Combined model based on optimized multi-variable grey model and multiple linear regression

The construction method of background value is improved in the original multi-variable grey model （MGM（1,m）） from its source of construction errors. The MGM（1,m） with optimized background value is used to eliminate the random fluctuations or errors of the observational data of all variables, and the combined prediction model together with the multiple linear regression is established in order to improve the simulation and prediction accuracy of the combined model. Finally, a combined model of the MGM（1,2） with optimized background value and the binary linear regression is constructed by an example. The results show that the model has good effects for simulation and prediction.

Application of Grey System GM (1,1) model and unary linear regression model in coal consumption of Jilin Province

The data on the coal production and consumption in Jilin Province for the last ten years were collected,and the Grey System GM( 1,1) model and unary linear regression model were applied to predict the coal consumption of Jilin Production in 2014 and 2015. Through calculation,the predictive value on the coal consumption of Jilin Province was attained,namely consumption of 2014 is 114. 84 × 106 t and of 2015 is 117. 98 ×106t,respectively. Analysis of error data indicated that the predicted accuracy of Grey System GM( 1,1) model on the coal consumption in Jilin Province improved 0. 21% in comparison to unary linear regression model.

Correlation Analysis of Fiscal Revenue and Housing Sales Price Based on Multiple Linear Regression Model

This paper selects seven indicators of financial revenue and housing sales price in recent 19 years in China,and uses SPSS and Excel to carry out descriptive statistics,independent sample t-test,correlation analysis and regression analysis to comprehensively study the correlation between financial revenue and housing sales price in China,and establishes the relationship between financial revenue and housing sales price When the average selling price of commercial housing increases by one unit,the fiscal revenue will increase by 27.855 points.

Regression analysis and its application to oil and gas exploration:A case study of hydrocarbon loss recovery and porosity prediction,China

In oil and gas exploration,elucidating the complex interdependencies among geological variables is paramount.Our study introduces the application of sophisticated regression analysis method at the forefront,aiming not just at predicting geophysical logging curve values but also innovatively mitigate hydrocarbon depletion observed in geochemical logging.Through a rigorous assessment,we explore the efficacy of eight regression models,bifurcated into linear and nonlinear groups,to accommodate the multifaceted nature of geological datasets.Our linear model suite encompasses the Standard Equation,Ridge Regression,Least Absolute Shrinkage and Selection Operator,and Elastic Net,each presenting distinct advantages.The Standard Equation serves as a foundational benchmark,whereas Ridge Regression implements penalty terms to counteract overfitting,thus bolstering model robustness in the presence of multicollinearity.The Least Absolute Shrinkage and Selection Operator for variable selection functions to streamline models,enhancing their interpretability,while Elastic Net amalgamates the merits of Ridge Regression and Least Absolute Shrinkage and Selection Operator,offering a harmonized solution to model complexity and comprehensibility.On the nonlinear front,Gradient Descent,Kernel Ridge Regression,Support Vector Regression,and Piecewise Function-Fitting methods introduce innovative approaches.Gradient Descent assures computational efficiency in optimizing solutions,Kernel Ridge Regression leverages the kernel trick to navigate nonlinear patterns,and Support Vector Regression is proficient in forecasting extremities,pivotal for exploration risk assessment.The Piecewise Function-Fitting approach,tailored for geological data,facilitates adaptable modeling of variable interrelations,accommodating abrupt data trend shifts.Our analysis identifies Ridge Regression,particularly when augmented by Piecewise Function-Fitting,as superior in recouping hydrocarbon losses,and underscoring its utility in resource quantification refinement.Meanwhile,Kernel Ridge Regression emerges as a noteworthy strategy in ameliorating porosity-logging curve prediction for well A,evidencing its aptness for intricate geological structures.This research attests to the scientific ascendancy and broad-spectrum relevance of these regression techniques over conventional methods while heralding new horizons for their deployment in the oil and gas sector.The insights garnered from these advanced modeling strategies are set to transform geological and engineering practices in hydrocarbon prediction,evaluation,and recovery.

Empirical Likelihood Diagnosis of Modal Linear Regression Models

In this paper, we investigate the empirical likelihood diagnosis of modal linear regression models. The empirical likelihood ratio function based on modal regression estimation method for the regression coefficient is introduced. First, the estimation equation based on empirical likelihood method is established. Then, some diagnostic statistics are proposed. At last, we also examine the performance of proposed method for finite sample sizes through simulation study.

