6	1.06
Y, USD (thousands)	136.62	109.44	5.80	82.23	106.63	160.77	798.98	3.18	0.0	-
(C)
Variable	Median		Q1		Q3		Minimum		Maximum	Zero, n
X1	185.87		143.38		271.73		73.40		1108.47	0
X2	227.68		148.71		370.78		78.00		2997.24	0
X3	15.00		13.00		17.00		7.00		56.00	0
X4	2.00		1.00		2.00		1.00		5.00	0
X5	250.00		0.00		386.79		0.00		2100.00	83
X6	118.48		0.00		181.60		0.00		750.00	102
X7	20.43		14.43		37.55		0.00		415.76	19
X8	1.02		0.00		5.17		0.00		34.42	112
X9	13.85		6.38		25.10		0.00		188.10	42
X10	0.87		0.00		2.30		0.00		43.01	91
Y	148.02		114.37		223.48		8.03		1105.47	0
(D)
Field	Recorded Content/Source				Timing and Cost Maturity				Implication
X5, X6	Insulation quantities in the LH-derived extract				Scope/version timestamps unavailable				Component-cost-free does not mean verified early-stage
X7	Window replacement amount; archived monetary field				Preliminary/contract/final status unverified				Retrospective known component
X8	Door installation amount; archived monetary field				Preliminary/contract/final status unverified				Retrospective known component
X9	High-efficiency HVAC amount; archived monetary field				Preliminary/contract/final status unverified				Retrospective known component
X10	High-efficiency boiler amount; archived monetary field				Preliminary/contract/final status unverified				Retrospective known component
Y	Total recorded retrofit cost; archived outcome field				Price date and final-outturn status unverified				Prediction target is recorded cost

(A) Sample basis: unfiltered n = 250. (B) Sample basis: unfiltered n = 250. (C) Primary sample n = 246 after excluding IDs 7, 13, 142 and 204. Units: X₁, X₂, X₅ and X₆ in m²; X₃ in years; X₄ in floors; X₇–X₁₀ and Y in million KRW. C/Y median = 27.36%; Q1 = 21.42%; Q3 = 34.94%. Zero counts describe recorded values without inferring absence of work. Full-sample descriptions remain in Panel (B). (D) Field-level timestamps, estimate versions and contract/payment status were not available for the present extract. No field timing was imputed.

Table A2. Comparator models (Panel (A)). Selected model settings (Panel (B)).

(A)
Estimator Specification	Repeated Scope, %	Repeated Cost, %	Delta, pp	Ordered Scope, %	Ordered Cost, %	Delta, pp
CBR, equal-weight baseline	26.61	24.00	−2.61	36.14	38.00	+1.86
Extra Trees, unconstrained baseline	25.74	14.59	−11.15	32.28	26.33	−5.95
Ridge, median-scaled logarithmic inputs	38.86	29.03	−9.83	35.52	28.13	−7.39
Ridge, log1p USD (thousands) sensitivity	38.76	26.40	−12.37	38.19	29.70	−8.49
Ridge, log1p recorded-unit sensitivity	38.76	27.84	−10.92	38.19	35.12	−3.07
Ridge, raw inputs sensitivity	47.12	42.75	−4.37	39.01	38.94	−0.07
Histogram gradient boosting	25.89	20.48	−5.41	32.17	28.99	−3.17
(B)
Specification		Distinct Configurations		Modal Configuration		Modal Frequency
Scope CBR		7		k = 7; p = 1; distance weighting		10/25
Component-cost-informed CBR		4		k = 5; p = 1; distance weighting		11/25
Scope Extra Trees		7		depth = 8; features = 1.0; leaf = 2		10/25
Component-cost-informed direct Extra Trees		3		unrestricted depth; features = 1.0; leaf = 1		16/25
Scope-informed remaining-cost Extra Trees		5		depth = 8; features = 1.0; leaf = 2		9/25
Full residual Extra Trees		6		unrestricted depth; features = 0.6; leaf = 1		9/25
Scope median-scaled logarithmic Ridge		2		alpha = 10		19/25
Component-cost-informed median-scaled logarithmic Ridge		2		alpha = 10		23/25

(A) Sample basis: unfiltered n = 250. (B) Sample basis: unfiltered n = 250.

Table A2. Comparator models (Panel (A)). Selected model settings (Panel (B)).

(A)
Estimator Specification	Repeated Scope, %	Repeated Cost, %	Delta, pp	Ordered Scope, %	Ordered Cost, %	Delta, pp
CBR, equal-weight baseline	26.61	24.00	−2.61	36.14	38.00	+1.86
Extra Trees, unconstrained baseline	25.74	14.59	−11.15	32.28	26.33	−5.95
Ridge, median-scaled logarithmic inputs	38.86	29.03	−9.83	35.52	28.13	−7.39
Ridge, log1p USD (thousands) sensitivity	38.76	26.40	−12.37	38.19	29.70	−8.49
Ridge, log1p recorded-unit sensitivity	38.76	27.84	−10.92	38.19	35.12	−3.07
Ridge, raw inputs sensitivity	47.12	42.75	−4.37	39.01	38.94	−0.07
Histogram gradient boosting	25.89	20.48	−5.41	32.17	28.99	−3.17
(B)
Specification		Distinct Configurations		Modal Configuration		Modal Frequency
Scope CBR		7		k = 7; p = 1; distance weighting		10/25
Component-cost-informed CBR		4		k = 5; p = 1; distance weighting		11/25
Scope Extra Trees		7		depth = 8; features = 1.0; leaf = 2		10/25
Component-cost-informed direct Extra Trees		3		unrestricted depth; features = 1.0; leaf = 1		16/25
Scope-informed remaining-cost Extra Trees		5		depth = 8; features = 1.0; leaf = 2		9/25
Full residual Extra Trees		6		unrestricted depth; features = 0.6; leaf = 1		9/25
Scope median-scaled logarithmic Ridge		2		alpha = 10		19/25
Component-cost-informed median-scaled logarithmic Ridge		2		alpha = 10		23/25

(A) Sample basis: unfiltered n = 250. (B) Sample basis: unfiltered n = 250.

Table A3. Errors by insulation quantity (Panel (A)). Nearest neighbor support (Panel (B)). Case level calibration (Panel (C)). Nearest-neighbor geometry (Panel (D)).

(A)
Validation Setting		X5 > 0, n	X5 > 0 MAPE, %		X5 = 0, n	X5 = 0 MAPE, %	X5 = 0/X5 > 0 Error Ratio
Repeated validation, case-mean out-of-fold predictions		164	8.64		86	19.34	2.24
Ordered 200/50 holdout		29	16.47		21	21.36	1.30
(B)
Support Group		n	Y-MAPE, % (95% Interval)		Y-WAPE, %	Aggregate Bias, % (95% Interval)
Inside development P95		26	16.14 (11.14 to 21.55)		17.51	−10.34 (−18.01 to −0.92)
Outside development P95		24	21.12 (15.59 to 26.82)		24.14	−21.57 (−28.00 to −13.46)
Outside minus inside		24 versus 26	+4.98 (−2.83 to 12.49)		—	—
(C)
Measure			Estimate		Case-Bootstrap 95% Interval
Log-scale intercept, USD thousands			−0.124		−0.359 to 0.122
Log-scale slope			1.032		0.980 to 1.081
Mean log observed/predicted ratio			0.023		0.001 to 0.046
Aggregate observed/predicted minus 1, %			6.34		3.32 to 9.61
(D)
Inputs	Distance/Scaling	Dev. NN Median	Dev. NN P95	Holdout NN Median	Above P95, n/N	Above P95, %	Median Ratio
X1–X6	Manhattan distance/6	0.0106	0.0445	0.0432	25/50	50.0	4.08
X1–X10	Manhattan distance/10	0.0231	0.0788	0.0751	24/50	48.0	3.25

(A) Sample basis: unfiltered n = 250. Repeated-validation values are calculated once per case after averaging its five out-of-fold predictions. Ordered-holdout values use one prediction per case. X₅ is an observed input state, not a verified measure of scope completeness. (B) Sample basis: ordered unfiltered development n = 200 and holdout n = 50. The support flag uses the X₁–X₁₀ Manhattan nearest-neighbor distance scaled on development cases 1–200 and the development leave-one-out P95 threshold. Intervals are percentile case-bootstrap intervals with 10,000 resamples for individual groups; the final MAPE-difference row uses 20,000 resamples (seed 20260978). Its interval includes zero, so the point difference is descriptive and does not confirm a group effect. Negative aggregate bias denotes underprediction. Source: authors’ analysis. (C) Sample basis: unfiltered n = 250. Each case contributes the mean of its five out-of-fold predictions. The intercept and slope come from log(observed Y) regressed on log(predicted Y) after expressing both in USD thousands. Intervals use 10,000 percentile case-bootstrap resamples. These stabilized case-level diagnostics are distinct from the 25 fold-level MAPE estimates. Source: authors’ analysis. (D) This diagnostic uses all 250 archived rows and is retained as a sensitivity analysis. Variables were min-max scaled using development cases 1–200 only. The threshold is the 95th percentile of leave-one-out nearest-neighbor distances within development data; holdout distances use the nearest development case. The diagnostic describes data-support coverage and neither excludes cases nor retunes models. NN = nearest-neighbor; LOO = leave one out.

