Classical Linear Regression Model Research Articles

Analysis of Traffic Injury Crash Proportions Using Geographically Weighted Beta Regression

The classical linear regression model allows for a continuous quantitative variable to be modeled simply from other variables. However, this model assumes independence between observations, which, if ignored, can lead to methodological issues. Additionally, not all data follow a normal distribution, prompting the need for alternative modeling methods. In this context, geographically weighted beta regression (GWBR) incorporates spatial dependence into the modeling process and analyzes rates or proportions using the beta distribution. In this study, GWBR was applied to the traffic injury (fatal and non-fatal) crash proportions in Fortaleza, Ceará, Brazil, from 2009 to 2011. The results demonstrated that the local approach using the beta distribution is a viable model for explaining the traffic injury crash proportions, due to its flexibility in handling both symmetric and skewed distributions. Therefore, when analyzing rates or proportions, the use of the GWBR model is recommended.

High dimensional variable selection through group Lasso for multiple function‐on‐function linear regression: A case study in PM10 monitoring

SummaryAnalyzing the effect of chemical and local meteorological variables over the behaviour in concentrations in the Abruzzo region (Italy), with the objective of forecasting and controlling air quality, motivates the current work. Given that the available data are curves that represent the day‐to‐day variations, a multiple function‐on‐function linear regression (MFFLR) model is considered. By assuming the Karhunen‐Loève expansion, MFFLR model can be reduced to a classical linear regression model for each principal component of the functional response in terms of all principal components (PCs) of the functional predictors. In this sense, a regularization approach for functional principal component regression based on the merge of functional data analysis with group Lasso is proposed. This novel methodology allows to estimate the model and, simultaneously, select those relevant functional predictors with the functional response, where each functional independent variable is represented by a group of input variables derived by the PCs.

Multilayer perceptron and support vector regression models for feline parturition date prediction

A crucial challenge in feline obstetric care is the accurate prediction of the parturition date during late pregnancy. The classic simple linear regression (SLR) model, which employed the fetal biparietal diameter (BPD) as the single input feature, was frequently applied for such prediction with limited accuracy. Since Multilayer Perceptron (MLP) and Support Vector Regression (SVR) are now two of the most potent scientific regression models, this study, for the first time, introduced such models as the new promising tools for feline parturition date prediction. The following features were candidate inputs for our models: biparietal diameter (BPD), litter size, and maternal weight. We observed and compared the performance results for each model. As the best-performed model, MLP delivered the highest coefficient score (0.972 ± 0.006), lowest mean absolute error score (1.110 ± 0.060), and lowest mean squared error score (1.540 ± 0.141), respectively. For the first time in this study, BPD, litter size, and maternal weight were considered the essential features for the innovative MLP and SVR modeling. With the optimized model parameters and the described analytical platform, further verification of these advanced models in feline obstetric practices is feasible.

Robust variable selection under cellwise contamination

Cellwise outliers are widespread in real world data analysis. Traditional robust methods may fail when applied to datasets under such contamination. We introduce a variable selection procedure, that uses the Gaussian rank estimator to obtain an initial empirical covariance matrix among the response and potential predictors. We re-parameterize the classical linear regression model design matrix and the response vector such that we are able to take advantage of these robustly estimated components before applying the adaptive Lasso to obtain consistent variable selection results. The procedure is robust to cellwise outliers in low and high-dimensional settings. Empirical results show good performance compared with recently proposed robust techniques, particularly in the challenging environment when contamination rates are high but the magnitude of outliers is moderate.

Determinants of profitability of insurance companies in Ethiopia: evidence from insurance companies from 2011 to 2020 years

The profitability of insurance companies has been the focus of several studies within the rise of economies across the countries worldwide. This study aimed to identify determinants of profitability of insurance companies in Ethiopian. The study used nine insurance companies selected by purposive sampling technique among the total 17 insurance companies in Ethiopia from period of 2011 to 2020 based on their establishment. Descriptive, causal research design and quantitative research approach were adopted in carrying out this study. Classical linear regression model under estimation of ordinary least square was employed to identify the determinants of profitability of insurance companies in Ethiopia at 5% level of significance. The classical linear regression model revealed that variable age of the company, tangibility of an asset, size of the company, managerial efficiency, leverage ratio, premium growth and GDP have a positive coefficient relationship with return on asset while loss ratio and inflation have a negative coefficient relationship with return on asset. On the other hand, age of the company size, managerial efficiency, leverage ratio, liquidity ration inflation and premium growth have statistically significant at 5% confidence interval level, whereas the other variables such tangibility of asset and GDP have no statistical significance at 5% confidence interval level. The insurance companies’ previous profit, age of the company, company size, managerial efficiency, leverage ratio, liquidity ratio, loss ratio, premium growth and inflation rate variables are significant key drivers of profitability of Ethiopian insurance companies. Giving due attention to the sector in line with key factors affecting the profitability will improve the overall performance of the insurance companies in Ethiopia.

