Classical Multiple Linear Regression Research Articles

Enhancing riverine load prediction of anthropogenic pollutants: Harnessing the potential of feed-forward backpropagation (FFBP) artificial neural network (ANN) models

Assessing riverine pollutant loads is a more realistic method for analysing point and non-point anthropogenic pollution sources throughout a watershed. This study compares numerous mathematical modelling strategies for estimating riverine loads based on the chosen water quality parameters: Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Suspended Solids (SS), and Ammoniacal Nitrogen (NH3–N). A riverine load model was developed by employing various input variables including river flow and pollutant concentration values collected at several monitoring sites. Among the mathematical modelling methods employed are artificial neural networks with feed-forward backpropagation algorithms and radial basis functions. The classical multiple linear regression (MLR) statistical model was used for the comparison. Four widely used statistical performance assessment metrics were adopted to evaluate the performance of the various developed models: the root mean square error (RMSE), mean absolute error (MAE), mean relative error (MRE), and coefficient of determination (R2). The considerable number of errors (with RMSE, MAE, and MRE) discovered in estimating riverine loads using the multiple linear regression (MLR) statistical model can be attributed to the nonlinear relationship between the independent variables (Q and Cx) and dependent variables (W). The feed-forward neural network model with a backpropagation algorithm and Bayesian regularisation training algorithm outperformed the radial basis neural network. This finding implies that, in addition to suspended sediment loads, riverine loads may be predicted using an artificial neural network using pollutant concentration (Cx) and river discharge (Q) as input variables. Other geographical and temporal fluctuation characteristics that may impact river water quality, on the other hand, may be incorporated as input variables to enhance riverine load prediction. Finally, riverine load analyses were successfully conducted to reduce the riverine load.

Identifying and Exploring the Impact Factors for Intraocular Pressure Prediction in Myopic Children with Atropine Control Utilizing Multivariate Adaptive Regression Splines.

The treatment of childhood myopia often involves the use of topical atropine, which has been demonstrated to be effective in decelerating the progression of myopia. It is crucial to monitor intraocular pressure (IOP) to ensure the safety of topical atropine. This study aims to identify the optimal machine learning IOP-monitoring module and establish a precise baseline IOP as a clinical safety reference for atropine medication. Data from 1545 eyes of 1171 children receiving atropine for myopia were retrospectively analyzed. Nineteen variables including patient demographics, medical history, refractive error, and IOP measurements were considered. The data were analyzed using a multivariate adaptive regression spline (MARS) model to analyze the impact of different factors on the End IOP. The MARS model identified age, baseline IOP, End Spherical, duration of previous atropine treatment, and duration of current atropine treatment as the five most significant factors influencing the End IOP. The outcomes revealed that the baseline IOP had the most significant effect on final IOP, exhibiting a notable knot at 14 mmHg. When the baseline IOP was equal to or exceeded 14 mmHg, there was a positive correlation between atropine use and End IOP, suggesting that atropine may increase the End IOP in children with a baseline IOP greater than 14 mmHg. MARS model demonstrates a better ability to capture nonlinearity than classic multiple linear regression for predicting End IOP. It is crucial to acknowledge that administrating atropine may elevate intraocular pressure when the baseline IOP exceeds 14 mmHg. These findings offer valuable insights into factors affecting IOP in children undergoing atropine treatment for myopia, enabling clinicians to make informed decisions regarding treatment options.

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.

Assessing the length of hospital stay for patients with myasthenia gravis based on the data mining MARS approach.

Predicting the length of hospital stay for myasthenia gravis (MG) patients is challenging due to the complex pathogenesis, high clinical variability, and non-linear relationships between variables. Considering the management of MG during hospitalization, it is important to conduct a risk assessment to predict the length of hospital stay. The present study aimed to successfully predict the length of hospital stay for MG based on an expandable data mining technique, multivariate adaptive regression splines (MARS). Data from 196 MG patients' hospitalization were analyzed, and the MARS model was compared with classical multiple linear regression (MLR) and three other machine learning (ML) algorithms. The average hospital stay duration was 12.3 days. The MARS model, leveraging its ability to capture non-linearity, identified four significant factors: disease duration, age at admission, MGFA clinical classification, and daily prednisolone dose. Cut-off points and correlation curves were determined for these risk factors. The MARS model outperformed the MLR and the other ML methods (including least absolute shrinkage and selection operator MLR, classification and regression tree, and random forest) in assessing hospital stay length. This is the first study to utilize data mining methods to explore factors influencing hospital stay in patients with MG. The results highlight the effectiveness of the MARS model in identifying the cut-off points and correlation for risk factors associated with MG hospitalization. Furthermore, a MARS-based formula was developed as a practical tool to assist in the measurement of hospital stay, which can be feasibly supported as an extension of clinical risk assessment.