Table A3. Errors by insulation quantity (Panel (A)). Nearest neighbor support (Panel (B)). Case level calibration (Panel (C)). Nearest-neighbor geometry (Panel (D)).

(A)
Validation Setting		X5 > 0, n	X5 > 0 MAPE, %		X5 = 0, n	X5 = 0 MAPE, %	X5 = 0/X5 > 0 Error Ratio
Repeated validation, case-mean out-of-fold predictions		164	8.64		86	19.34	2.24
Ordered 200/50 holdout		29	16.47		21	21.36	1.30
(B)
Support Group		n	Y-MAPE, % (95% Interval)		Y-WAPE, %	Aggregate Bias, % (95% Interval)
Inside development P95		26	16.14 (11.14 to 21.55)		17.51	−10.34 (−18.01 to −0.92)
Outside development P95		24	21.12 (15.59 to 26.82)		24.14	−21.57 (−28.00 to −13.46)
Outside minus inside		24 versus 26	+4.98 (−2.83 to 12.49)		—	—
(C)
Measure			Estimate		Case-Bootstrap 95% Interval
Log-scale intercept, USD thousands			−0.124		−0.359 to 0.122
Log-scale slope			1.032		0.980 to 1.081
Mean log observed/predicted ratio			0.023		0.001 to 0.046
Aggregate observed/predicted minus 1, %			6.34		3.32 to 9.61
(D)
Inputs	Distance/Scaling	Dev. NN Median	Dev. NN P95	Holdout NN Median	Above P95, n/N	Above P95, %	Median Ratio
X1–X6	Manhattan distance/6	0.0106	0.0445	0.0432	25/50	50.0	4.08
X1–X10	Manhattan distance/10	0.0231	0.0788	0.0751	24/50	48.0	3.25

(A) Sample basis: unfiltered n = 250. Repeated-validation values are calculated once per case after averaging its five out-of-fold predictions. Ordered-holdout values use one prediction per case. X₅ is an observed input state, not a verified measure of scope completeness. (B) Sample basis: ordered unfiltered development n = 200 and holdout n = 50. The support flag uses the X₁–X₁₀ Manhattan nearest-neighbor distance scaled on development cases 1–200 and the development leave-one-out P95 threshold. Intervals are percentile case-bootstrap intervals with 10,000 resamples for individual groups; the final MAPE-difference row uses 20,000 resamples (seed 20260978). Its interval includes zero, so the point difference is descriptive and does not confirm a group effect. Negative aggregate bias denotes underprediction. Source: authors’ analysis. (C) Sample basis: unfiltered n = 250. Each case contributes the mean of its five out-of-fold predictions. The intercept and slope come from log(observed Y) regressed on log(predicted Y) after expressing both in USD thousands. Intervals use 10,000 percentile case-bootstrap resamples. These stabilized case-level diagnostics are distinct from the 25 fold-level MAPE estimates. Source: authors’ analysis. (D) This diagnostic uses all 250 archived rows and is retained as a sensitivity analysis. Variables were min-max scaled using development cases 1–200 only. The threshold is the 95th percentile of leave-one-out nearest-neighbor distances within development data; holdout distances use the nearest development case. The diagnostic describes data-support coverage and neither excludes cases nor retunes models. NN = nearest-neighbor; LOO = leave one out.

Table A4. Feature importance (Panel (A)). Selection loss sensitivity (Panel (B)).

(A)
Variable	Extra Trees Rank	Mean Permutation Decrease in R2 (SD)		Ridge Rank	Mean Standardized Coefficient (SD)
X5	1	0.781 (0.159)		1	0.363 (0.026)
X6	2	0.536 (0.154)		3	0.291 (0.022)
X7	3	0.164 (0.041)		2	0.295 (0.048)
X8	4	0.025 (0.025)		4	0.116 (0.015)
X4	5	0.015 (0.012)		6	0.040 (0.011)
X2	6	0.012 (0.049)		8	−0.013 (0.027)
X1	7	0.010 (0.014)		5	−0.048 (0.025)
X10	8	0.007 (0.015)		7	0.029 (0.034)
X3	9	0.005 (0.009)		10	0.005 (0.018)
X9	10	−0.005 (0.013)		9	0.020 (0.020)
(B)
Inner Selection Criterion	Y-MAPE, %	Split SD, pp	R-MAPE, %	R-WAPE, %	R-MAE, Million KRW
Y-MAPE	12.56	1.57	30.39	18.71	24.87
R-MAPE	12.91	1.64	31.82	19.48	25.88
R-WAPE	12.68	1.80	31.32	18.57	24.70
R-MAE	12.73	1.78	31.70	18.67	24.83

(A) Sample basis: unfiltered n = 250. (B) Sample basis: unfiltered n = 250. All four criteria used the same five-times-repeated fivefold outer partitions and the same 12-candidate Extra Trees grid. Selection occurred only within each outer-training sample. Y-MAPE selection reproduces the unfiltered 250-record result of 12.56%. Source: authors’ analysis.

Table A4. Feature importance (Panel (A)). Selection loss sensitivity (Panel (B)).

(A)
Variable	Extra Trees Rank	Mean Permutation Decrease in R2 (SD)		Ridge Rank	Mean Standardized Coefficient (SD)
X5	1	0.781 (0.159)		1	0.363 (0.026)
X6	2	0.536 (0.154)		3	0.291 (0.022)
X7	3	0.164 (0.041)		2	0.295 (0.048)
X8	4	0.025 (0.025)		4	0.116 (0.015)
X4	5	0.015 (0.012)		6	0.040 (0.011)
X2	6	0.012 (0.049)		8	−0.013 (0.027)
X1	7	0.010 (0.014)		5	−0.048 (0.025)
X10	8	0.007 (0.015)		7	0.029 (0.034)
X3	9	0.005 (0.009)		10	0.005 (0.018)
X9	10	−0.005 (0.013)		9	0.020 (0.020)
(B)
Inner Selection Criterion	Y-MAPE, %	Split SD, pp	R-MAPE, %	R-WAPE, %	R-MAE, Million KRW
Y-MAPE	12.56	1.57	30.39	18.71	24.87
R-MAPE	12.91	1.64	31.82	19.48	25.88
R-WAPE	12.68	1.80	31.32	18.57	24.70
R-MAE	12.73	1.78	31.70	18.67	24.83

(A) Sample basis: unfiltered n = 250. (B) Sample basis: unfiltered n = 250. All four criteria used the same five-times-repeated fivefold outer partitions and the same 12-candidate Extra Trees grid. Selection occurred only within each outer-training sample. Y-MAPE selection reproduces the unfiltered 250-record result of 12.56%. Source: authors’ analysis.

Table A5. Project composition.

Variable	Description	Unit	Training Median	Holdout Median	KS D	Raw p	Holm p
X2	Gross floor area	m2	180.750	413.435	0.480	<0.001	<0.001
C	Recorded component subtotal	USD thousands	26.833	48.304	0.340	<0.001	0.002
R	Remaining cost	USD thousands	76.965	106.248	0.335	<0.001	0.002
Y	Total cost	USD thousands	102.576	146.508	0.330	<0.001	0.003
X9	High-efficiency HVAC	USD thousands	9.910	14.418	0.325	<0.001	0.003
X7	Window replacement	USD thousands	13.960	24.263	0.295	0.002	0.014
X3	Years since completion	years	15.000	16.000	0.265	0.006	0.050
X4	Floors	count	2.000	2.000	0.250	0.012	0.083
X1	Building area	m2	179.620	249.430	0.230	0.026	0.156
X10	High-efficiency boiler	USD thousands	0.561	1.122	0.225	0.031	0.157
X5	External-wall insulation quantity	m2	244.885	274.500	0.205	0.063	0.254
X6	Roof-insulation quantity	m2	114.650	145.000	0.160	0.242	0.727
C/Y	Recorded component share	%	26.901	29.554	0.155	0.275	0.727
X8	Door installation	USD thousands	0.729	0.829	0.135	0.438	0.727

Sample basis: ordered unfiltered development n = 200 and holdout n = 50. Cases 1–200 form the development sample and cases 201–250 the fixed holdout. Two-sided Kolmogorov–Smirnov p values are adjusted by Holm’s method across all 14 listed comparisons. Monetary fields use the fixed reporting conversion in the manuscript. The table demonstrates concentrated changes in selected size and cost variables; it does not imply that every covariate shifted or that the ordered split is temporal. Source: authors’ analysis.

Table A5. Project composition.

