Classical Linear Regression Model Research Articles

A Small Sigma Asymptomatic Approach Generalized Quasi Minimax and Mock Minimax Estimators in Linear Regression Model

In this paper concern with priority two generalized classes of estimators utilizing both types of information apriori and sample, for the estimation of coefficient vector in classical linear regression model in the presence of ellipsoidal Constraints on the parameter vector when the variance of the distribution are unknown. A vectors mean square matrices and weighted quadratic risk are found employing small sigma asymptotic. Some better estimators in the sense of having lesser risk than those of the estimators.

Determinants of Healthcare Expenditure: A Cross-Sectional Analysis at the Country Level

This study examines the determinants of healthcare expenditure through a cross-sectional analysis of 153 countries using 2018 data. The research employs a classical linear regression model to identify key socioeconomic and demographic factors influencing healthcare spending per capita, expressed in PPP (Purchasing Power Parity). The results show that GDP per capita, public health expenditure as a percentage of GDP, physician availability, and out-of-pocket healthcare costs are statistically significant determinants of healthcare spending. Specifically, the analysis highlights the non-linear relationship between GDP and healthcare expenditure, where wealthier nations tend to spend disproportionately more on healthcare. Public investment in healthcare and the availability of medical professionals also play crucial roles in shaping national healthcare expenditures. Out-of-pocket expenses by households further increase overall healthcare costs, especially in countries with lower public funding. The proposed model explains 96.5% of the variation in healthcare expenditure, suggesting that the selected variables are strong predictors of healthcare spending. These findings provide valuable insights for policymakers, particularly in the context of balancing public healthcare financing and improving access to medical services while managing overall costs.

Stock Market Development and Economic Growth: The Case of Kazakhstan

The purpose of the article. The relationship between economic growth and financial development has long been widely discussed in scientific circles. Most empirical research has led to the clear conclusion that financial markets stimulate economic development. However, in the case of financial markets in developing countries, this conclusion is not so obvious. The aim of this study is to empirically verify the relationship between economic growth and the development of the stock market (Kazakhstan Stock Exchange). Methodology. Empirical verification of the strength and shape of the cause-and-effect relationship between real GDP growth and independent predictors will be carried out using classic linear regression models with many independent variables. Results of the research. The results of empirical verification of the strength and shape of the cause-and-effect relationship between the growth of real GDP and independent predictors indicate that the development of the stock market has a positive impact on the growth of the country's real GDP but is not the basic factor of Kazakhstan's economic growth.

Copula-based regression estimation in the presence of outliers

Ordinary least square estimators for linear regression models are highly influenced by outliers. Copula is a powerful tool for studying the dependence between response and predictor variables and may overcome several limitations associated with the classical linear regression models. In this study, we investigate the efficacy of the copula-based regression models over classical linear regression in the presence of outliers in the x, y, and x-y directions. We also examine the performance of several robust regression estimation techniques when variables are related via elliptical and Archimedean family of copulas and outliers are present in the data. Finally, real and artificial data sets are analyzed to compare the performance of various robust regression techniques.

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.

Prognostic Modelling of Biomethane Production from Waste: Application of Extreme Gradient Boosting

The escalating fossil fuel prices and greenhouse gases need urgent attention for a sustainable solution. The present study explores as modern machine learning approaches can be employed to prognosticate the complex biomethane generation process from organic wastes, like biowaste or food waste. The research investigates the use of organic sludges and how intelligent approaches can be employed to comprehend the complex nonlinear processes involved in biomethane production. Linear regression and Extreme gradient boosting (XGBoost) based prediction-models were developed and assessed employing a diverse set of statistical parameters, including R, R2, Mean Squared Error (MSE), Mean Absolute Error (MAE), and Kling-Gupta Efficiency (KGE). The results show that the XGBoost model beat the classical Linear Regression (LR) model in both the training and testing phases. During training, the XGBoost had an impressive R2 value of 0.99994, indicating a perfect fit to the data. In contrast, LR achieved an R2 value of 0.65464. Similarly, during the test period, XGBoost outperformed LR with R2 values ​​of 0.9553 to 0.9902. Furthermore, XGBoost reduced prediction errors, with significantly lower MSE and MAE values ​​than LR. Taylor’s graph better illustrates the excellent performance of the XGBoost over LR in both training and testing. These data demonstrate the ability of XGBoost to predict biomethane production, as well as its ability to improve the biomethane production process.

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.

Exploring Heat Demand Forecasting in District Heating Networks Using Random Parameter Linear Regression Model

Abstract Accurate forecasting of heat demand in district heating networks is essential for their efficient and sustainable operation. This paper presents a novel approach using a random parameter linear regression model to forecast heat demand, distinguishing itself from classical linear regression models by its ability to address unobserved heterogeneity among parameters. Through a case study in Estonia and utilizing data from 2018 to 2023 and considering seasonality and consumption patterns, the study investigates determinants of heating demand in district heating networks. Two models were trained for heating and non-heating seasons. Results indicate significant impacts of weather conditions, energy prices, time of day, and network infrastructure on heat supply during the heating season, while only time of day and electricity prices were significant drivers during the non-heating season, with no notable influence of weather conditions. Prediction accuracy was slightly enhanced using the random parameter linear regression model, with a mean absolute percentage error of 9.66 % compared to 9.99 % for the Multi Linear Regression Model on the testing set.

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.

A Quantitative Impact Assessment of English Translation Errors on the Authenticity of News Dissemination

Abstract To improve the accuracy of news communication between readers and audiences, it is necessary to avoid the errors generated in the process of news translation so as to make the English translation of news content expression more in line with the actual situation, thus ensuring the authenticity of news dissemination. In this paper, the MapReduce multiple regression model is constructed by optimizing the classical multiple linear regression model in terms of maximum likelihood estimation and gradient descent algorithm with the aim of reducing the errors in the process of English translation of news. This model is used to analyze the errors generated by the English translation process and finally proposes a method for improving translation accuracy based on the factors causing the errors. After testing, the F-value, P-value, and R² of the degree of fit of the MapReduce model are 54.39, 0.005, and 0.893, respectively. Furthermore, the model passed the significance test. The Pearson coefficients of the 4 types of translation errors in the MapReduce multiple linear regression model were −0.673, −0.622, −0.584, and −0.736, respectively, all of which were significantly negatively correlated with the truthfulness of news dissemination at the 1% level. The model analyzes that the three kinds of translation errors are basically between 2%-4%, 7%-20%, and 2%-4%, and puts forward reasonable opinions on the avoidance of the four kinds of errors, namely, “pragmatic translation, cultural translation, linguistic translation and text-specific translation”, which generate errors in the process of the English translation of news.

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.