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This article studies identification problems of multiple linear regression models, which may be described a class of multi-input multi-output systems (i.e. multivariable systems). Based on the coupling identification concept, a novel coupled-least-squares (C-LS) parameter identification algorithm is introduced for the purpose of avoiding the matrix inversion in the multivariable recursive least-squares (RLS) algorithm for estimating the parameters of the multiple linear regression models. The analysis indicates that the C-LS algorithm does not involve the matrix inversion and requires less computationally efforts than the multivariable RLS algorithm, and that the parameter estimates given by the C-LS algorithm converge to their true values. Simulation results confirm the presented convergence theorems.

The article firstly combed the relevant factors affecting the effect of brand promotion of agricultural products, and after collecting the relevant data, it used principal component analysis to reduce the dimensionality of the characteristic factors affecting the effect of brand promotion of agricultural products. After determining the factors influencing the effect of agricultural brand promotion, the assessment model was established by using the multiple linear regression model, and the assessment test and model fitting were carried out on the model. The main findings of the article are: in the principal component coefficient matrix analysis, the three indicators of cycle continuity, product reliability, and information exhaustiveness are the first principal component, and their contribution rate is 42.24%. Project innovativeness, cycle continuity, product reliability, information exhaustiveness, project word-of-mouth, initiator’s word-of-mouth, financing effect, and number of initial fans all positively influence the effect of agricultural brand promotion.

Agricultural green production has been regarded as an effective way to solve the increasing level of agricultural environmental pollution and the frequent safety crises of agricultural products. As the main decision makers of agricultural production, farmers’ agricultural green production behavior directly determines the process of agricultural green development. However, few studies have explored farmers’ agricultural green production behavior from the perspective of environmental literacy, and the formation mechanism of farmers’ agricultural green production behavior is still unclear. This study aims to clarify the effect of environmental literacy on farmers’ agricultural green production behavior and its impact mechanism. Based on survey data from 830 farmers in China, this study constructs comprehensive index systems to evaluate farmers’ environmental literacy and agricultural green production behavior, and adopts multiple linear regression models and quantile regression model to explore the impact of environmental literacy on this behavior. Meanwhile, the mediation effect model is used to explore the mediation effect of agricultural green production cognition and agricultural green production willingness in the influence of environmental literacy on farmers’ agricultural green production behavior. Three conclusions arise. First, farmers’ environmental literacy and agricultural green production behavior are at the middle level, both of which should be strengthened. Second, environmental literacy has a significant positive impact on farmers’ agricultural green production behavior. Finally, environmental literacy influences farmers’ AGP behavior through the independent and chain mediation effects of AGP cognition and AGP willingness. Environmental literacy has heterogeneity impact on farmers’ agricultural green production behavior under different level of agricultural green production and external environment. This research not only provides theoretical support for the study of farmers’ agricultural green production behavior from the perspective of environmental literacy, it also provides a reference to the relevant government departments so that they can guide farmers to adopt more agricultural green production behavior.

The Zhejiang coastal waters (ZCW), which exhibit various turbidity levels, including low, medium, and high turbidity levels, are vital for regional ecological balance and sustainable marine resource utilization. Dissolved oxygen (DO) significantly affects marine organism survival and ecosystem health, yet there is limited research on remote sensing monitoring of DO in the ZCW, and the underlying mechanisms are unclear. This study addresses this gap by utilizing high-resolution Landsat 8/9 imagery and sea surface temperature (SST) data to develop a multiple linear regression (MLR) model for DO estimation. Compared to previous studies that utilize remote sensing band reflectance data as inputs, the results show that the red and blue bands are more suitable for establishing DO inversion models for such water bodies. The model was applied to analyze variations in the DO concentrations in the ZCW from 2013 to 2023, with a focus on Hangzhou Bay (HZB), Xiangshan Bay (XSB), Sanmen Bay (SMB), and Yueqing Bay (YQB). The temporal and spatial distributions of DO concentrations and their relationships with environmental factors, such as chlorophyll-a (Chl-a) concentrations, total suspended matter (TSM) concentrations, and thermal effluents, are analyzed. The results reveal significant seasonal fluctuations in DO concentrations, which peak in winter (e.g., 9.02 mg/L in HZB) and decrease in summer (e.g., 6.83 mg/L in HZB). Changes in the aquatic environment, particularly in the thermal effluents from the Sanmen Nuclear Power Plant (SNPP), significantly decrease coastal dissolved oxygen (DO) concentrations near drainage outlets. Chl-a and TSM directly or indirectly affect DO concentrations, with notable correlations observed in XSB. This study offers a novel approach for monitoring and managing water quality in the ZCW, facilitating the early detection of potential hypoxia issues in critical zones, such as nuclear power plant heat discharge outlets.

Given the significant impact of air pollution on global health, the continuous and precise monitoring of air quality in all populated environments is crucial. Unfortunately, even in the most developed economies, current air quality monitoring networks are largely inadequate. The high cost of monitoring stations has been identified as a key barrier to widespread coverage, making cost-effective air quality monitoring devices a potential game changer. However, the accuracy of the measurements obtained from low-cost sensors is affected by many factors, including gas cross-sensitivity, environmental conditions, and production inconsistencies. Fortunately, machine learning models can capture complex interdependent relationships in sensor responses and thus can enhance their readings and sensor accuracy. After gathering measurements from cost-effective air pollution monitoring devices placed alongside a reference station, the data were used to train such models. Assessments of their performance showed that models tailored to individual sensor units greatly improved measurement accuracy, boosting their correlation with reference-grade instruments by up to 10%. Nonetheless, this research also revealed that inconsistencies in the performance of similar sensor units can prevent the creation of a unified correction model for a given sensor type.