Variable	Description	Unit	Training Median	Holdout Median	KS D	Raw p	Holm p
X2	Gross floor area	m2	180.750	413.435	0.480	<0.001	<0.001
C	Recorded component subtotal	USD thousands	26.833	48.304	0.340	<0.001	0.002
R	Remaining cost	USD thousands	76.965	106.248	0.335	<0.001	0.002
Y	Total cost	USD thousands	102.576	146.508	0.330	<0.001	0.003
X9	High-efficiency HVAC	USD thousands	9.910	14.418	0.325	<0.001	0.003
X7	Window replacement	USD thousands	13.960	24.263	0.295	0.002	0.014
X3	Years since completion	years	15.000	16.000	0.265	0.006	0.050
X4	Floors	count	2.000	2.000	0.250	0.012	0.083
X1	Building area	m2	179.620	249.430	0.230	0.026	0.156
X10	High-efficiency boiler	USD thousands	0.561	1.122	0.225	0.031	0.157
X5	External-wall insulation quantity	m2	244.885	274.500	0.205	0.063	0.254
X6	Roof-insulation quantity	m2	114.650	145.000	0.160	0.242	0.727
C/Y	Recorded component share	%	26.901	29.554	0.155	0.275	0.727
X8	Door installation	USD thousands	0.729	0.829	0.135	0.438	0.727

Sample basis: ordered unfiltered development n = 200 and holdout n = 50. Cases 1–200 form the development sample and cases 201–250 the fixed holdout. Two-sided Kolmogorov–Smirnov p values are adjusted by Holm’s method across all 14 listed comparisons. Monetary fields use the fixed reporting conversion in the manuscript. The table demonstrates concentrated changes in selected size and cost variables; it does not imply that every covariate shifted or that the ordered split is temporal. Source: authors’ analysis.

Table A6. Data quality sensitivity (Panel (A)). Area and floor checks (Panel (B)). Component share groups (Panel (C)). Predicted cost deciles (Panel (D)). Preprocessing sensitivity (Panel (E)). Remaining cost sensitivity (Panel (F)). Retrospective screening audit (Panel (G)).

(A)
Model		Full n	Excluding Flagged n	Full Y-MAPE, %	Excluding Flagged Y-MAPE, %	Change, pp
CBR, X1–X6		250	246	26.61	25.29	−1.32
CBR, X1–X10		250	246	24.00	23.04	−0.96
GA-weighted CBR, X1–X6		250	246	24.62	23.35	−1.27
GA-weighted CBR, X1–X10		250	246	17.41	17.30	−0.11
Direct Extra Trees, X1–X6		250	246	25.74	23.05	−2.70
Direct Extra Trees, X1–X10 unconstrained		250	246	14.59	14.68	+0.09
Direct Extra Trees, X1–X10 with lower bound		250	246	14.52	14.60	+0.08
Remaining-cost Extra Trees, X1–X10 + C		250	246	12.56	12.72	+0.15
(B)
Floors	n	X1 Greater than X2, n	X1 Greater than X2, %	Median X2/X1	Minimum X2/X1	Maximum X2/X1
1	104	79	75.96	0.960	0.695	1.240
2	126	0	0.00	1.465	1.068	3.071
3	15	1	6.67	2.969	0.164	3.933
4	4	0	0.00	4.252	3.277	4.852
5	1	0	0.00	5.752	5.752	5.752
(C)
Component-Share Third				X5 State	n	Y-MAPE, %
Low				X5 = 0	17	24.24
Low				X5 > 0	67	10.85
Middle				X5 = 0	14	13.99
Middle				X5 > 0	69	7.71
High				X5 = 0	55	19.52
High				X5 > 0	28	7.17
(D)
Predicted-Cost Decile		n	Median Predicted Y, KRW Million	Aggregate Bias, % of Actual Cost	Required Uplift, % of Predicted Cost	MAPE, %
1		25	35.94	+0.80	−0.80	18.80
2		25	97.81	−7.33	+7.91	15.90
3		24	119.52	+4.66	−4.45	9.72
4		25	129.56	+2.41	−2.35	7.60
5		24	140.01	−3.90	+4.06	10.35
6		25	160.03	−12.45	+14.21	14.85
7		24	187.91	−4.07	+4.25	13.76
8		25	218.50	+0.09	−0.09	7.44
9		24	253.53	−2.88	+2.97	12.11
10		25	373.37	−13.93	+16.18	14.44
(E)
CBR Input Set		Outer-Fold MAPE, Mean ± SD, %			Selected Preprocessing, Folds
X1–X6		26.40 ± 5.71			log1p-min-max 15/25; min-max 10/25
X1–X10		22.21 ± 3.68			empirical rank 23/25; min-max 2/25
Extra-Trees-minus-CBR interaction		−6.96 points			corrected 95% interval −12.32 to −1.60; p = 0.013
(F)
Largest Case-Mean R-APE Values Excluded		n	R-MAPE, %	R-MdAPE, %	R-WAPE, %	Excluded Share of Summed R-APE, %
0		246	29.08	13.08	19.11	0.00
1		245	22.05	12.98	18.88	24.47
2		244	20.37	12.67	18.86	30.52
5		241	18.68	12.30	18.62	37.07
(G)
ID	Affected Field and Recorded Value	Flag Rule			Chronology and Action
7	X8 = KRW 6	0 < component amount < KRW 1000			Retrospective flag; excluded in n = 246; retained unchanged in n = 250
13	X8 = KRW 10	0 < component amount < KRW 1000			Retrospective flag; excluded in n = 246; retained unchanged in n = 250
142	X1 = 1057.91 m2; X2 = 173.00 m2; X4 = 3	X1 > X2 and X4 > 1			Definition-dependent consistency flag, not proven error; same sample treatment
204	X7 = KRW 70	0 < component amount < KRW 1000			Retrospective flag; excluded in n = 246; retained unchanged in n = 250

(A) Sample basis: flag-excluded n = 246 primary and unfiltered n = 250 sensitivity, as labeled by row. Rows 7, 13, 142 and 204 were excluded from the flag-excluded primary analysis. Models were rerun with the same repeated nested-validation design, split-specific seeds, tuning grids and lower-bound convention. The reduced-sample Extra-Trees-minus-equal-weight-CBR interaction was −6.11 percentage points (Nadeau–Bengio-corrected 95% interval −9.61 to −2.61; p = 0.001), compared with −8.54 points in the full sample. The reduced-sample Extra-Trees-minus-GA-CBR interaction was −2.31 points (−5.20 to 0.58; p = 0.112), compared with −3.94 points in the full sample. Corrected standard errors use the observed test-to-training-size ratio, approximately 0.25 in fivefold validation. The results do not establish whether the flagged values are correct; they quantify their influence while retaining the n = 250 analysis as a sensitivity check. Source: authors’ analysis. (B) Sample basis: unfiltered n = 250. X₁ is recorded building area and X₂ is recorded gross floor area. The screen reports arithmetic relationships between these fields. The published one-floor profiles in Table 6 of Park et al. [27], also include building area greater than gross floor area; this inequality alone is not treated as a source error. Measurement conventions should be checked before combining or relabeling the two fields. Source: authors’ analysis. (C) Sample basis: unfiltered n = 250. Each case contributes the mean of its five out-of-fold predictions from the selected X₁–X₁₀ remaining-cost Extra Trees model. Component-share thirds are based on observed C/Y and were examined after inspection. The table is descriptive because C/Y requires observed costs, cells are unequal and zero X₅ does not establish absence of work. Source: authors’ analysis. (D) Deciles use predicted rather than observed total cost. Aggregate bias equals 100 times summed predicted minus summed actual cost divided by summed actual cost; negative values denote underprediction. Required uplift uses predicted cost as denominator. Source: authors’ analysis. (E) This unfiltered n = 250 sensitivity selected preprocessing inside each outer-training sample together with neighbor count, Manhattan or Euclidean distance, and uniform or inverse-distance neighbor weights. Candidate transformations were partition-wise min-max scaling, log1p followed by min-max scaling, and an empirical-rank-to-uniform transformation fitted only on training data. Negative interaction values denote a larger MAPE reduction for Extra Trees after X₇–X₁₀ were added. Source: authors’ analysis. (F) Cases are ranked by R-APE calculated after averaging their five flag-excluded repeated out-of-fold predictions. Main Table 2 averages metrics across 25 outer folds: R-MAPE 29.42%, R-MdAPE 12.03%, R-WAPE 19.28% and R-squared for R of 0.730. Case 212 alone accounts for 24.47% of summed case-mean R-APE. Exclusions in this panel are diagnostic only and do not alter the selected model or the n = 246 primary sample. Source: authors’ analysis. (G) The history does not establish that criteria were fixed before predictive accuracy was inspected. The positive-cost threshold does not remove recorded zeros. The three small monetary entries differ from their linked workbook entries; they were not silently corrected. One-floor X1 > X2 records were retained. Case 212 was retained because a small positive R alone did not meet either rule.

Table A6. Data quality sensitivity (Panel (A)). Area and floor checks (Panel (B)). Component share groups (Panel (C)). Predicted cost deciles (Panel (D)). Preprocessing sensitivity (Panel (E)). Remaining cost sensitivity (Panel (F)). Retrospective screening audit (Panel (G)).