Online sales prediction approach using methodology of CRISP-DM

This article studies the sales forecasting problem in the field of e-commerce. Based on the CRISP-DM methodology, innovative data mining technology is used to construct a variety of forecasting models, and is compared and optimized. This article improves the quality and quantity of sales forecasts and provides enterprises with more accurate and effective decision support. In terms of modeling optimization in this article, data mining models such as random forest, support vector machine, and neural network are used for comprehensive prediction, and comparative analysis is conducted with the classic multiple linear regression model. Through model evaluation and optimization, this paper achieved better prediction performance and accuracy. This research has certain theoretical significance and practical value, and provides new ideas and methods for the marketing decisions and business development of e-commerce enterprises.

Mitigating Multicollinearity in Linear Regression Model with Two Parameter Kibria-Lukman Estimators

This study delves into the challenges faced by the ordinary least square (OLS) estimator, traditionally regarded as the Best Linear Unbiased Estimator in classical linear regression models. Despite its reliability under specific conditions, OLS falters in the face of multicollinearity, a problem frequently encountered in regression analyses. To combat this issue, various ridge regression estimators have been developed, characterized as one-parameter and two-parameter ridge-type estimators. In this context, our research introduces novel two-parameter estimators, building upon a recently developed one-parameter ridge estimator to mitigate the impact of multicollinearity in linear regression models. Theoretical analysis and simulation experiments were conducted to assess the performance of the proposed estimators. Remarkably, our results reveal that, under certain conditions, these new estimators outperform existing estimators, displaying a significantly reduced mean square error. To validate these findings, real-life data was employed, aligning with the outcomes derived from theoretical analysis and simulations.

Factors affecting tourist visits to archaeological sites in Turkey: A spatial regression analysis

The study focuses on the factors affecting visitor numbers to archaeological sites in Turkey. The aim is to investigate the geographical, economic, and demographic factors underlying the visits using statistical methods. The study covers 117 archaeological site visits in 2019. Although existing studies analysed determinants of visits to archaeological sites of different countries, the evidence needs to be explicit. Methodologically, the classical linear regression models are primarily applied in the literature, whereas the incorporation of spatial dependence has largely been ignored. This study contributes to the literature by employing demographic, economic, and climatic factors and spatial relations between the sites. Therefore, spatial autoregressive (SAR) and spatial error models (SEM) are developed in the analyses. According to the results, WHL inscription and distance to the city centre are crucial factors for the visits. In addition, the study emphasizes the significant negative effect of spatial dependence on visitor numbers of archaeological sites near each other.

The Analysis of the Relationship between Corporate Social Responsibility and Financial Performance of Company

Corporate SCorporate Social Responsibility (CSR) has been forming very dynamically and intensively for several decades. The rapid development, as well as the relatively large scope of this concept, which is cross-sectionally related to a number of different social disciplines, so far causes a very significant terminological inconsistency. The paper focuses on the relationship between CSR and the financial performance of companies, or on the positive consequences of applying the concept of CSR in business on the example of a selected company Deutsche Telekom AG, which applies CSR in its business and which achieves positive results not only from this point of view, but also from the point of view of company profitability. When analyzing the company from the point of view of the global market, it quantitatively monitors the impact of the measured indicators on the profitability of total assets (ROA) and on net profit, by testing the basic assumptions made on the classical linear regression model. The main goal of the paper was to find out the impact of CSR on the financial results of the parent company Deutsche Telekom AG for the period 2001-2021 and to find the relationship between CSR and economic benefits.

Analyzing the Importance of International Law in Current International Relations Based on Linear Programming Models

Abstract International law is mainly the law between countries, which is the code of conduct for countries to conduct international interactions, and this paper researches the role of international law in international relations interactions. First of all, this paper combines the fuzzy set on the basis of the classical linear regression model algorithm, establishes the fuzzy linear programming model, and explores the fuzzy correlation analysis. Then, taking EU law as an example, the role of EU law in EU relations is analyzed through the theory of EU law, EU and the role of EU law in the EU embodied. Finally, based on the role of EU law, the importance of international law in international relations is studied through a fuzzy linear programming model, and the role of strengthening international law is considered. The results show that the countries consider the legitimacy of EU law to be above 0.9, and the countries’ participation in EU law also ranges from 0.9 to 1.0, and the countries’ self-identification increases by about 0.1 to 0.2 after the enactment of EU law. The correlation coefficients of international law on the construction of the identities of the 10 countries are all greater than 0.75, and the interests of the countries have increased by about 2.3, and international law promotes the order of international relations.

