Traditional Linear Regression Model Research Articles

Subway track foundation settlement deformation prediction based on the BiLSTM-AdaBoost model

The rapid economic expansion has spurred extensive construction near subway networks, impacting the stability of their track foundations. Consequently, it’s crucial to monitor and predict settlement in subway track foundations. However, the dynamic deformation patterns often exhibit nonlinearity and non-stationarity, posing challenges for traditional linear regression models. To tackle this, our study integrates the BiLSTM (bi-directional long short-term memory) network with the AdaBoost ensemble learning algorithm. Using settlement data from Shanghai metro monitoring points, the model is trained and evaluated employing R2 (coefficient of determination), MAE (mean absolute error), and RMSE (root mean square error). Results show that our proposed model displays superior predictive accuracy compared to the LSTM and the BiLSTM, with an average training set R2 of 0.99, test set R2 of 0.78, average MAE of 0.32 mm, and average RMSE of 0.4 mm. Consequently, for forecasting subway track foundation deformations, employing our network model ensures highly accurate predictive capabilities.

Private Firm Valuation Using Multiples: Can Artificial Intelligence Algorithms Learn Better Peer Groups?

Forming optimal peer groups is a crucial step in multiplier valuation. Among others, the traditional regression methodology requires the definition of the optimal set of peer selection criteria and the optimal size of the peer group a priori. Since there exists no universally applicable set of closed and complementary rules on selection criteria due to the complexity and the diverse nature of firms, this research exclusively examines unlisted companies, rendering direct comparisons with existing studies impractical. To address this, we developed a bespoke benchmark model through rigorous regression analysis. Our aim was to juxtapose its outcomes with our unique approach, enriching the understanding of unlisted company transaction dynamics. To stretch the performance of the linear regression method to the maximum, various datasets on selection criteria (full as well as F- and NCA-optimized) were employed. Using a sample of over 20,000 private firm transactions, model performance was evaluated employing multiplier prediction error measures (emphasizing bias and accuracy) as well as prediction superiority directly. Emphasizing five enterprise and equity value multiples, the results allow for the overall conclusion that the self-organizing map algorithm outperforms the traditional linear regression model in both minimizing the valuation error as measured by the multiplier prediction error measures as well as in direct prediction superiority. Consequently, the machine learning methodology offers a promising way to improve peer selection in private firm multiplier valuation.

Development of an artificial neural network based-prediction model for bond strength of FRP bars in concrete

Fiber-reinforced polymer (FRP) bars have garnered increasing attention in recent years due to their superior corrosion resistance, offering a potential solution to the significant drawback of steel corrosion in concrete. For the widespread utilization of FRP bars in concrete structures, determining the bond strength between FRP bars and concrete is a crucial topic. This study seeks to develop a prediction model to estimate the bond strength of FRP bars in concrete, utilizing an extended dataset from 1010 pull-out tests. Initially, the study evaluates the applicability of several bond strength formulas from existing codes. Subsequently, two prediction models, namely a multivariate linear regression model and an artificial neural network (ANN) model, are introduced for estimating the bond strength of FRP bars in concrete. The results indicate that the correlation between the evaluation values of existing formulas and the experimental value is very low. This is because these formulas have not yet been updated to encompass the expanded usage scopes of FRP bars with various surface processing methods and types of concrete. While the multivariate linear regression model outperforms these formulas, its accuracy is still relatively low; in contrast, the ANN demonstrates superior performance, achieving an R^2 value for both the validation and test set of more than 0.92. The findings highlight that, when considering a broader range of applications, the ANN serves as a robust tool for accurately predicting the bond strength of FRP bars in concrete, in comparison to traditional formulas and linear regression models. This assessment approach provides engineers with a convenient, high-precision tool for designs utilizing various forms of FRP bars and diverse types of concrete in practical design scenarios

Going a Step Deeper Down the Rabbit Hole: Deep Learning Model to Measure the Size of the Unregistered Economy Activity

AbstractAccurately estimating the size of unregistered economies is crucial for informed policymaking and economic analysis. However, many studies seem to overfit partial data as these use simple linear regression models. Recent studies adopted a more advanced approach, using non-linear models obtained using machine learning techniques. In this study, we take a step forward on the road of data-driven models for the unregistered economy activity’s (UEA) size prediction using a novel deep-learning approach. The proposed two-phase deep learning model combines an AutoEncoder for feature representation and a Long Short-Term Memory (LSTM) for time-series prediction. We show it outperforms traditional linear regression models and current state-of-the-art machine learning-based models, offering a more accurate and reliable estimation. Moreover, we show that the proposed model is better in generalizing UEA’s dynamics across countries and timeframes, providing policymakers with a more profound group to design socio-economic policies to tackle UEA.