Bayesian-Optimization-Based Long Short-Term Memory (LSTM) Super Learner Approach for Modeling Long-Term Electricity Consumption

This study utilized different methods, namely classical multiple linear regression (MLR), statistical approach exponential smoothing (EXPS), and deep learning algorithm long short-term memory (LSTM) to forecast long-term electricity consumption in the Kingdom of Saudi Arabia. The originality of this research lies in (1) specifying exogenous variables that significantly affect electrical consumption; (2) utilizing the Bayesian optimization algorithm (BOA) to develop individual super learner BOA-LSTM models for forecasting the residential and total long-term electric energy consumption; (3) measuring forecasting performances of the proposed super learner models with classical and statistical models, viz. MLR and EXPS, by employing the broadly used evaluation measures regarding the computational efficiency, model accuracy, and generalizability; and finally (4) estimating forthcoming yearly electric energy consumption and validation. Population, gross domestic products, imports, and refined oil products significantly impact residential and total annual electricity consumption. The coefficient of determination (R2) for all the proposed models is greater than 0.93, representing an outstanding fitting of the models with historical data. Moreover, the developed BOA-LSTM models have the best performance with R2>0.99, enhancing the predicting accuracy (Mean Absolute Percentage Error (MAPE)) by 59.6% and 54.8% compared to the MLR and EXPS models, respectively, of total annual electricity consumption. This forecasting accuracy in residential electricity consumption for the BOA-LSTM model is improved by 62.7% and 68.9% compared to the MLR and EXPS models. This study achieved a higher accuracy and consistency of the proposed super learner model in long-term electricity forecasting, which can be utilized in energy strategy management to secure the sustainability of electric energy.

Construction and evaluation of hourly average indoor PM2.5 concentration prediction models based on multiple types of places.

People usually spend most of their time indoors, so indoor fine particulate matter (PM2.5) concentrations are crucial for refining individual PM2.5 exposure evaluation. The development of indoor PM2.5 concentration prediction models is essential for the health risk assessment of PM2.5 in epidemiological studies involving large populations. In this study, based on the monitoring data of multiple types of places, the classical multiple linear regression (MLR) method and random forest regression (RFR) algorithm of machine learning were used to develop hourly average indoor PM2.5 concentration prediction models. Indoor PM2.5 concentration data, which included 11,712 records from five types of places, were obtained by on-site monitoring. Moreover, the potential predictor variable data were derived from outdoor monitoring stations and meteorological databases. A ten-fold cross-validation was conducted to examine the performance of all proposed models. The final predictor variables incorporated in the MLR model were outdoor PM2.5 concentration, type of place, season, wind direction, surface wind speed, hour, precipitation, air pressure, and relative humidity. The ten-fold cross-validation results indicated that both models constructed had good predictive performance, with the determination coefficients (R2) of RFR and MLR were 72.20 and 60.35%, respectively. Generally, the RFR model had better predictive performance than the MLR model (RFR model developed using the same predictor variables as the MLR model, R2 = 71.86%). In terms of predictors, the importance results of predictor variables for both types of models suggested that outdoor PM2.5 concentration, type of place, season, hour, wind direction, and surface wind speed were the most important predictor variables. In this research, hourly average indoor PM2.5 concentration prediction models based on multiple types of places were developed for the first time. Both the MLR and RFR models based on easily accessible indicators displayed promising predictive performance, in which the machine learning domain RFR model outperformed the classical MLR model, and this result suggests the potential application of RFR algorithms for indoor air pollutant concentration prediction.

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.

COVID-19 Prediction Using Black-Box Based Pearson Correlation Approach.