Subgroup analysis for the functional linear model

Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended to allow heterogeneous coefficient functions across different subgroups of subjects. The greatest challenge is that the subgroup structure is usually unknown to us. To this end, we develop a penalization-based approach which innovatively applies the penalized fusion technique to simultaneously determine the number and structure of subgroups and coefficient functions within each subgroup. An effective computational algorithm is derived. We also establish the oracle properties and estimation consistency. Extensive numerical simulations demonstrate its superiority compared to several competing methods. The analysis of an air quality dataset leads to interesting findings and improved predictions.

Livelihood Changes, Spatial Anticontagion Policy Effects, and Structural Resilience of National Food Systems in a Sub-Saharan African Country Context: A Panel Machine Learning Approach

The livelihood changes due to the COVID-19 policies in low-income and transitional economies serve as a lever for gauging the structural resilience of national food systems. Yet, few studies have addressed the cascading effects of the pandemic policies on the livelihood changes of farming system actors or modeled and provided coherent hypotheses about the transitory structural shifts at the micro-level. Other studies on the subject have either captured the early impacts of the pandemic on food systems with limited or no insight into the sub-Saharan African context or have used macro-level data, due to sparsely available micro-level data. These early insights are relevant for the design of early warning systems. However, an ongoing and deeper insight into the effects of pandemic policies is critical, since new and more comprehensive policies are needed to address the economic fallout and the extenuating effects of COVID-19 on food supply chain disruptions. The overriding questions are as follows: what are the effects of the pandemic policies on the livelihoods of food system actors and are there spatial-economic variations in the effects of the pandemic policies on the livelihoods of the farming system actors? Using 2019 and 2020 primary data from 836 farming system actors in Ghana, we offer fresh insights into the transitory micro-level livelihood changes caused by the COVID-19 anticontagion policies. We analyzed the data using the generalized additive, subset regression, classical linear, and logistic regression models in a machine learning framework. We show that the changes in the livelihood outcomes of the food system actors in Ghana coincide with the nature of pandemic mitigation policies adopted in the spatial units. We found that the lockdown policies had a negative and significant effect on the livelihoods of the farming system actors in the lockdown areas. The policies also negatively affected the livelihoods of the farming system actors in distant communities that shared no direct boundary with the lockdown areas. On the contrary, the lockdown policies positively affected the livelihoods of the farming system actors in the directly contiguous communities to the lockdown areas. We also document the shifts in the livelihood outcomes of the farming system actors, such as income, employment, food demand, and food security in the different spatial policy areas.

A Monte Carlo Experiment on the Asymptotic Efficiency of System Estimators under Multicollinearity

Classical linear regression model assumes that there is no multicollinearity among the explanatory variables in a regression model. Contrary to this assumption, where multicollinearity is perfect, the regression coefficients of the explanatory variables are indeterminable and their standard errors are infinite. On the other hand, where multicollinearity is less than perfect, the regression coefficients, although determinable, possess large standard errors. This implies that the coefficients cannot be estimated with great precision. Hence multicollinearity problem is a major problem in econometric analysis. Using Monte Carlo Simulation, we evaluated the asymptotic efficiency of six estimators (OLS, ILS,2SLS, 3SLS, LIML and FIML), under different magnitudes of the unintended linear relationship between the exogenous variables. Using the SSR criteria, we found that OLS followed by ILS turned out the best estimates amongst the six estimators under multicollinearity. We also found that with increasing sample size, there is no remarkable asymptotic effect in the performance of the estimators at the levels of multicollinearity.

Traumatic Brain Injury Rehabilitation Outcome Prediction Using Machine Learning Methods