(A)
Model		Full n	Excluding Flagged n	Full Y-MAPE, %	Excluding Flagged Y-MAPE, %	Change, pp
CBR, X1–X6		250	246	26.61	25.29	−1.32
CBR, X1–X10		250	246	24.00	23.04	−0.96
GA-weighted CBR, X1–X6		250	246	24.62	23.35	−1.27
GA-weighted CBR, X1–X10		250	246	17.41	17.30	−0.11
Direct Extra Trees, X1–X6		250	246	25.74	23.05	−2.70
Direct Extra Trees, X1–X10 unconstrained		250	246	14.59	14.68	+0.09
Direct Extra Trees, X1–X10 with lower bound		250	246	14.52	14.60	+0.08
Remaining-cost Extra Trees, X1–X10 + C		250	246	12.56	12.72	+0.15
(B)
Floors	n	X1 Greater than X2, n	X1 Greater than X2, %	Median X2/X1	Minimum X2/X1	Maximum X2/X1
1	104	79	75.96	0.960	0.695	1.240
2	126	0	0.00	1.465	1.068	3.071
3	15	1	6.67	2.969	0.164	3.933
4	4	0	0.00	4.252	3.277	4.852
5	1	0	0.00	5.752	5.752	5.752
(C)
Component-Share Third				X5 State	n	Y-MAPE, %
Low				X5 = 0	17	24.24
Low				X5 > 0	67	10.85
Middle				X5 = 0	14	13.99
Middle				X5 > 0	69	7.71
High				X5 = 0	55	19.52
High				X5 > 0	28	7.17
(D)
Predicted-Cost Decile		n	Median Predicted Y, KRW Million	Aggregate Bias, % of Actual Cost	Required Uplift, % of Predicted Cost	MAPE, %
1		25	35.94	+0.80	−0.80	18.80
2		25	97.81	−7.33	+7.91	15.90
3		24	119.52	+4.66	−4.45	9.72
4		25	129.56	+2.41	−2.35	7.60
5		24	140.01	−3.90	+4.06	10.35
6		25	160.03	−12.45	+14.21	14.85
7		24	187.91	−4.07	+4.25	13.76
8		25	218.50	+0.09	−0.09	7.44
9		24	253.53	−2.88	+2.97	12.11
10		25	373.37	−13.93	+16.18	14.44
(E)
CBR Input Set		Outer-Fold MAPE, Mean ± SD, %			Selected Preprocessing, Folds
X1–X6		26.40 ± 5.71			log1p-min-max 15/25; min-max 10/25
X1–X10		22.21 ± 3.68			empirical rank 23/25; min-max 2/25
Extra-Trees-minus-CBR interaction		−6.96 points			corrected 95% interval −12.32 to −1.60; p = 0.013
(F)
Largest Case-Mean R-APE Values Excluded		n	R-MAPE, %	R-MdAPE, %	R-WAPE, %	Excluded Share of Summed R-APE, %
0		246	29.08	13.08	19.11	0.00
1		245	22.05	12.98	18.88	24.47
2		244	20.37	12.67	18.86	30.52
5		241	18.68	12.30	18.62	37.07
(G)
ID	Affected Field and Recorded Value	Flag Rule			Chronology and Action
7	X8 = KRW 6	0 < component amount < KRW 1000			Retrospective flag; excluded in n = 246; retained unchanged in n = 250
13	X8 = KRW 10	0 < component amount < KRW 1000			Retrospective flag; excluded in n = 246; retained unchanged in n = 250
142	X1 = 1057.91 m2; X2 = 173.00 m2; X4 = 3	X1 > X2 and X4 > 1			Definition-dependent consistency flag, not proven error; same sample treatment
204	X7 = KRW 70	0 < component amount < KRW 1000			Retrospective flag; excluded in n = 246; retained unchanged in n = 250

(A) Sample basis: flag-excluded n = 246 primary and unfiltered n = 250 sensitivity, as labeled by row. Rows 7, 13, 142 and 204 were excluded from the flag-excluded primary analysis. Models were rerun with the same repeated nested-validation design, split-specific seeds, tuning grids and lower-bound convention. The reduced-sample Extra-Trees-minus-equal-weight-CBR interaction was −6.11 percentage points (Nadeau–Bengio-corrected 95% interval −9.61 to −2.61; p = 0.001), compared with −8.54 points in the full sample. The reduced-sample Extra-Trees-minus-GA-CBR interaction was −2.31 points (−5.20 to 0.58; p = 0.112), compared with −3.94 points in the full sample. Corrected standard errors use the observed test-to-training-size ratio, approximately 0.25 in fivefold validation. The results do not establish whether the flagged values are correct; they quantify their influence while retaining the n = 250 analysis as a sensitivity check. Source: authors’ analysis. (B) Sample basis: unfiltered n = 250. X₁ is recorded building area and X₂ is recorded gross floor area. The screen reports arithmetic relationships between these fields. The published one-floor profiles in Table 6 of Park et al. [27], also include building area greater than gross floor area; this inequality alone is not treated as a source error. Measurement conventions should be checked before combining or relabeling the two fields. Source: authors’ analysis. (C) Sample basis: unfiltered n = 250. Each case contributes the mean of its five out-of-fold predictions from the selected X₁–X₁₀ remaining-cost Extra Trees model. Component-share thirds are based on observed C/Y and were examined after inspection. The table is descriptive because C/Y requires observed costs, cells are unequal and zero X₅ does not establish absence of work. Source: authors’ analysis. (D) Deciles use predicted rather than observed total cost. Aggregate bias equals 100 times summed predicted minus summed actual cost divided by summed actual cost; negative values denote underprediction. Required uplift uses predicted cost as denominator. Source: authors’ analysis. (E) This unfiltered n = 250 sensitivity selected preprocessing inside each outer-training sample together with neighbor count, Manhattan or Euclidean distance, and uniform or inverse-distance neighbor weights. Candidate transformations were partition-wise min-max scaling, log1p followed by min-max scaling, and an empirical-rank-to-uniform transformation fitted only on training data. Negative interaction values denote a larger MAPE reduction for Extra Trees after X₇–X₁₀ were added. Source: authors’ analysis. (F) Cases are ranked by R-APE calculated after averaging their five flag-excluded repeated out-of-fold predictions. Main Table 2 averages metrics across 25 outer folds: R-MAPE 29.42%, R-MdAPE 12.03%, R-WAPE 19.28% and R-squared for R of 0.730. Case 212 alone accounts for 24.47% of summed case-mean R-APE. Exclusions in this panel are diagnostic only and do not alter the selected model or the n = 246 primary sample. Source: authors’ analysis. (G) The history does not establish that criteria were fixed before predictive accuracy was inspected. The positive-cost threshold does not remove recorded zeros. The three small monetary entries differ from their linked workbook entries; they were not silently corrected. One-floor X1 > X2 records were retained. Case 212 was retained because a small positive R alone did not meet either rule.

Table A7. Composition holdouts (Panel (A)). Example predictions (Panel (B)).

(A)
Held-Out Reference Class	Train/Test n	Median X2, m2	MAPE, %	Aggregate Bias, %	Coverage at 12.72%, %	P90, %	P90 Bootstrap 95% Interval, %
ID block 1–50	198/48	172.75	11.50	+0.13	83.33	28.17	7.86 to 48.38
ID block 51–100	196/50	163.15	14.25	−5.38	78.00	41.85	16.42 to 108.33
ID block 101–150	197/49	221.29	10.96	−5.75	87.76	18.00	5.84 to 38.56
ID block 151–200	196/50	171.01	10.97	−1.42	82.00	20.77	11.32 to 24.99
ID block 201–250	197/49	418.89	18.88	−17.93	57.14	55.33	41.87 to 59.89
Largest 50 projects by X2	196/50	622.24	23.84	−29.53	30.00	98.07	52.18 to 118.33
(B)
Case and Selection Basis	Recorded Inputs (X1–X6; C)		Observed Y, KRW million	Four Predictions, KRW million	Selected-Model Y-APE/R-APE, %		Ordered P90 Reserve/Budget/Gap, KRW million
202: X5 > 0, nearest holdout-median Y	X1 120.2; X2 93.4; X3 24; X4 1; X5 350; X6 150; C 38.0		203.5	CBR6 122.0; ET6 129.0; direct ET10 138.7; remaining ET10 145.2	28.7/35.3		80.3/225.5/+22.0
247: X5 = 0, nearest holdout-median Y	X1 170.3; X2 742.5; X3 23; X4 4; X5 0; X6 0; C 101.5		199.5	CBR6 87.5; ET6 78.8; direct ET10 120.2; remaining ET10 144.7	27.5/55.9		80.0/224.7/+25.2
225: largest observed Y in ordered holdout	X1 874.7; X2 2979.8; X3 11; X4 3; X5 0; X6 0; C 615.5		1084.6	CBR6 118.0; ET6 105.5; direct ET10 204.7; remaining ET10 682.8	37.0/85.7		377.6/1060.4/−24.2

(A) Each C-conditional remaining-cost Extra Trees model was selected within the complementary flag-excluded training records. Aggregate bias uses actual cost as the denominator; negative values denote underprediction. Coverage applies the primary repeated-validation MAPE of 12.72% as an illustrative allowance. P90 intervals use 10,000 percentile case-bootstrap resamples. These are internal composition tests rather than temporal or external validation. Source: authors’ analysis. (B) This unfiltered n = 250 sensitivity uses CBR6 and ET6 with X1–X6; direct ET10 predicts total cost from X1–X10; remaining ET10 predicts R from X1–X10 and adds C. The selected-model error and P90 columns refer to remaining ET10 and use the tuned unfiltered ordered 200/50 holdout P90 of 55.31%. It differs from the flag-excluded ID-block 201–250 P90 of 55.33% in main Table 2, Panel C. Gap equals P90 budget minus observed Y. The three examples are deliberately not presented as typical accuracy. Source: authors’ analysis.

Table A7. Composition holdouts (Panel (A)). Example predictions (Panel (B)).