The novel coronavirus (COVID-19), also known as SARS-CoV-2, is a highly contagious respiratory disease that first emerged in Wuhan, China in 2019 and has since become a global pandemic. The virus is spread through respiratory droplets produced when an infected person coughs or sneezes, and it can lead to a range of symptoms, from mild to severe. Some people may not have any symptoms at all and can still spread the virus to others. The best way to prevent the spread of COVID-19 is to practice good hygiene. It is also important to follow the guidelines set by local health authorities, such as physical distancing and quarantine measures. The World Health Organization (WHO), on the other hand, has classified this virus as a pandemic, and as a result, all nations are attempting to exert control and secure all public spaces. The current study aimed to (I) compare the weekly COVID-19 cases between Israel and Greece, (II) compare the monthly COVID-19 mortality cases between Israel and Greece, (III) evaluate and report the influence of the vaccination rate on COVID-19 mortality cases in Israel, and (IV) predict the number of COVID-19 cases in Israel. The advantage of completing these tasks is the minimization of the spread of the virus by deploying different mitigations. To attain our objective, a correlation analysis was carried out, and two distinct artificial intelligence (AI)-based models-specifically, an artificial neural network (ANN) and a classical multiple linear regression (MLR)-were developed for the prediction of COVID-19 cases in Greece and Israel by utilizing related variables as the input variables for the models. For the evaluation of the models, four evaluation metrics (determination coefficient (R2), mean square error (MSE), root mean square error (RMSE), and correlation coefficient (R)) were considered in order to determine the performance of the deployed models. From a variety of perspectives, the corresponding determination coefficient (R2) demonstrated the statistical advantages of MLR over the ANN model by following a linear pattern. The MLR predictive model was both efficient and accurate, with 98% accuracy, while ANN showed 94% accuracy in the effective prediction of COVID-19 cases.

Autoregressive distributed lag estimation of bank financing and Nigerian manufacturing sector capacity utilization

<abstract> <p>This study examined the short-term and long-term relationship between credit financing by commercial banks and capacity utilization of the manufacturing sector in Nigeria. The study employed both classical Multiple Linear Regression (OLS-MLR) and the autoregressive distributed lag model (ARDL) to analyze data representing the period 1981–2020 relating to sectoral credit finance,labor employment,and capacity utilization from the <xref ref-type="bibr" rid="b6">Central Bank of Nigeria Statistical Bulletin (2020)</xref> and <xref ref-type="bibr" rid="b38">World Bank Development Indicators (2021)</xref>. Further,the two estimation procedures were performed within a classical endogenous Cobb-Douglas production function framework that takes technical change into consideration. The bounds test indicated no long-term relationship between bank financing and average capacity utilization of the manufacturing sector in Nigeria. However,the ARDL results revealed that bank financing exerts a positive but insignificant short-term impact on the average capacity utilization of the manufacturing sector in Nigeria. Consequently,the researchers affirm that credit financing by commercial banks in Nigeria has no significant impact on the capacity utilization of the country's manufacturing sector,in neither the short run nor the long run.</p> </abstract>

The Effect of Taxpayer Compliance, Tax Collection and Self Assessment System on Tax Revenue

This study aims to determine and analyze taxpayer compliance, tax collection, and the self-assessment system of individual tax receipts in the city of Palembang. The type of research used is descriptive and associative. Sampling used a random method, the sample used was 100 respondents. The data used is primary data by distributing questionnaires to respondents. The analysis used is descriptive statistical analysis and inferential statistical analysis (assumption test and classical multiple linear regression, and hypothesis testing). The results showed that taxpayer compliance has an effect on tax revenue (t count 4.759 > t table 1.660). Tax Collection on Tax Revenue (t count 5,262 > t table 1,660). Self Assessment System has an effect on Tax Revenue (t count 8.394 > t table 1.660) and significant average 0.000 > 0.05 Keywords: Taxpayer Compliance, Tax Collection, System and Taxe revenue

Forecasting annual electric power consumption using a random parameters model with heterogeneity in means and variances