The association between PM2.5 components and blood pressure changes in late pregnancy: A combined analysis of traditional and machine learning models

BackgroundPM2.5 is a harmful mixture of various chemical components that pose a challenge in determining their individual and combined health effects due to multicollinearity issues with traditional linear regression models. This study aimed to develop an analytical methodology combining traditional and novel machine learning models to evaluate PM2.5's combined effects on blood pressure (BP) and identify the most toxic components. MethodsWe measured late-pregnancy BP of 1138 women from the Heshan cohort while simultaneously analyzing 31 PM2.5 components. We utilized multiple linear regression modeling to establish the relationship between PM2.5 components and late-pregnancy BP and applied Random Forest (RF) and generalized Weighted Quantile Sum (gWQS) regression to identify the most toxic components contributing to elevated BP and to quantitatively evaluate the cumulative effect of the PM2.5 component mixtures. ResultsThe results revealed that 16 PM2.5 components, such as EC, OC, Ti, Fe, Mn, Cu, Cd, Mg, K, Pb, Se, Na+, K+, Cl−, NO3−, and F−, contributed to elevated systolic blood pressure (SBP), while 26 components, including two carbon components (EC, OC), fourteen metallics (Ti, Fe, Mn, Cr, Mo, Co, Cu, Zn, Cd, Na, Mg, Al, K, Pb), one metalloid (Se), and nine water-soluble ions (Na+, K+, Mg2+, Ca2+, NH4+, Cl−, NO3−, SO42−, F−), contributed to elevated diastolic blood pressure (DBP). Mn and Cr were the most toxic components for elevated SBP and DBP, respectively, as analyzed by RF and gWQS models and verified against each other. Exposure to PM2.5 component mixtures increased SBP by 1.04 mmHg (95% CI: 0.33–1.76) and DBP by 1.13 mmHg (95% CI: 0.47–1.78). ConclusionsOur study highlights the effectiveness of combining traditional and novel models as an analytical strategy to quantify the health effects of PM2.5 constituent mixtures.

Unveiling Microbial Nitrogen Metabolism in Rivers using a Machine Learning Approach.

Microbial nitrogen metabolism is a complicated and key process in mediating environmental pollution and greenhouse gas emissions in rivers. However, the interactive drivers of microbial nitrogen metabolism in rivers have not been identified. Here, we analyze the microbial nitrogen metabolism patterns in 105 rivers in China driven by 26 environmental and socioeconomic factors using an interpretable causal machine learning (ICML) framework. ICML better recognizes the complex relationships between factors and microbial nitrogen metabolism than traditional linear regression models. Furthermore, tipping points and concentration windows were proposed to precisely regulate microbial nitrogen metabolism. For example, concentrations of dissolved organic carbon (DOC) below tipping points of 6.2 and 4.2 mg/L easily reduce bacterial denitrification and nitrification, respectively. The concentration windows for NO3--N (15.9-18.0 mg/L) and DOC (9.1-10.8 mg/L) enabled the highest abundance of denitrifying bacteria on a national scale. The integration of ICML models and field data clarifies the important drivers of microbial nitrogen metabolism, supporting the precise regulation of nitrogen pollution and river ecological management.

Driving forces of digital transformation in chinese enterprises based on machine learning

With advanced science and digital technology, digital transformation has become an important way to promote the sustainable development of enterprises. However, the existing research only focuses on the linear relationship between a single characteristic and digital transformation. In this study, we select the data of Chinese A-share listed companies from 2010 to 2020, innovatively use the machine learning method and explore the differences in the predictive effects of multi-dimensional features on the digital transformation of enterprises based on the Technology-Organization-Environment (TOE) theory, thus identifying the main drivers affecting digital transformation and the fitting models with stronger predictive effect. The study found that: first, by comparing machine learning and traditional linear regression models, it is found that the prediction ability of ensemble earning method is generally higher than that of tradition measurement method. For the sample data selected in this research, XGBoost and LightGBM have strong explanatory ability and high prediction accuracy. Second, compared with the technical driving force and environmental driving force, the organizational driving force has a greater impact. Third, among these characteristics, equity concentration and executives’ knowledge level in organizational dimension have the greatest impact on digital transformation. Therefore, enterprise managers should always pay attention to the decision-making role of equity concentration and executives’ knowledge level. This study further enriches the literature on digital transformation in enterprises, expands the application of machine learning in economics, and provides a theoretical basis for enterprises to enhance digital transformation.