ObjectiveTo investigate the performance of machine learning (ML) methods for predicting outcomes from inpatient rehabilitation for subjects with TBI using a dataset with a large number of predictor variables. Our second objective was to identify top predictive features selected by the ML models for each outcome and to validate the interpretability of the models. DesignSecondary analysis using computational modeling of relationships between patients, injury and treatment activities and 6 outcomes, applied to the large multi-site, prospective, longitudinal observational dataset collected during the traumatic brain injury inpatient rehabilitation study. SettingAcute inpatient rehabilitation. Participants1946 patients aged 14 years or older, who sustained a severe, moderate, or complicated mild TBI, and were admitted to 1 of 9 US inpatient rehabilitation sites between 2008 and 2011 (N=1946). Main Outcome MeasuresRehabilitation length of stay, discharge to home, FIM cognitive and FIM motor at discharge and at 9-months post discharge. ResultsAdvanced ML models, specifically gradient boosting tree model, performed consistently better than all other models, including classical linear regression models. Top ranked predictive features were identified for each of the 6 outcome variables. Level of effort, days to rehabilitation admission, age at rehabilitation admission, and advanced mobility activities were the most frequently top ranked predictive features. The highest-ranking predictive feature differed across the specific outcome variable. ConclusionsIdentifying patient, injury, and rehabilitation treatment variables that are predictive of better outcomes will contribute to cost-effective care delivery and guide evidence-based clinical practice. ML methods can contribute to these efforts.

Impact of Board of Directors on Funds Raising: Evidence for Green Bonds

The present paper attempts to reveal influence of characteristic features of the board of directors (BD) on fund raising using green bonds. The research involved a sample of 87 public companies which issued green bonds in 2021. We analyzed influence of such factors as the proportion of women and independent directors on the BD, CEO duality and the numberof the BD members by the share of green bonds in the total debt of the company. The share of debt in the assets, the natural logarithm of total assets (company size) and return on equity (ROE) were used as control variables.
 The logarithmic specification of the classical linear regression model was chosen as the optimal one. So, heteroscedasticity, autocorrelation and multicollinearity were not detected in the model with the dependent variable logarithm (the share of green bonds in the total debt). The least squares method (LSM) was applied to evaluate this model. As long as the initial sample of companies which issued green bonds in 2021 comprises both financial and non-financial companies we verified the validity of the obtained results for two types of companies. Assessment of the optimal model for two subsamples of financial and non-financial companies yielded results somewhat different from the ones obtained from analysis of the total sample. Evaluation of the regression for financial and non-financial companies showed a reduction in significance of influence exerted by women’s representation and the size of the BD. However, in case of non-financial companies the significance of such factor as presence of the sustainable development committee increases. According to the obtained results the companies with the CSR committee attract relatively larger financing using green bonds.

Regression Models of the Ultrasound Score of Madrid Sonographic Enthesis Index in Patients with Spondyloarthritis

Background Machine learning regression models are built by minimizing the generalization error in the prediction while avoiding overfitting. These techniques enhance the models and forecasts of earlier medical research by achieving greater accuracy than traditional econometric techniques. Objectives To predict the Madrid Sonographic Enthesis Index (MASEI) in spondyloarthritis (SpA) patients using the best predictor variables, including disease activity and other factors. Methods There were cross-sectional, descriptive, and observational investigations conducted. We gathered data from 24 SpA patients who received treatment in our clinics from May 2021 to September 2021 and underwent musculoskeletal ultrasonography utilizing the MASEI. Using F-tests and mutual information, we narrowed down the variables to the most important ones. Finally, we used machine learning to estimate a few regression models. Results The predictor variables with higher values in the feature selection tests explaining the MASEI are activity, Ankylosing Spondylitis Disease Activity Score (ASDAS), corticosteroids, enthesophytes, and male sex. The most accurate regression model was the Support Vector Machine model (R-squared=0.81 in validation). Since this model is a black box, we also computed a classical linear regression (R-Squared=0.60 in validation) because it provides an explicit model given by: MASEI=-4.02+2,75 Enthesofites+4.838 ASDAS. Conclusion To date, the correlation between MASEI and disease activity in patients with SpA were known. In order to further examine this relationship, we predicted two regressive models to forecast the MASEI index: a classical linear regression model and a Support Vector Machine model with the lowest estimated Root Mean Square Error among 32 alternative machine learning models.

Modelling inland Arctic bathymetry from space using cloud-based machine learning and Sentinel-2