This paper develops heterogeneity-based econometric models that forecast the yearly consumption of electricity. Unlike previous research, this paper departs from classical econometric regression models and explicitly accounts for unobserved heterogeneity and corresponding interactions. More specifically, three modeling approaches are applied: a random parameter linear regression model (RPLRM), a correlated random parameter linear model (C-RPLRM), and a random parameter linear model with heterogeneity in means and variances (RP-HMV). In addition, a grey model is estimated based on historical consumption data. The estimation results clearly demonstrate that the random parameter methodology is statistically superior to the classical multiple linear regression model. Moreover, based on the test results reported in this paper, as well as the forecasting accuracy measures, the RP-HMV model is shown to be statistically outstanding, with a very low forecasting error (MAPE of 0.04%) compared to the other models, including the grey model. Our estimation results show that two variables, namely the average electricity price and contribution of renewable energy to the national and distribution grids, produced statistically significant random parameters with heterogeneous variances and means. Moreover, the results show that factors including the number of households on the distribution grid, average electric power price, and availability of all-season air conditioners with hot and cold inverter characteristics significantly influenced the electricity consumption. These empirical results reveal that random-parameters models with heterogeneity in their means and variances can provide a detailed analysis of the predictor variables shaping the annual electricity consumption, and they highlight the importance of including unobserved heterogeneity and related interactions in econometric models.

A Radial Basis Function Neural Network Approach to Predict Preschool Teachers' Technology Acceptance Behavior.

With the continual development of artificial intelligence and smart computing in recent years, quantitative approaches have become increasingly popular as an efficient modeling tool as they do not necessitate complicated mathematical models. Many nations have taken steps, such as transitioning to online schooling, to decrease the harm caused by coronaviruses. Inspired by the demand for technology in early education, the present research uses a radial basis function (RBF) neural network (NN) modeling technique to predict preschool instructors’ technology usage in classes based on recognized determinant characteristics of technology acceptance. In this regard, this study utilized the RBFNN approach to predict preschool teachers’ technology acceptance behavior, based on the theory of planned behavior, which states that behavioral achievement, in our case the actual technology use in class, depends on motivation, intention and ability, and behavioral control. Thus, this research design is based on an adapted version of the technology acceptance model (TAM) with eight dimensions: D1. Perceived usefulness, D2. Perceived ease of use, D3. Perceived enjoyment, D4. Intention to use, D5. Actual use, D6. Compatibility, D7. Attitude, and D8. Self-efficacy. According to the TAM, actual usage is significantly predicted by the other seven dimensions used in this research. Instead of using the classical multiple linear regression statistical processing of data, we opted for a NN based on the RBF approach to predict the actual usage behavior. This study included 182 preschool teachers who were randomly chosen from a project-based national preschool teacher training program and who responded to our online questionnaire. After designing the RBF function with the actual usage as an output variable and the other seven dimensions as input variables, in the model summary, we obtained in the training sample a sum of squares error of 37.5 and a percent of incorrect predictions of 43.3%. In the testing sample, we obtained a sum of squares error of 14.88 and a percent of incorrect predictions of 37%. Thus, we can conclude that 63% of the classified data are correctly assigned to the models’ dependent variable, i.e., actual technology use, which is a significant rate of correct predictions in the testing sample. This high significant percentage of correct classification represents an important result, mainly because this is the first study to apply RBFNN’s prediction on psychological data, opening up a new interdisciplinary field of research.

Regional thermal analysis approach: A management tool for predicting water temperature metrics relevant for thermal fish habitat

The field of water resource management, including fisheries, is facing new challenges associated with climate change. This study sheds light on the modeling of water temperature indices (metrics) that describe critical thermal maxima of the Atlantic salmon (salmo salar). These thermal metrics include MaxWaterTmax (interannual mean of maximum summer temperature), MaxNumDay (interannual mean of the number of consecutive days with maximum water temperature > 25 °C and minimum water temperature > 20 °C). The latter is an important indicator to evaluate thermal variability. Three other parameters of a Gaussian function fitted to the interannual daily mean temperatures characterizing the thermal regime of 146 stations located in Eastern Canada were estimated. These three parameters are Gaussian_a (maximum of interannual daily mean temperature), Gaussian_b (mean duration of the warm period), and Gaussian_c (date of occurrence of the interannual maximum temperature). The classical Multiple linear regression model (MLR) and the non-linear Generalized additive model (GAM) were tested and compared to estimate the five thermal metrics. The regression-based approaches involve the identification of thermally homogeneous regions based on three approaches: hierarchical clustering analysis (HCA), regions of influence (ROI) as well as canonical correlation analysis (CCA). Then, the regional MLR and GAM models were applied within the delineated homogenous regions. Also, the regional models were compared to models encompassing all stations (i.e., one region). For each regional estimation model and each thermal metric, a set of optimal explanatory variables were selected using a forward stepwise procedure. The database consisted of 22 environmental predictors related to physiography, topography, climate, land cover and surface deposits. To assess performance of the models, the following statistical metrics were used: coefficient of determination R2, root mean square error (RMSE), bias, relative root mean square error (RRMSE) and percent bias (PBias). The results demonstrate that the non-linear GAM model was consistently better than the simpler MLR model for estimating the five thermal metrics. Results also show that the best practice consists in delineating homogeneous regions before applying the regional GAM model. According to all performance criteria, delineation of regions with the HCA approach is considered to be more flexible and to lead to better performances than neighborhood-based approaches (CCA and ROI).