(A)
Held-Out Reference Class	Train/Test n	Median X2, m2	MAPE, %	Aggregate Bias, %	Coverage at 12.72%, %	P90, %	P90 Bootstrap 95% Interval, %
ID block 1–50	198/48	172.75	11.50	+0.13	83.33	28.17	7.86 to 48.38
ID block 51–100	196/50	163.15	14.25	−5.38	78.00	41.85	16.42 to 108.33
ID block 101–150	197/49	221.29	10.96	−5.75	87.76	18.00	5.84 to 38.56
ID block 151–200	196/50	171.01	10.97	−1.42	82.00	20.77	11.32 to 24.99
ID block 201–250	197/49	418.89	18.88	−17.93	57.14	55.33	41.87 to 59.89
Largest 50 projects by X2	196/50	622.24	23.84	−29.53	30.00	98.07	52.18 to 118.33
(B)
Case and Selection Basis	Recorded Inputs (X1–X6; C)		Observed Y, KRW million	Four Predictions, KRW million	Selected-Model Y-APE/R-APE, %		Ordered P90 Reserve/Budget/Gap, KRW million
202: X5 > 0, nearest holdout-median Y	X1 120.2; X2 93.4; X3 24; X4 1; X5 350; X6 150; C 38.0		203.5	CBR6 122.0; ET6 129.0; direct ET10 138.7; remaining ET10 145.2	28.7/35.3		80.3/225.5/+22.0
247: X5 = 0, nearest holdout-median Y	X1 170.3; X2 742.5; X3 23; X4 4; X5 0; X6 0; C 101.5		199.5	CBR6 87.5; ET6 78.8; direct ET10 120.2; remaining ET10 144.7	27.5/55.9		80.0/224.7/+25.2
225: largest observed Y in ordered holdout	X1 874.7; X2 2979.8; X3 11; X4 3; X5 0; X6 0; C 615.5		1084.6	CBR6 118.0; ET6 105.5; direct ET10 204.7; remaining ET10 682.8	37.0/85.7		377.6/1060.4/−24.2

(A) Each C-conditional remaining-cost Extra Trees model was selected within the complementary flag-excluded training records. Aggregate bias uses actual cost as the denominator; negative values denote underprediction. Coverage applies the primary repeated-validation MAPE of 12.72% as an illustrative allowance. P90 intervals use 10,000 percentile case-bootstrap resamples. These are internal composition tests rather than temporal or external validation. Source: authors’ analysis. (B) This unfiltered n = 250 sensitivity uses CBR6 and ET6 with X1–X6; direct ET10 predicts total cost from X1–X10; remaining ET10 predicts R from X1–X10 and adds C. The selected-model error and P90 columns refer to remaining ET10 and use the tuned unfiltered ordered 200/50 holdout P90 of 55.31%. It differs from the flag-excluded ID-block 201–250 P90 of 55.33% in main Table 2, Panel C. Gap equals P90 budget minus observed Y. The three examples are deliberately not presented as typical accuracy. Source: authors’ analysis.

Table A8. Included versus other records in the research archive (Panel (A)). Recorded scope and floor composition (Panel (B)).

(A)
Characteristic	Included 250 Median [IQR]	Other 169 Median [IQR]	SMD	KS D
Building area (m2)	185.87 [143.38, 271.73]	240.50 [178.94, 319.16]	−0.205	0.236
Gross floor area (m2)	223.64 [149.03, 369.15]	387.00 [262.40, 526.78]	−0.126	0.318
Age at reference year 2022 (years)	15.00 [13.00, 17.00]	16.00 [13.00, 25.00]	−0.511	0.266
Number of floors (count)	2.00 [1.00, 2.00]	2.00 [1.00, 2.00]	−0.229	0.098
External wall insulation quantity (m2)	247.92 [0.00, 379.34]	308.00 [0.00, 510.00]	−0.183	0.182
Roof insulation quantity (m2)	118.48 [0.00, 184.90]	149.00 [0.00, 247.65]	−0.108	0.176
Window component cost (KRW million)	20.37 [14.28, 37.40]	32.63 [15.59, 47.32]	−0.082	0.221
Door component cost (KRW million)	1.17 [0.00, 5.17]	2.55 [0.00, 5.85]	−0.136	0.228
HVAC component cost (KRW million)	13.92 [6.38, 25.10]	22.77 [8.41, 38.61]	−0.291	0.24
Boiler component cost (KRW million)	0.83 [0.00, 2.30]	1.44 [0.00, 3.41]	−0.23	0.171
Total recorded cost (KRW million)	147.54 [113.77, 222.43]	216.26 [132.18, 320.02]	−0.294	0.262
Recorded component subtotal (KRW million)	38.87 [27.87, 67.37]	63.97 [37.69, 90.72]	−0.207	0.246
Remaining cost (KRW million)	108.31 [77.06, 162.75]	156.83 [81.18, 227.89]	−0.298	0.256
Component share of total (percent)	27.47 [21.52, 35.03]	29.31 [22.44, 40.10]	−0.153	0.112
(B)
Recorded Characteristic	Included n/250 (%)		Other n/169 (%)
Floors 1	104 (41.6)		57 (33.7)
Floors 2	126 (50.4)		82 (48.5)
Floors other noninteger value	0 (0.0)		1 (0.6)
Floors grouped 3 or more	20 (8.0)		29 (17.2)
X5 recorded positive	164 (65.6)		108 (63.9)
X6 recorded positive	146 (58.4)		95 (56.2)
X7 recorded positive	230 (92.0)		159 (94.1)
X8 recorded positive	137 (54.8)		121 (71.6)
X9 recorded positive	207 (82.8)		143 (84.6)
X10 recorded positive	156 (62.4)		109 (64.5)

(A) Both groups use the same 419-record source workbook; monetary fields are million nominal KRW after reversing the stored conversion factor of 0.00072. This reverses a reporting scale and is not inflation adjustment. SMD = (included mean − other mean)/sqrt((included variance + other variance)/2); KS D is the largest empirical-CDF difference. These finite-archive descriptions are not equivalence tests or evidence of population representativeness. (B) A positive recorded amount or quantity is a field state, not verified intervention typology. One noninteger floor value in the other group is retained as recorded rather than silently rounded. The primary n = 246 inclusion sensitivity yielded the same direction of scale/cost differences; full aggregate statistics are retained with the analysis records.

Table A8. Included versus other records in the research archive (Panel (A)). Recorded scope and floor composition (Panel (B)).

(A)
Characteristic	Included 250 Median [IQR]	Other 169 Median [IQR]	SMD	KS D
Building area (m2)	185.87 [143.38, 271.73]	240.50 [178.94, 319.16]	−0.205	0.236
Gross floor area (m2)	223.64 [149.03, 369.15]	387.00 [262.40, 526.78]	−0.126	0.318
Age at reference year 2022 (years)	15.00 [13.00, 17.00]	16.00 [13.00, 25.00]	−0.511	0.266
Number of floors (count)	2.00 [1.00, 2.00]	2.00 [1.00, 2.00]	−0.229	0.098
External wall insulation quantity (m2)	247.92 [0.00, 379.34]	308.00 [0.00, 510.00]	−0.183	0.182
Roof insulation quantity (m2)	118.48 [0.00, 184.90]	149.00 [0.00, 247.65]	−0.108	0.176
Window component cost (KRW million)	20.37 [14.28, 37.40]	32.63 [15.59, 47.32]	−0.082	0.221
Door component cost (KRW million)	1.17 [0.00, 5.17]	2.55 [0.00, 5.85]	−0.136	0.228
HVAC component cost (KRW million)	13.92 [6.38, 25.10]	22.77 [8.41, 38.61]	−0.291	0.24
Boiler component cost (KRW million)	0.83 [0.00, 2.30]	1.44 [0.00, 3.41]	−0.23	0.171
Total recorded cost (KRW million)	147.54 [113.77, 222.43]	216.26 [132.18, 320.02]	−0.294	0.262
Recorded component subtotal (KRW million)	38.87 [27.87, 67.37]	63.97 [37.69, 90.72]	−0.207	0.246
Remaining cost (KRW million)	108.31 [77.06, 162.75]	156.83 [81.18, 227.89]	−0.298	0.256
Component share of total (percent)	27.47 [21.52, 35.03]	29.31 [22.44, 40.10]	−0.153	0.112
(B)
Recorded Characteristic	Included n/250 (%)		Other n/169 (%)
Floors 1	104 (41.6)		57 (33.7)
Floors 2	126 (50.4)		82 (48.5)
Floors other noninteger value	0 (0.0)		1 (0.6)
Floors grouped 3 or more	20 (8.0)		29 (17.2)
X5 recorded positive	164 (65.6)		108 (63.9)
X6 recorded positive	146 (58.4)		95 (56.2)
X7 recorded positive	230 (92.0)		159 (94.1)
X8 recorded positive	137 (54.8)		121 (71.6)
X9 recorded positive	207 (82.8)		143 (84.6)
X10 recorded positive	156 (62.4)		109 (64.5)

(A) Both groups use the same 419-record source workbook; monetary fields are million nominal KRW after reversing the stored conversion factor of 0.00072. This reverses a reporting scale and is not inflation adjustment. SMD = (included mean − other mean)/sqrt((included variance + other variance)/2); KS D is the largest empirical-CDF difference. These finite-archive descriptions are not equivalence tests or evidence of population representativeness. (B) A positive recorded amount or quantity is a field state, not verified intervention typology. One noninteger floor value in the other group is retained as recorded rather than silently rounded. The primary n = 246 inclusion sensitivity yielded the same direction of scale/cost differences; full aggregate statistics are retained with the analysis records.