Landscape and site-scale data analyses aid the interpretation of biological data and thereby help us develop more cost-effective natural resource management strategies. Our study focused on environmental influences on stream assemblages and we evaluated how three classes of environmental variables (geophysical landscape, land use and cover, and site habitat), influence fish and macroinvertebrate assemblage richness in the Brazilian Cerrado biome. We analyzed our data through use of multiple linear regression (MLR) models using the three classes of predictor variables alone and in combination. The four MLR models explained dissimilar amounts of benthic macroinvertebrate taxa richness (geophysical landscape R ² ≈ 35 %, land use and cover R ² ≈ 28 %, site habitat R ² ≈ 36 %, and combined R ² ≈ 51 %). For fish assemblages, geophysical landscape, land use and cover, site habitat, and combined models explained R ² ≈ 28 %, R ² ≈ 10 %, R ² ≈ 31 %, and R ² ≈ 47 % of the variability in fish species richness, respectively. We conclude that (1) environmental variables differed in the degree to which they explain assemblage richness, (2) the amounts of variance in assemblage richness explained by geophysical landscape and site habitat were similar, (3) the variables explained more variability in macroinvertebrate taxa richness than in fish species richness, and (4) all three classes of environmental variables studied were useful for explaining assemblage richness in Cerrado headwater streams. These results help us to understand the drivers of assemblage patterns at regional scales in tropical areas.

Exposure to indoor particulate matter less than 2.5 µm in diameter (PM2.5) is a critical health risk factor. Therefore, measuring indoor PM2.5 concentrations is important for assessing their health risks and further investigating the sources and influential factors. However, installing monitoring instruments to collect indoor PM2.5 data is difficult and expensive. Therefore, several indoor PM2.5 concentration prediction models have been developed. However, these prediction models only assess the daily average PM2.5 concentrations in cold or temperate regions. The factors that influence PM2.5 concentration differ according to climatic conditions. In this study, we developed a prediction model for hourly indoor PM2.5 concentrations in Taiwan (tropical and subtropical region) by using a multiple linear regression model and investigated the impact factor. The sample comprised 93 study cases (1979 measurements) and 25 potential predictor variables. Cross-validation was performed to assess performance. The prediction model explained 74% of the variation, and outdoor PM2.5 concentrations, the difference between indoor and outdoor CO2 levels, building type, building floor level, bed sheet cleaning, bed sheet replacement, and mosquito coil burning were included in the prediction model. Cross-validation explained 75% of variation on average. The results also confirm that the prediction model can be used to estimate indoor PM2.5 concentrations across seasons and areas. In summary, we developed a prediction model of hourly indoor PM2.5 concentrations and suggested that outdoor PM2.5 concentrations, ventilation, building characteristics, and human activities should be considered. Moreover, it is important to consider outdoor air quality while occupants open or close windows or doors for regulating ventilation rate and human activities changing also can reduce indoor PM2.5 concentrations.

Ridge regression model is a widely used model with many successful applications, especially in managing correlated covariates in a multiple regression model. Multicollinearity represents a serious threat in fuzzy regression models as well. We address this issue by combining ridge regression with the fuzzy regression model. Our proposed algorithm uses the α -level estimation method to evaluate the parameters of the ridge fuzzy regression model. Two examples are given to illustrate the ridge fuzzy regression model with crisp input/fuzzy output and fuzzy coefficients.

This paper aims to explore the integration of Marxism and Chinese-style modernization and its practical application in the context of the digital intelligence era. Through theoretical Analysis and empirical research, a system for assessing development of Marxist Chinese-style modernization has been established. The study finds that Marxism’s multiple characteristics, such as political, scientific, people’s, practical, developmental, and revolutionary, provide theoretical support for Chinese-style modernization. This paper uses grey correlation analysis and multiple linear regression models to evaluate the modernization development of 31 provinces, municipalities, and autonomous regions in China during 2010-2019. The study results show that the Marxist Chinese-style modernization index has grown from 0.164 in 2010 to 0.731 in 2020, with an average annual growth rate of 34.57%. The index significantly impacts the quality of the regional economy, cultural industry, and ecological environment. The study shows that the application of Marxism in China accelerates economic development and promotes the governance of cultural industry and ecological environment, which provides impetus for the construction of socialist modernization with Chinese characteristics.

In this research, two types of bias estimator were studied in linear regression model which are; (almost unbiased generalized ridge estimator, almost unbiased two-parameter estimator and Modified ridge-type estimator) and (The (r-k) class estimator and modified (r-k) class ridge regression estimator) as a method of repressing the multicollinearity problem on parameter estimation in multiple linear regression models. Also, a simulation analysis was used to test the relative efficiency of certain types of biased estimators as well as the thirty-nine proposed estimated ridge parameters (k) that have been shown in the literature. Moreover, the mean square error was also assigned to study the quality of those estimators in different circumstances and for different correlations. Finally, a practical example was applied to illustrate the obtained results. All proposed estimators of (k) are, according to the results, superior to ordinary least squared estimator (LSE), but there is no 'optimal' estimator guarantee that can come out, and the best estimator option will depend on the study conditions.