A critical view on the suitability of machine learning techniques to downscale climate change projections: Illustration for temperature with a toy experiment

AbstractMachine learning is a growing field of research with many applications. It provides a series of techniques able to solve complex nonlinear problems, and that has promoted their application for statistical downscaling. Intercomparison exercises with other classical methods have so far shown promising results. Nevertheless, many evaluation studies of statistical downscaling methods neglect the analysis of their extrapolation capability. In this study, we aim to make a wakeup call to the community about the potential risks of using machine learning for statistical downscaling of climate change projections. We present a set of three toy experiments, applying three commonly used machine learning algorithms, two different implementations of artificial neural networks and a support vector machine, to downscale daily maximum temperature, and comparing them with the classical multiple linear regression. We have tested the four methods in and out of their calibration range, and have found how the three machine learning techniques can perform poorly under extrapolation. Additionally, we have analysed the impact of this extrapolation issue depending on the degree of overlapping between the training and testing datasets, and we have found very different sensitivities for each method and specific implementation.

Pengaruh Informasi Akuntansi, Persepsi Risiko dan Citra Perusahaan dalam Pengambilan Keputusan Investasi di Masa Pandemi Covid-19

Investment decisions are policies used in the use of existing company funds on assets that are expected to provide future benefits with a certain level of risk. The purpose of this study was to determine whether accounting information, risk perception, and company image have a significant influence on investment decision making during the Covid-19 pandemic. This study uses quantitative research methods. The population in this study are investors who are registered in the BEI Investment Gallery, Faculty of Economics, Padang State University. The sample in this study used the Simple Random Sampling technique, the number of samples in this study was 110. The data was collected using questionnaires distributed online. The data were analyzed using descriptive analysis, Data Quality Test, Classical Assumption Test and Multiple Linear Regression Analysis. The results show that 1) accounting information influences investment decisions during the covid 19 pandemic, 2) risk perception affects investment decisions during the covid 19 pandemic, 3) company image affects investment decisions during the covid 19 pandemic. Based on the conclusions above, some suggestions can be given as follows: 1) For further researchers, it is expected to distinguish respondents who have become stock investors in the capital market or each who have not become investors, 2) It is hoped that further researchers will examine more deeply about the factors that influence investment decisions during the COVID-19 pandemic.

The Influence of Banking Understanding, Communication and Intensity of Assignment on Banking Accounting Learning Outcomes

The purpose of this study was to analyze the effect of understanding banking, communication with banks, and the intensity of assignment on banking accounting learning outcomes partially and simultaneously in class XI PKM students at SMK Negeri 10 Surabaya. This type of research uses a quantitative research approach. The number of samples in this study were 81 students of XI PKM. The sampling technique used is proportional random sampling. Data collection techniques using tests and questionnaires. Classical assumption test and multiple linear regression analysis were used to analyze the collected data using the IBM SPSS Statistic 24 program. The results showed that banking understanding, communication with banks, and the intensity of assignment had a significant effect on banking accounting learning outcomes with an Fcount of 5, 112 and a significance of 0.003. Partially, understanding of banking affects the learning outcomes of banking accounting with a significance value of 0.011. Communication with the bank affects the learning outcomes of banking accounting with a significance value of 0.025. The intensity of the assignment affects the learning outcomes of banking accounting with a significance value of 0.047.