As a supplementary archive check, the 15 test-case profiles published in Table 6 of [27] were compared using building area, gross floor area, completion year and floor count. Areas were compared within the rounding tolerance of the published two-decimal values, with exact year and floor-count agreement. None matched the 250-record extract; 14 had unique four-field matches among the other 169 archive records. These are profile matches, not confirmation of identical cost entries. This limited check supports a connection with the retained archive but does not establish the full record-level overlap with the published 401-case sample or reconstruct the historical selection procedure.

Table A9. Additional common-partition family and target benchmark (Panel (A)). Search settings and preprocessing (Panel (B)).

(A)
Route	Y-MAPE %	R-MAPE %	MAE KRW m	RMSE KRW m	Y-WAPE %	R-WAPE %	R2 for R
Median Y	74.67	180.03	88.67	149.76	46.10	66.35	−1.418
Median R	59.90	160.02	64.92	99.94	33.97	48.76	−0.060
OLS log(Y)	28.69	64.43	56.99	144.56	29.12	42.13	−1.548
OLS log(R)	26.28	53.11	60.22	146.31	30.88	44.63	−1.736
Ridge log(Y)	28.55	64.76	53.50	130.40	27.43	39.65	−1.031
Ridge log(R)	26.30	55.58	53.56	122.69	27.51	39.72	−0.932
kNN log(Y)	24.65	61.95	45.22	85.30	23.45	33.77	0.220
kNN log(R)	19.07	47.05	35.26	63.45	18.46	26.50	0.554
HGB log(Y)	21.07	41.68	43.87	85.58	22.85	32.93	0.143
HGB log(R)	17.69	33.25	36.66	64.22	19.19	27.57	0.530
RF log(Y)	18.67	41.43	35.11	68.26	18.21	26.24	0.446
RF log(R)	13.90	26.53	27.99	54.07	14.65	21.03	0.671
ET log(Y)	14.69	32.21	30.29	61.53	15.71	22.64	0.552
ET log(R)	12.64	29.19	25.47	48.67	13.32	19.14	0.735
Inner-selected family and target	12.64	29.19	25.47	48.67	13.32	19.14	0.735
(B)
Family	Settings Searched for Each Log Target				Training-Only Processing
Extra Trees	250 trees; max_features {0.6, 1.0}; min_samples_leaf {1, 2, 4}; max_depth {8, unrestricted}				Raw recorded inputs; randomized seed recorded in code
Random forest	250 trees; max_features {0.6, 1.0}; min_samples_leaf {1, 2, 4}				Raw recorded inputs
Histogram gradient boosting	150 iterations; max_leaf_nodes {7, 15, 31}; L2 = 1				Raw recorded inputs
OLS and Ridge	OLS; Ridge alpha {0.1, 1, 10, 100}				log1p(X/positive training median), then training standardization
k-nearest neighbors	k {3, 5, 10}; uniform or inverse-distance case weights; p = 2				Training min-max scales; equal feature weights
Median baseline	Training median Y or R; add C for R				No predictor fit or hyperparameter search

(A) n = 246; means over the same 25 outer folds with common fivefold inner partitions. All fitted feature models use X1–X10. For direct Y and median-Y routes, R metrics use the implied remainder Ŷ − C, which can be negative. MAE/RMSE are identical for Y and its implied or reconstructed R. The final row selects family, target and settings inside each outer training set; ET log(R) was selected 25/25 times. Original GA-CBR is not in this new search pool. These exploratory results are separate from the archived Table 2 results. (B) Outer repeated-fivefold seed = 20262507; inner seed = 20260807 + 80000 + split index. Inner mean Y-MAPE is the common selection loss. The pool contains seven families × two targets. It does not select the information boundary: X1–X10 is supplied throughout. Full seeds and deterministic implementation are retained with the analysis code.

Table A9. Additional common-partition family and target benchmark (Panel (A)). Search settings and preprocessing (Panel (B)).

(A)
Route	Y-MAPE %	R-MAPE %	MAE KRW m	RMSE KRW m	Y-WAPE %	R-WAPE %	R2 for R
Median Y	74.67	180.03	88.67	149.76	46.10	66.35	−1.418
Median R	59.90	160.02	64.92	99.94	33.97	48.76	−0.060
OLS log(Y)	28.69	64.43	56.99	144.56	29.12	42.13	−1.548
OLS log(R)	26.28	53.11	60.22	146.31	30.88	44.63	−1.736
Ridge log(Y)	28.55	64.76	53.50	130.40	27.43	39.65	−1.031
Ridge log(R)	26.30	55.58	53.56	122.69	27.51	39.72	−0.932
kNN log(Y)	24.65	61.95	45.22	85.30	23.45	33.77	0.220
kNN log(R)	19.07	47.05	35.26	63.45	18.46	26.50	0.554
HGB log(Y)	21.07	41.68	43.87	85.58	22.85	32.93	0.143
HGB log(R)	17.69	33.25	36.66	64.22	19.19	27.57	0.530
RF log(Y)	18.67	41.43	35.11	68.26	18.21	26.24	0.446
RF log(R)	13.90	26.53	27.99	54.07	14.65	21.03	0.671
ET log(Y)	14.69	32.21	30.29	61.53	15.71	22.64	0.552
ET log(R)	12.64	29.19	25.47	48.67	13.32	19.14	0.735
Inner-selected family and target	12.64	29.19	25.47	48.67	13.32	19.14	0.735
(B)
Family	Settings Searched for Each Log Target				Training-Only Processing
Extra Trees	250 trees; max_features {0.6, 1.0}; min_samples_leaf {1, 2, 4}; max_depth {8, unrestricted}				Raw recorded inputs; randomized seed recorded in code
Random forest	250 trees; max_features {0.6, 1.0}; min_samples_leaf {1, 2, 4}				Raw recorded inputs
Histogram gradient boosting	150 iterations; max_leaf_nodes {7, 15, 31}; L2 = 1				Raw recorded inputs
OLS and Ridge	OLS; Ridge alpha {0.1, 1, 10, 100}				log1p(X/positive training median), then training standardization
k-nearest neighbors	k {3, 5, 10}; uniform or inverse-distance case weights; p = 2				Training min-max scales; equal feature weights
Median baseline	Training median Y or R; add C for R				No predictor fit or hyperparameter search

(A) n = 246; means over the same 25 outer folds with common fivefold inner partitions. All fitted feature models use X1–X10. For direct Y and median-Y routes, R metrics use the implied remainder Ŷ − C, which can be negative. MAE/RMSE are identical for Y and its implied or reconstructed R. The final row selects family, target and settings inside each outer training set; ET log(R) was selected 25/25 times. Original GA-CBR is not in this new search pool. These exploratory results are separate from the archived Table 2 results. (B) Outer repeated-fivefold seed = 20262507; inner seed = 20260807 + 80000 + split index. Inner mean Y-MAPE is the common selection loss. The pool contains seven families × two targets. It does not select the information boundary: X1–X10 is supplied throughout. Full seeds and deterministic implementation are retained with the analysis code.

Table A10. Disjoint calibration and evaluation (Panel (A)). Back-transformation and allowance summaries (Panel (B)). Archived fixed-model sensitivity (Panel (C)).

(A)
Split	Naive P90%	Naive Covered (%)	Exact 95% CI %	Smeared P90%	Smeared Covered (%)	Naive Rank-46 Covered (%)
1	41.36	47/50 (94%)	83.5–98.7	31.38	47/50 (94%)	48/50 (96%)
2	43.63	47/50 (94%)	83.5–98.7	33.62	46/50 (92%)	48/50 (96%)
3	16.39	38/50 (76%)	61.8–86.9	13.23	39/50 (78%)	41/50 (82%)
4	38.59	44/50 (88%)	75.7–95.5	29.24	44/50 (88%)	45/50 (90%)
5	43.26	43/50 (86%)	73.3–94.2	35.53	43/50 (86%)	43/50 (86%)
6	39.20	45/50 (90%)	78.2–96.7	32.65	45/50 (90%)	45/50 (90%)
7	23.86	44/50 (88%)	75.7–95.5	8.61	44/50 (88%)	44/50 (88%)
8	40.75	49/50 (98%)	89.4–99.9	33.23	49/50 (98%)	49/50 (98%)
9	27.66	46/50 (92%)	80.8–97.8	20.94	46/50 (92%)	47/50 (94%)
10	22.28	46/50 (92%)	80.8–97.8	12.49	47/50 (94%)	47/50 (94%)
(B)
Procedure			Empirical P90 Range %		Coverage Range %	Mean Coverage %
Naive, linear empirical quantile			16.39–43.63		76–98	89.8
Naive, finite-rank quantile			27.60–55.34		82–98	91.4
Smeared, linear empirical quantile			8.61–35.53		78–98	90.0
Smeared, finite-rank quantile			12.48–43.64		84–98	91.8
(C)
Validation/Transformation			Case MAPE %		Bias %	P90%
Repeated CV, naive exponential			12.30		−5.10	31.50
Repeated CV, Duan smearing			14.93		+0.70	24.64
ID-order 200/50, naive exponential			18.86		−17.81	55.95

(A) Each split uses 146 training, 50 calibration and 50 evaluation records, with no overlap within a split. P90 is estimated on calibration records only; a single frozen fit supplies both prediction sets. Exact Clopper–Pearson intervals describe each unsmeared empirical quantile evaluation. Trials overlap; neither the coverage counts nor intervals are pooled. Rank-46 uses ceil((50 + 1) × 0.9), with nonnegative uplift. This analysis fixes the originally selected ET/log(R) family/target and tests calibration internally; it is not an external validation of the historical 35.47%. (B) Means summarize ten overlapping internal splits. They are not estimates based on 500 independent projects. The smearing factor is trained without calibration or evaluation outcomes. An allowance must be interpreted jointly with its underlying point predictor. (C) Historical n = 250 fixed Extra Trees specification with 250 trees and default settings; outer seed 42 and inner smearing seed 1. This does not estimate the sensitivity of the selected n = 246 model and is not directly comparable with Table 4B. ID order is not calendar time.