Lakes and ponds are extensive features throughout the circumpolar region, spanning a broad range of environmental conditions which controls their hydro-ecological processes and spatiotemporal distribution. The physical characteristics of these freshwater ecosystems, including their extent and depth, are particularly responsive to climatic conditions. Thus, having the ability to efficiently map and monitor these elements is crucial as the climate continues to warm, especially over large spatial extents. In this study, satellite derived bathymetry (SDB) methods were implemented to model regional inland Arctic water depths within the open-source and cloud-based Google Earth Engine (GEE) platform. High-resolution (10 m) spectral reflectance data from Sentinel-2 was used as covariates in non-parametric and non-linear machine learning (ML) models, namely random forest (RF), support vector regression (SVR), and classification and regression trees (CART). These three ML models were also compared to a more classical and parametric multiple linear regression (MLR) model. All models were calibrated using in situ bathymetric data collected near the Toolik Field Station, in the Alaskan Arctic tundra. With such a large sample repository available, the effects of training set size, noise, and multicollinearity on model performance was comprehensively investigated. Results clearly demonstrated the superior efficacy and robustness of the RF algorithm for predicting water depths, achieving a best coefficient of determination (R2) of 0.74, mean absolute error (MAE) of 2.12 m, and root mean square error (RMSE) of 3.04 m. Overall, this study highlights the potential of advanced and flexible ML algorithms within the GEE, and demonstrates the capabilities of the polar-orbiting Copernicus Sentinel-2 satellite for this Arctic application. In the future, this ML-driven methodology can be applied using GEE’s cloud infrastructure to produce updated, cost-effective, and accurate bathymetry maps over large expanses of the Arctic tundra.

Machine learning-based prediction of conversion coefficients for I-123 metaiodobenzylguanidine heart-to-mediastinum ratio

PurposeWe developed a method of standardizing the heart-to-mediastinal ratio in 123I-labeled meta-iodobenzylguanidine (MIBG) images using a conversion coefficient derived from a dedicated phantom. This study aimed to create a machine-learning (ML) model to estimate conversion coefficients without using a phantom. Methods210 Monte Carlo (MC) simulations of 123I-MIBG images to obtain conversion coefficients using collimators that differed in terms of hole diameter, septal thickness, and length. Simulated conversion coefficients and collimator parameters were prepared as training datasets, then a gradient-boosting ML was trained to estimate conversion coefficients from collimator parameters. Conversion coefficients derived by ML were compared with those that were MC simulated and experimentally derived from 613 phantom images. ResultsConversion coefficients were superior when estimated by ML compared with the classical multiple linear regression model (root mean square deviations: 0.021 and 0.059, respectively). The experimental, MC simulated, and ML-estimated conversion coefficients agreed, being, respectively, 0.54, 0.55, and 0.55 for the low-; 0.74, 0.70, and 0.72 for the low-middle; and 0.88, 0.88, and 0.88 for the medium-energy collimators. ConclusionsThe ML model estimated conversion coefficients without the need for phantom experiments. This means that conversion coefficients were comparable when estimated based on collimator parameters and on experiments.

A comparison of machine learning methods for predicting the direction of the US stock market on the basis of volatility indices

This paper investigates the information content of volatility indices for the purpose of predicting the future direction of the stock market. To this end, different machine learning methods are applied. The dataset used consists of stock index returns and volatility indices of the US stock market from January 2011 until July 2022. The predictive performance of the resulting models is evaluated on the basis of three evaluation metrics: accuracy, the area under the ROC curve, and the F-measure. The results indicate that machine learning models outperform the classical least squares linear regression model in predicting the direction of S&P 500 returns. Among the models examined, random forests and bagging attain the highest predictive performance based on all the evaluation metrics adopted.

Bayesian model averaging for predicting factors associated with length of COVID-19 hospitalization

IntroductionThe length of hospital stay (LOHS) caused by COVID-19 has imposed a financial burden, and cost on the healthcare service system and a high psychological burden on patients and health workers. The purpose of this study is to adopt the Bayesian model averaging (BMA) based on linear regression models and to determine the predictors of the LOHS of COVID-19.MethodsIn this historical cohort study, from 5100 COVID-19 patients who had registered in the hospital database, 4996 patients were eligible to enter the study. The data included demographic, clinical, biomarkers, and LOHS. Factors affecting the LOHS were fitted in six models, including the stepwise method, AIC, BIC in classical linear regression models, two BMA using Occam's Window and Markov Chain Monte Carlo (MCMC) methods, and GBDT algorithm, a new method of machine learning.ResultsThe average length of hospitalization was 6.7 ± 5.7 days. In fitting classical linear models, both stepwise and AIC methods (R2 = 0.168 and adjusted R2 = 0.165) performed better than BIC (R2 = 0.160 and adjusted = 0.158). In fitting the BMA, Occam's Window model has performed better than MCMC with R2 = 0.174. The GBDT method with the value of R2 = 0.64, has performed worse than the BMA in the testing dataset but not in the training dataset. Based on the six fitted models, hospitalized in ICU, respiratory distress, age, diabetes, CRP, PO2, WBC, AST, BUN, and NLR were associated significantly with predicting LOHS of COVID-19.ConclusionThe BMA with Occam's Window method has a better fit and better performance in predicting affecting factors on the LOHS in the testing dataset than other models.