Evaluation Of Sailing Boat Performance Based on Ridge Regression and Mathematical Model Optimization

The traditional linear regression model can analyze and determine the coefficient between variables, reflecting the interpretation degree of variables in the equation. However, if the model is too complex, the training data is too few or too extreme, overfitting will occur, and the prediction effect of multicollinearity data is not good. The regularized ridge regression model can solve this problem. In this paper, Ridge regression analysis is carried out on the sailing performance data. Firstly, the data are preprocessed, and then the root-mean-square error RMSE=10.68 is obtained through the ridge regression model evaluation. The model fitting effect is good, and the regression coefficient corresponding to the variable Fr is the largest, indicating that the Froude number is the most obvious to the performance of the yacht. The variable beam draft ratio of B/Dr Is the least important to the yacht's performance. The conclusion of this paper can predict the performance of yachts more accurately, and provide corresponding improvement suggestions for enterprises.

Assessing influential factors of Chinese industrial aqueous cadmium emissions based on machine learning and shapley additive explanations

As the main contributor of cadmium (Cd) pollution in China, industrial aqueous Cd emissions are influenced by both industrial and socioeconomic characteristics owing to their “environmental service” nature. It is essential to understand the relationship between these characteristics and industrial aqueous Cd emissions during industrialization. In this study, a data-driven framework was proposed to reveal these relationships. The framework comprises two key steps. i) Three state-of-the-art tree-based machine learning models, including LightGBM, Gradient Boosting Decision Tree and Random Forest, were trained to capture the relationships among variables. ii) Shapley additive explanation was utilized to decompose the contribution of the characteristics to the prediction for each sample. The trained LightGBM model demonstrated the most superior performance in predicting industrial aqueous Cd emissions in test datasets (R2=0.881±0.0431， RMSE=58.260±11.839， MAE=27.743±3.274), significantly overperforming traditional linear regression model. Our analysis revealed that during our sample period, the influence of industrial characteristics on regional industrial aqueous Cd emissions was approximately 1.796 times greater than that of socioeconomic characteristics. Shifts in the characteristics of the non-ferrous metal industry contributed to approximately 74% of the average increase in industrial aqueous Cd emissions in China approximately. Regional emissions were found to be positively affected by average size and density but negatively affected by the operation duration of local non-ferrous metal industrial firms. Further driver analysis showed that the growth trajectory of emissions in China can be split into three stages based on the main drivers and growth rate: 2000–2002, 2003–2004, and 2005–2007. The proposed framework overcomes the limitations of the previous methods in terms of application scope, potential factor considerations, and regression structure predefinition. Our analysis implies that policymakers should proactively adjust industrial policies and emissions regulations in response to market shocks and industrial shifts, to a better management of industrial aqueous Cd emissions.

Locally optimal tests against periodic linear regression in short panels

This paper aims to detect the periodic coefficients of a Linear Regression model with Panel Data. Nonparametric locally and asymptotically optimal tests are proposed for testing the null hypothesis of a traditional linear regression model, against an alternative of a Periodic Coefficient Regression model. The Uniform Local Asymptotic Normality (ULAN) property is established for Periodic Linear Regression (PLR) model, to construct Locally asymptotically optimal tests. The rank-based version of the optimal parametric test is provided in particular cases. The performance of the proposed tests is valid with numerical simulations using the Monte Carlo study. Real data was studied for applying the periodic linear regression model which compared to both traditional regression and random coefficient regression models.

How to make calibration less painful-A proposition for an automatic, reliable and time-efficient procedure.

In behavioral and neurophysiological pain studies, multiple types of calibration methods are used to quantify the individual pain sensation stimuli. Often, studies lack a detailed calibration procedure description, data linearity, and quality quantification and omit required control for sex pain differences. This hampers study repetition and interexperimental comparisons. Moreover, typical calibration procedures require a high number of stimulations, which may cause discomfort and stimuli habituation among participants. To overcome those shortcomings, we present an automatic calibration procedure with a novel stimuli estimation method for intraepidermal stimulation. We provide an in-depth data analysis of the collected self-reports from 70 healthy volunteers (37 males) and propose a method based on a dynamic truncated linear regression model (tLRM). We compare its estimates for the sensation (t) and pain (T) thresholds and mid-pain stimulation (MP), with those calculated using traditional estimation methods and standard linear regression models. Compared to the other methods, tLRM exhibits higher R2 and requires 36% fewer stimuli applications and has significantly higher t intensity and lower T and MP intensities. Regarding sex differences, t and T were found to be lower for females compared to males, regardless of the estimation method. The proposed tLRM method quantifies the calibration procedure quality, minimizes its duration and invasiveness, and provides validation of linearity between stimuli intensity and subjective scores, making it an enabling technique for further studies. Moreover, our results highlight the importance of control for sex in pain studies.