Table A10. Disjoint calibration and evaluation (Panel (A)). Back-transformation and allowance summaries (Panel (B)). Archived fixed-model sensitivity (Panel (C)).

(A)
Split	Naive P90%	Naive Covered (%)	Exact 95% CI %	Smeared P90%	Smeared Covered (%)	Naive Rank-46 Covered (%)
1	41.36	47/50 (94%)	83.5–98.7	31.38	47/50 (94%)	48/50 (96%)
2	43.63	47/50 (94%)	83.5–98.7	33.62	46/50 (92%)	48/50 (96%)
3	16.39	38/50 (76%)	61.8–86.9	13.23	39/50 (78%)	41/50 (82%)
4	38.59	44/50 (88%)	75.7–95.5	29.24	44/50 (88%)	45/50 (90%)
5	43.26	43/50 (86%)	73.3–94.2	35.53	43/50 (86%)	43/50 (86%)
6	39.20	45/50 (90%)	78.2–96.7	32.65	45/50 (90%)	45/50 (90%)
7	23.86	44/50 (88%)	75.7–95.5	8.61	44/50 (88%)	44/50 (88%)
8	40.75	49/50 (98%)	89.4–99.9	33.23	49/50 (98%)	49/50 (98%)
9	27.66	46/50 (92%)	80.8–97.8	20.94	46/50 (92%)	47/50 (94%)
10	22.28	46/50 (92%)	80.8–97.8	12.49	47/50 (94%)	47/50 (94%)
(B)
Procedure			Empirical P90 Range %		Coverage Range %	Mean Coverage %
Naive, linear empirical quantile			16.39–43.63		76–98	89.8
Naive, finite-rank quantile			27.60–55.34		82–98	91.4
Smeared, linear empirical quantile			8.61–35.53		78–98	90.0
Smeared, finite-rank quantile			12.48–43.64		84–98	91.8
(C)
Validation/Transformation			Case MAPE %		Bias %	P90%
Repeated CV, naive exponential			12.30		−5.10	31.50
Repeated CV, Duan smearing			14.93		+0.70	24.64
ID-order 200/50, naive exponential			18.86		−17.81	55.95

(A) Each split uses 146 training, 50 calibration and 50 evaluation records, with no overlap within a split. P90 is estimated on calibration records only; a single frozen fit supplies both prediction sets. Exact Clopper–Pearson intervals describe each unsmeared empirical quantile evaluation. Trials overlap; neither the coverage counts nor intervals are pooled. Rank-46 uses ceil((50 + 1) × 0.9), with nonnegative uplift. This analysis fixes the originally selected ET/log(R) family/target and tests calibration internally; it is not an external validation of the historical 35.47%. (B) Means summarize ten overlapping internal splits. They are not estimates based on 500 independent projects. The smearing factor is trained without calibration or evaluation outcomes. An allowance must be interpreted jointly with its underlying point predictor. (C) Historical n = 250 fixed Extra Trees specification with 250 trees and default settings; outer seed 42 and inner smearing seed 1. This does not estimate the sensitivity of the selected n = 246 model and is not directly comparable with Table 4B. ID order is not calendar time.

Table A11. Error within the largest-area holdout.

Ascending Area Group	n	Median X2 m2	Mean R KRW m	Mean Predicted R KRW m	Y-MAE KRW m	Y-RMSE KRW m	Coverage at 35.47%
1	10	408.11	148.15	116.94	31.44	39.79	80%
2	10	464.16	163.41	130.36	46.25	63.08	90%
3	10	622.24	234.99	133.07	101.93	120.34	40%
4	10	992.93	220.70	124.01	97.07	168.39	80%
5	10	2295.15	369.36	116.18	254.60	293.35	20%

All 50 test records have X2 above the complementary training maximum 393.32 m². Training n = 196; training maximum R = KRW 318.95 million; 11/50 test R values exceed that maximum. The largest ten form group 5. Groups contain ten records and reveal aggregate diagnostics without disclosing record-level outputs. The 35.47% threshold was derived historically using all 246 records, so this is a fixed-threshold stress test, not independent allowance validation. Figure 6 and Figure 7 distinguish the original six holdouts from this expanded diagnosis.

Table A11. Error within the largest-area holdout.

Ascending Area Group	n	Median X2 m2	Mean R KRW m	Mean Predicted R KRW m	Y-MAE KRW m	Y-RMSE KRW m	Coverage at 35.47%
1	10	408.11	148.15	116.94	31.44	39.79	80%
2	10	464.16	163.41	130.36	46.25	63.08	90%
3	10	622.24	234.99	133.07	101.93	120.34	40%
4	10	992.93	220.70	124.01	97.07	168.39	80%
5	10	2295.15	369.36	116.18	254.60	293.35	20%

All 50 test records have X2 above the complementary training maximum 393.32 m². Training n = 196; training maximum R = KRW 318.95 million; 11/50 test R values exceed that maximum. The largest ten form group 5. Groups contain ten records and reveal aggregate diagnostics without disclosing record-level outputs. The 35.47% threshold was derived historically using all 246 records, so this is a fixed-threshold stress test, not independent allowance validation. Figure 6 and Figure 7 distinguish the original six holdouts from this expanded diagnosis.

The expanded benchmark uses 25 common outer partitions, and the three-way design uses ten separately seeded random partitions of the available IDs (seeds and full grids are available on request; see the Data Availability Statement). Within each three-way split the ID sets are disjoint, while repetitions reuse records. Recalculated metrics and split membership were checked against saved predictions. Nominal KRW MAE/RMSE are computed within each outer test fold before averaging. Code and aggregate outputs can be supplied on request; source records and individual predictions remain access-controlled.

Appendix A.2. Reproducibility Details

Project-quantile intervals use 10,000 case-bootstrap draws with seed 20291807. Subset contingency uses 10,000 draws per intermediate size, without replacement within each draw, with seed 20292807. Composition-test P90 intervals use 10,000 draws and seed 20293807 plus the test index, numbered 1–6. Historical quantiles use NumPy linear interpolation; the new rank-46 sensitivity explicitly uses an order statistic instead. Analysis code and archived aggregate results are available from the corresponding author on reasonable request; regenerating project-level diagnostics requires authorized access to the source data.

The fixed smearing sensitivity uses all 250 cases, X₁–X₁₀ and log(R). Fivefold inner out-of-fold residuals (shuffle seed 1) estimate the mean exponentiated log residual. Extra Trees uses 250 trees, default hyperparameters and seed 0; outer repeated fivefold validation uses seed 42. These results use a different protocol from the tuned primary model.

The primary case-mean Y-MAPE is 12.51285%, distinct from fold-mean Y-MAPE 12.72%. Case-mean aggregate bias is −6.10922% for Y and −8.78465% for R. Predicted cost and project uplift have Spearman correlation 0.15902; this weak positive association does not establish a unique cause of the nonmonotonic P80. The full-sample X₅ MAPE ratios 2.24 and 1.30 compare repeated-validation case-means with the separate ordered holdout; the support-group difference interval is a distinct analysis.

Appendix A.3. Supporting Figures

Figure A1 reports rank correlations and marginal cost distributions in the unfiltered sample. Figure A2 compares permutation-based Extra Trees reliance with standardized Ridge coefficients; these are association diagnostics, not causal effects.

Figure A1. Data correlations and distributions.

Figure A1. Data correlations and distributions.

Figure A2. Feature importance comparisons.

Figure A2. Feature importance comparisons.

Appendix A.4. Additional Sensitivity Analyses

Table A12. Aggregation and source-version sensitivity. (A). Historical P90 under alternative aggregation. Aggregation and source-version sensitivity. (B). Fixed-model source-version substitution.