Estimating Dam Reservoir Level Change of Istanbul Alibey Dam with The Fuzzy SMRGT Method

Accurate estimation of the dam reservoir level in a dam reservoir is very important for the planning and operation of water structures. In this study, monthly dam reservoir level data between 1989 and 2020 obtained from the State Hydraulic Works (DSI) was used to estimate the monthly dam reservoir level change. For the monthly dam reservoir level estimation, it has been tried to be estimated using the Simple Membership Functionsand Fuzzy Rules Generation Technique (Fuzzy-SMRGT), Artificial Neural Network (ANN) and the classical Multiple Linear Regression (MLR) methods. Alibey Dam located in Sultangazi district of Istanbul was chosen as the study area. The monthly evaporation, water entering into the lake, consumption of drinking water and amount of water discharged from the dam amounts were used to estimate the monthly Alibey Dam reservoir average dam reservoir level. The model results were compared with the actual observation dam reservoir levels. When the results were evaluated, it was observed that the models were successful in estimating the dam reservoir level and gave results close to each other

Factors Affecting the ICI during Indonesia's Economic Recession During the Covid-19 Pandemic

The study used in this study aims to determine the factors that can affect the JCI, namely the rupiah exchange rate, inflation, and interest rates during the Indonesian economic recession during the Covid-19 pandemic. The research method used in this study uses quantitative and The secondary data used is secondary data from the BEI and BI which was collected from 6 Nov 2020 to 3 Feb 2021 with a data collection technique, namely the documentation method. Saturated sampling is used in the sampling technique. So that obtained as many as 59 samples. While the techniques used in data analysis in this study are classical assumption test and multiple linear regression analysis as hypothesis testing. JCI. However, inflation in a partial test does not have a significant effect on the JCI.

Factors Affecting Dissolved Oxygen at Bengawan Solo River: A Spatial Filtering with Eigenvector Technique

The quality of the river changes according to the development of the surrounding environment which is influenced by various human activities. Analysis of factors affecting Dissolved Oxygen (DO) at Bengawan Solo River is crucial for river management purpose and pollution control. Previous research suggested the use classic multiple linear regression. However, DO measurement were usually took place of sampling sites along the river channel. Therefore, there is a high chance that the measurements results may spatially correlated. As the consequence, the utilization of multiple linear regression technique for the dataset can be inappropriate. In this paper, we applied a modification of multiple linear regression model to incorporate with spatial autocorrelation that exist in the data by adding control variable such vector eigen to the model which known as Spatial Filtering with Eigenvector (SFE). The results showed that nitrate and nitrite were the predictor variables that have a negative and significant effect. However, the model contains spatial autocorrelation. The application of SFE technique by adding three eigenvectors as control variables in the model succeeded in making the residual model free from spatial autocorrelation. However, a new problem arose where there was a violation of the non-heteroscedasticity assumption.

Модели машинного обучения в задаче прогнозирования природно-ресурсного потенциала Пермского края

In the article we consider a complex indicator of region natural resource potential modeling and forecasting quality improvement using different machine learning models. Problem under consideration importance is determined by the fact that the models traditionally used for these purposes demonstrate either low quality, or high configuration and parameters evaluation difficulty. The aim of the study is determination of machine learning models that provide the optimal values of various modeling quality metrics. Materials and methods. For this study purposes we considered the multiple linear regression, decision tree, random forest, gradient boosting and multilayer perceptron mo¬dels. We used the determination coefficient R2, the root mean square error of modeling RMSE, the average absolute error of modeling MAE, and the relative error of prediction for 1 and 2 time intervals as quality metrics. This study is based on data of the complex indicator of the Perm Region natural resource potential and the system of its determining factors in the time interval from 2001 to 2018. We evaluate models and calculate quality metrics using Pandas and Scikit-learn Python libraries in Jupiter Notebook environment. Results. According to our research the classical multiple linear regression model demonstrates the worst results for all quality metrics under consideration. The decision tree model demonstrates determination coefficient maximum value and minimum root mean square error and mean absolute error. Minimum relative forecasting error for 2017 is provided by the gradient boosting model, for 2018 – by the multilayer perceptron model. Conclusion. Our study allows us to affirm that nonlinear machine learning models for the task of region natural resource potential modeling and forecasting demonstrate better approximating and predictive properties compared to multiple linear regression and thus can be used to improve the quality of natural resource management.