Predicting Microbiologically Influenced Concrete Corrosion in Self-Cleansing Sewers Using Meta-Learning Techniques

Sewer networks are not only necessary as an infrastructure for human societies, but they can also help humans achieve a stable situation with the surrounding natural environment by controlling and preventing the spread of pollution in the environment. As a result, concrete sewer maintenance and analysis of their damaging elements are critical. In this regard, modeling microbiologically influenced corrosion (MIC) is a challenging phenomenon. Due to the complicated aspects related to the interaction of microorganisms and concrete degradation, this research suggests several machine-learning models as well as traditional multiple linear regression model to predict the MIC in sewer pipelines. The models can be categorized into three sections: (i) stand-alone models (group method of data handling, generalized regression neural network, radial basis function neural network, multilayer perceptron neural network, chi-square automatic interaction detection, and classification and regression tree); (ii) integrative models (adaptive neuro-fuzzy inference system and support vector regression with particle swarm optimization, artificial bee colony, and firefly algorithm); and (iii) ensemble meta-learner stepwise regression (SR) model. After implementing the models, statistical measures, including root mean square error, mean absolute error, mean bias error, Pearson correlation coefficient, and Nash-Sutcliffe model efficiency are considered for evaluating models’ performances. The results indicate that the ensemble meta-learner-SR model is significantly more precise than other models. They also demonstrate that using an integrative model can improve the accuracy of stand-alone models by at least up to 42%. The durability and lifespan of the sewer system are also estimated with the aid of the best predictive model (meta-learner-SR) for two scenario cases of (i) gas phase and (ii) submerged conditions. It is concluded that the sewer systems have a considerably lower life span (24 y less) exposed to submerged sewage than the gas phase with 56 y of durability.

Stress begets stress: The moderating role of childhood adversity in the relationship between job stress and sleep quality among nurses

Nurses exhibit considerable variations in sleep quality and experience high job stress levels. Distal factors, such as childhood adversity, and proximal factors, both influence sleep quality. We investigated the moderating role of childhood adversity with job stress and sleep quality, and whether this aligns with the stress-sensitization or stress-amplification models. The impact of job stressors' total score and its dimensions on sleep quality was analyzed using traditional linear regression models and the extreme gradient boosting machine learning algorithm. The hierarchical regression examined the moderating role of childhood adversity in the relationship between job stress and sleep quality. An interactive tool was used to visualize the results. Among the dimensions of job stress, "time allocation and workload" strongly correlated with sleep quality, followed by "nursing profession and work problems," "patient care issues," "management and interpersonal problems," and "working environment and equipment problems." The moderating role of childhood adversity in the relationship between different dimensions of job stressors (except working environment and equipment problems) and sleep quality aligns with the stress-sensitization model. This study was susceptible to recall bias and objective sleep data were unavailable. Cross-sectional study design was used, thus limiting causal inferences. Finally, the moderating effect of childhood adversity on subsequent stress among nurses remains unclear. Childhood adversity and job stress were integrated into a stress-sensitization model, providing a nuanced and specific examination of sleep quality. Healthcare policymakers should focus on job stress and childhood adversity, improve nurses' sleep quality, and ultimately benefit patient care and outcomes.

A simple and efficient alginate hydrogel combined with surface-enhanced Raman spectroscopy for quantitative analysis of sodium nitrite in meat products.