(A)
Aggregation			Predictions	P90, %
Repetition 1: one prediction per case			246	34.36
Repetition 2: one prediction per case			246	37.01
Repetition 3: one prediction per case			246	35.01
Repetition 4: one prediction per case			246	34.19
Repetition 5: one prediction per case			246	35.13
All repetitions pooled (dependent)			1230	35.38
Five predictions averaged per case			246	35.47
(B)
n/Data Version	Y-MAPE, %	Y-MAE, KRW m	Y-RMSE, KRW m	Case-Mean P90, %
246/recorded extract	12.61	25.42	48.38	32.89
249/recorded extract	12.27	24.26	46.58	27.61
249/linked values	12.48	24.64	47.09	29.59
250/recorded extract	12.39	24.74	48.38	31.78
250/linked values	12.57	24.96	48.51	32.92

(A) The same archived n = 246 remaining-cost Extra Trees predictions underlie every row. Quantiles are calculated from Y/Ŷ − 1 with a zero lower bound. Pooling creates repeated measurements, not 1230 independent projects. The case-mean result lies within the repetition-specific range; averaging did not demonstrably lower P90 in these results. (B) ET log(R) + C; 250 trees, max_features = 0.6, min_samples_leaf = 1, unlimited depth. This modal archived setting was fixed for every fold and version; no retuning or GA-CBR search was performed. At n = 249 only ID 142 is excluded; n = 250 retains it. Linked values replace only the three discrepant monetary entries for IDs 7, 13 and 204 in an analytical copy. Versions at the same n share 25 outer partitions. Partitions differ across sample sizes. The n = 246 fixed-setting reference is distinct from the original tuned 12.72%/35.47% route. Version differences establish sensitivity, not which source is correct. MAPE, MAE and RMSE are means of 25 outer-fold metrics; P90 uses case-mean predictions.

Table A12. Aggregation and source-version sensitivity. (A). Historical P90 under alternative aggregation. Aggregation and source-version sensitivity. (B). Fixed-model source-version substitution.

(A)
Aggregation			Predictions	P90, %
Repetition 1: one prediction per case			246	34.36
Repetition 2: one prediction per case			246	37.01
Repetition 3: one prediction per case			246	35.01
Repetition 4: one prediction per case			246	34.19
Repetition 5: one prediction per case			246	35.13
All repetitions pooled (dependent)			1230	35.38
Five predictions averaged per case			246	35.47
(B)
n/Data Version	Y-MAPE, %	Y-MAE, KRW m	Y-RMSE, KRW m	Case-Mean P90, %
246/recorded extract	12.61	25.42	48.38	32.89
249/recorded extract	12.27	24.26	46.58	27.61
249/linked values	12.48	24.64	47.09	29.59
250/recorded extract	12.39	24.74	48.38	31.78
250/linked values	12.57	24.96	48.51	32.92

(A) The same archived n = 246 remaining-cost Extra Trees predictions underlie every row. Quantiles are calculated from Y/Ŷ − 1 with a zero lower bound. Pooling creates repeated measurements, not 1230 independent projects. The case-mean result lies within the repetition-specific range; averaging did not demonstrably lower P90 in these results. (B) ET log(R) + C; 250 trees, max_features = 0.6, min_samples_leaf = 1, unlimited depth. This modal archived setting was fixed for every fold and version; no retuning or GA-CBR search was performed. At n = 249 only ID 142 is excluded; n = 250 retains it. Linked values replace only the three discrepant monetary entries for IDs 7, 13 and 204 in an analytical copy. Versions at the same n share 25 outer partitions. Partitions differ across sample sizes. The n = 246 fixed-setting reference is distinct from the original tuned 12.72%/35.47% route. Version differences establish sensitivity, not which source is correct. MAPE, MAE and RMSE are means of 25 outer-fold metrics; P90 uses case-mean predictions.

Table A13. Conditional calibration and component-cost perturbation. (A). Training-OOF allowance check. Conditional calibration and component-cost perturbation. (B). Prediction-time input sensitivity.

(A)
Route	Target	Mean Allowance, %	Mean Coverage, %	Minimum Coverage, %
ET log(R) + C; X1–X10	P90	34.14	89.36	81.63
ET log(R) + C; X1–X10	P95	47.24	94.32	85.71
ET log(Y); X1–X10	P90	34.34	89.93	83.67
ET log(Y); X1–X10	P95	52.62	94.32	87.76
ET log(Y); X1–X6	P90	49.78	89.36	75.51
ET log(Y); X1–X6	P95	84.45	94.80	81.63
(B)
Perturbation of X7–X10		Remaining-Route Y-MAPE, %		Direct-Route Y-MAPE, %
Recorded components		12.72		14.68
Mean-one lognormal σ = 0.05		12.83 ± 0.12		14.78 ± 0.10
Mean-one lognormal σ = 0.10		13.11 ± 0.23		14.94 ± 0.18
Mean-one lognormal σ = 0.20		14.00 ± 0.42		15.40 ± 0.31
Mean-one lognormal σ = 0.30		15.22 ± 0.59		16.04 ± 0.42
All components × 0.8		14.25		15.17
All components × 0.9		12.86		14.72
All components × 1.1		13.94		15.56
All components × 1.2		15.99		16.53
Independent uniform [0.7, 1.3]		13.73 ± 0.30		15.25 ± 0.27

(A) Mean and minimum coverage summarize 25 overlapping outer folds. For each route, the original selected settings and original selection-fold OOF predictions within outer training supply the allowance. No outer-test outcome enters its calculation. Selection dependence and OOF/refit training-size differences remain; this is not the disjoint calibration design of Table A10. Separately seeded OOF folds gave mean P90 allowances of 33.98%, 33.56% and 51.01% and mean coverage of 89.85%, 89.85% and 89.68% for the rows’ three routes. A lower conditional allowance is not proof of a validated early-stage information advantage. (B) Original n = 246 selected Extra Trees fits and outer partitions are retained. Perturbations affect only test inputs, including the subtotal added to the remaining prediction; recorded outcomes are held fixed. Random multipliers are independent across project-component pairs, with 100 Monte Carlo replicates. Base seeds are 202611035 for lognormal and 202611036 for uniform perturbations. Within each replicate, the same project-component draw is retained across the five CV repetitions and shared across routes and lognormal σ values. Each replicate first averages MAPE over 25 folds; ± denotes SD across the 100 perturbation replicates, not sampling uncertainty. Z is standard normal and lognormal multipliers are exp(σZ − σ²/2), with mean one and no finite bound. At σ = 0.30, approximately 30.22% of multipliers lie outside [0.7, 1.3]. The uniform scenario separately imposes that bound. These assumed error mechanisms do not recover actual estimate-to-outturn differences or missing input timestamps. The unperturbed X1–X6 benchmark is 23.05%.

Table A13. Conditional calibration and component-cost perturbation. (A). Training-OOF allowance check. Conditional calibration and component-cost perturbation. (B). Prediction-time input sensitivity.

(A)
Route	Target	Mean Allowance, %	Mean Coverage, %	Minimum Coverage, %
ET log(R) + C; X1–X10	P90	34.14	89.36	81.63
ET log(R) + C; X1–X10	P95	47.24	94.32	85.71
ET log(Y); X1–X10	P90	34.34	89.93	83.67
ET log(Y); X1–X10	P95	52.62	94.32	87.76
ET log(Y); X1–X6	P90	49.78	89.36	75.51
ET log(Y); X1–X6	P95	84.45	94.80	81.63
(B)
Perturbation of X7–X10		Remaining-Route Y-MAPE, %		Direct-Route Y-MAPE, %
Recorded components		12.72		14.68
Mean-one lognormal σ = 0.05		12.83 ± 0.12		14.78 ± 0.10
Mean-one lognormal σ = 0.10		13.11 ± 0.23		14.94 ± 0.18
Mean-one lognormal σ = 0.20		14.00 ± 0.42		15.40 ± 0.31
Mean-one lognormal σ = 0.30		15.22 ± 0.59		16.04 ± 0.42
All components × 0.8		14.25		15.17
All components × 0.9		12.86		14.72
All components × 1.1		13.94		15.56
All components × 1.2		15.99		16.53
Independent uniform [0.7, 1.3]		13.73 ± 0.30		15.25 ± 0.27

(A) Mean and minimum coverage summarize 25 overlapping outer folds. For each route, the original selected settings and original selection-fold OOF predictions within outer training supply the allowance. No outer-test outcome enters its calculation. Selection dependence and OOF/refit training-size differences remain; this is not the disjoint calibration design of Table A10. Separately seeded OOF folds gave mean P90 allowances of 33.98%, 33.56% and 51.01% and mean coverage of 89.85%, 89.85% and 89.68% for the rows’ three routes. A lower conditional allowance is not proof of a validated early-stage information advantage. (B) Original n = 246 selected Extra Trees fits and outer partitions are retained. Perturbations affect only test inputs, including the subtotal added to the remaining prediction; recorded outcomes are held fixed. Random multipliers are independent across project-component pairs, with 100 Monte Carlo replicates. Base seeds are 202611035 for lognormal and 202611036 for uniform perturbations. Within each replicate, the same project-component draw is retained across the five CV repetitions and shared across routes and lognormal σ values. Each replicate first averages MAPE over 25 folds; ± denotes SD across the 100 perturbation replicates, not sampling uncertainty. Z is standard normal and lognormal multipliers are exp(σZ − σ²/2), with mean one and no finite bound. At σ = 0.30, approximately 30.22% of multipliers lie outside [0.7, 1.3]. The uniform scenario separately imposes that bound. These assumed error mechanisms do not recover actual estimate-to-outturn differences or missing input timestamps. The unperturbed X1–X6 benchmark is 23.05%.