Sodium nitrite is a commonly used preservative and color protectant in the food industry. Conventional analytical methods are highly susceptible to food matrix interference, time-consuming and costly. In this study, the ion cross-linking method was employed to prepare alginate hydrogel substrates, and phenosafranin was chosen as a single-molecule probe to analyze sodium nitrite. Our investigation centered on elucidating the effects of alginate and cross-linking ion concentrations on Raman signal characteristics. The optimal Raman response was observed in the precursor solution with 1% sodium alginate and 0.1 mol L-1 cross-linking ions. The relative standard deviations (RSDs) of the feature peaks from the three substrate batches ranged from 1.22% to 16.30%, attesting the robustness and consistency of the substrates. The signal reduction of the substrates after a four-week storage period remained below 10%, indicating that the substrates had good reproducibility and stability. The limits of detection (LODs) for sodium nitrite in extracts from cured meat, luncheon meat, and sliced ham were determined to range from 3.75 mg kg-1 to 8.11 mg kg-1, with low interference from the food matrix. The support vector machine algorithm was utilized to train and predict the data, which proved to be more accurate (98.6%-99.8% recovery) than the traditional linear regression model (81.9%-112.7% recovery) in predicting the spiked samples. The application of hydrogel-based surface-enhanced Raman spectroscopy (SERS) substrates for nitrite detection in food, combined with machine learning for regression prediction in data processing, collectively augmented the potential of SERS technology in the field of food analysis.

A breakdown-free block conjugate gradient method for large-scale discriminant analysis

<abstract><p>Rayleigh-Ritz discriminant analysis (RRDA) is an effective algorithm for linear discriminant analysis (LDA), but there are some drawbacks in its implementation. In this paper, we first improved Rayleigh-Ritz discriminant analysis (IRRDA) to make its framework more concise, and established the equivalence theory of the solution space between our discriminant analysis and RRDA. Second, we proposed a new model based on positive definite systems of linear equations for linear discriminant analysis, and certificated the rationality of the new model. Compared with the traditional linear regression model for linear discriminant analysis, the coefficient matrix of our model avoided forming a centralized matrix or appending the original data matrix, but the original matrix itself, which greatly reduced the computational complexity. According to the size of data matrix, we designed two solution schemes for the new model based on the block conjugate gradient method. Experiments in real-world datasets demonstrated the effectiveness and efficiency of our algorithm and it showed that our method was more efficient and faster than RRDA.</p></abstract>

Mathematical Modeling Using Multiple and Fully-Connected Linear Regressions

This article is devoted to the synthesis of traditional multiple linear regression models with fully connected linear regression models. It has been noted that these models, in a certain sense, complement each other — the disadvantages of multiple regression are compensated by the fully connected one, and the disadvantages of the fully connected one are compensated by the multiple one. Multiple regression estimates with partial multicollinearity of factors are unstable, and with complete multicollinearity they do not exist at all. There are no obstacles to the use of fully connected regression in such conditions, and its estimates, on the contrary, do not exist in the complete absence of linear dependence between factors. The estimated fully connected regression is an equation of a line in space, as opposed to a multiple regression, which is a hyperplane in space, so you can find estimates of a fully connected regression with only two observations at your disposal. An algorithm for estimating fully connected regressions using the maximum likelihood method is considered. Based on a sample size of 21, a multiple and fully connected linear regression of passenger rail traffic in the Irkutsk region was constructed, containing 23 input variables. During the construction process, it was possible to cope with multicollinearity and ensure protection of all input variables in the model. The constructed multiple and fully connected regression is adequate and fully satisfies the substantive meaning of the problem being solved, therefore its interpretation is given. Based on the results of the study, we can conclude that a combination of multiple and fully connected regressions can be very effective in solving data analysis problems.

Development and Validation of Data-Level Innovation Data-Balancing Machine Learning Models for Predicting Optimal Implantable Collamer Lens Size and Postoperative Vault.

There are only four sizes of implantable collamer lens (ICL) available for selection, which cannot completely fit all patients as a result of the discontinuity of ICL sizes. Sizing an optimal ICL and predicting postoperative vault are still unresolved problems. This study aimed to develop and validate innovative data-level data-balancing machine learning-based models for predicting ICL size and postoperative vault. The patients were randomly assigned to training and internal validation sets in a 4:1 ratio. Feature selection was performed using analysis of variance (ANOVA) and Kruskal-Wallis feature importance methods. Traditional linear regression model and machine learning-based models were used. The accuracy of models was assessed using the area under the curve (AUC) and confusion matrix. A total of 564 patients (1127 eyes) were eligible for this study, consisting of 808 eyes in the training set, 202 eyes in the internal validation set, and 117 eyes in the external validation set. Compared with the traditional linear regression method, the machine learning model bagging tree showed the best performance for ICL size selection, with an accuracy of 84.5% (95% confidence interval (CI) 83.2-85.8%), and the AUC ranged from 0.88 to 0.99; the prediction accuracy of 12.1mm and 13.7mm ICL sizes was improved by 49% and 59%, respectively. The bagging tree model achieved the best accuracy [90.2%, (95%CI 88.9-91.5%)] for predicting the postoperative vault, and the AUC ranged from 0.90 to 0.94. The prediction accuracies of internal and external validation dataset for ICL sizing were 82.2% (95%CI 81.1-83.3%) and 82.1% (95%CI 81.1-83.1%), respectively. The innovative data-level data balancing-based machine learning model can be used to predict ICL size and postoperative vault more accurately, which can assist surgeons in choosing optimal ICL size, thus reducing risks of postoperative complications and secondary surgery.

What is affecting the improvement of green innovation efficiency in the old industrial base: evidence from Northeast China.

Green innovation is an important driving force for high-quality development and is vital for reinvigorating the old industrial bases in Northeast China. As such, this study investigates the spatial-temporal evolution characteristics and factors influencing green innovation efficiency (GIE) in Northeast China from 2005 to 2020, using the super-efficient EBM-Malmquist model, kernel density estimation, and random forest model. The results show the following. (1) The "growth effect" of technological change is the main force driving GIE improvement; the "horizontal effect" of pure technical efficiency change has started to play an important role; and the club convergence characteristics of GIE in Northeast China have started to be optimized. (2) GIE in Northeast China shows significant spatial differentiation. The urban agglomeration of Mid-southern Liaoning and Harbin-Changchun has had high values for GIE, indicating that green innovation has a cyclic cumulative effect and the spatial pattern of green innovation needs to be further optimized. (3) The random forest model is more accurate and provides more trustworthy results compared with the traditional multiple linear regression model. The results of random forest model measurement illustrate that the number of digital economy enterprises, public finance expenditure, GDP per capita, and vegetation coverage play a positive role in promoting GIE. The proportion of the non-farm population and industrial agglomeration plays a negative role in GIE. In the same period, the contribution of the number of digital economy enterprises≥0.41, public expenditure ≥0.47, GDP per capita≥0.39, and vegetation coverage≥0.36 to GIE reach maximum values and then remain unchanged.

The stock price forecast under the failure of silicon valley bank based on the ARIMA model

The collapse of Silicon Valley Bank on March 10, 2023, had a profound impact on the stock prices of many companies in the United States. This study aims to examine the response of other banks in the US to this event by utilizing the Autoregressive Integrated Moving Average (ARIMA) model to forecast their stock prices. The research demonstrates that the ARIMA model effectively predicts the general trend of these banks' stock prices, with Root Mean Squared Error (RMSE) values below 1 for four out of six major US banks. These findings indicate that the proposed method is a promising tool for managing sudden fluctuations in stock prices, outperforming traditional linear regression models. Consequently, this research provides valuable insights for investors and financial institutions in managing and mitigating risks associated with abrupt market changes. Additionally, the study contributes to a greater understanding of the effects of bank collapses on the stock market. Overall, the research highlights the significance of incorporating advanced forecasting methods, such as ARIMA, in analyzing and predicting stock price movements in volatile market conditions.

Quality control prediction of electrolytic copper using novel hybrid nonlinear analysis algorithm

Traditional linear regression and neural network models demonstrate suboptimal fit and lower predictive accuracy while the quality of electrolytic copper is estimated. A more dependable and accurate model is essential for these challenges. Notably, the maximum information coefficient was employed initially to discern the non-linear correlation between the nineteen factors influencing electrolytic copper quality and the five quality control indicators. Additionally, the random forest algorithm elucidated the primary factors governing electrolytic copper quality. A hybrid model, integrating particle swarm optimization with least square support vector machine, was devised to predict electrolytic copper quality based on the nineteen factors. Concurrently, a hybrid model combining random forest and relevance vector machine was developed, focusing on primary control factors. The outcomes indicate that the random forest algorithm identified five principal factors governing electrolytic copper quality, corroborated by the non-linear correlation analysis via the maximum information coefficient. The predictive accuracy of the relevance vector machine model, when accounting for all nineteen factors, was comparable to the particle swarm optimization—least square support vector machine model, and surpassed both the conventional linear regression and neural network models. The predictive error for the random forest-relevance vector machine hybrid model was notably less than the sole relevance vector machine model, with the error index being under 5%. The intricate non-linear variation pattern of electrolytic copper quality, influenced by numerous factors, was unveiled. The advanced random forest-relevance vector machine hybrid model circumvents the deficiencies seen in conventional models. The findings furnish valuable insights for electrolytic copper quality management.