Inference Procedures on the Generalized Poisson Distribution from Multiple Samples: Comparisons with Nonparametric Models for Analysis of Covariance (ANCOVA) of Count Data

Count data that exhibit over dispersion (variance of counts is larger than its mean) are commonly analyzed using discrete distributions such as negative binomial, Poisson inverse Gaussian and other models. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial and the Poisson inverse Gaussian have variance larger than the mean and therefore are more appropriate to model over-dispersed count data. As an alternative to these two models, we shall use the generalized Poisson distribution for group comparisons in the presence of multiple covariates. This problem is known as the ANCOVA and is solved for continuous data. Our objectives were to develop ANCOVA using the generalized Poisson distribution, and compare its goodness of fit to that of the nonparametric Generalized Additive Models. We used real life data to show that the model performs quite satisfactorily when compared to the nonparametric Generalized Additive Models.

Robust Linear Regression Models:Use of a Stable Distribution for the Response Data

In this paper, we study some robustness aspects of linear regression models of the presence of outliers or discordant observations considering the use of stable distributions for the response in place of the usual normality assumption. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, under a Bayesian approach, the use of a latent or auxiliary random variable gives some simplification to obtain any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to a standard linear regression model with an explanatory variable and the other is related to a simulated data set assuming a 23 factorial experiment. Posterior summaries of interest are obtained using MCMC (Markov Chain Monte Carlo) methods and the OpenBugs software.

Analysis of radar fault prediction based on combined model

Based on modeling principle of GM（1,1）model and linear regression model,a combined prediction model is established to predict equipment fault by the fitting of two models.The new prediction model takes full advantage of prediction information provided by the two models and improves the prediction precision.Finally,this model is introduced to predict the system fault time according to the output voltages of a certain type of radar transmitter.

Rainfall Estimation using Image Processing and Regression Model on DWR Rainfall Product for Delhi-NCR Region

Observed rainfall is a very essential parameter for the analysis of rainfall,day to day weather forecast and its validation.The observed rainfall data is only available from five observatories of IMD;while no rainfall data is available at various important locations in and around Delhi-NCR.However,the 24-hour rainfall data observed by Doppler Weather Radar(DWR)for entire Delhi and surrounding region(up to 150 km)is readily available in a pictorial form.In this paper,efforts have been made to derive/estimate the rainfall at desired locations using DWR hydrological products.Firstly,the rainfall at desired locations has been estimated from the precipitation accumulation product(PAC)of the DWR using image processing in Python language.After this,a linear regression model using the least square method has been developed in R language.Estimated and observed rainfall data of year 2018(July,August and September)was used to train the model.After this,the model was tested on rainfall data of year 2019(July,August and September)and validated.With the use of linear regression model,the error in mean rainfall estimation reduced by 46.58% and the error in max rainfall estimation reduced by 84.53% for the year 2019.The error in mean rainfall estimation reduced by 81.36% and the error in max rainfall estimation reduced by 33.81%for the year 2018.Thus,the rainfall can be estimated with a fair degree of accuracy at desired locations within the range of the Doppler Weather Radar using the radar rainfall products and the developed linear regression model.

Biomass estimation of Shorea robusta with principal component analysis of satellite data

Spatio-temporal assessment of the above ground biomass （AGB） is a cumbersome task due to the difficulties associated with the measurement of different tree parameters such as girth at breast height and height of trees. The present research was conducted in the campus of Birla Institute of Technology, Mesra, Ranchi, India, which is predomi- nantly covered by Sal （Shorea robusta C. F. Gaertn）. Two methods of regression analysis was employed to determine the potential of remote sensing parameters with the AGB measured in the field such as linear regression analysis between the AGB and the individual bands, principal components （PCs） of the bands, vegetation indices （VI）, and the PCs of the VIs respectively and multiple linear regression （MLR） analysis be- tween the AGB and all the variables in each category of data. From the linear regression analysis, it was found that only the NDVI exhibited regression coefficient value above 0.80 with the remaining parameters showing very low values. On the other hand, the MLR based analysis revealed significantly improved results as evidenced by the occurrence of very high correlation coefficient values of greater than 0.90 determined between the computed AGB from the MLR equations and field-estimated AGB thereby ascertaining their superiority in providing reliable estimates of AGB. The highest correlation coefficient of 0.99 is found with the MLR involving PCs of VIs.

Function-on-Partially Linear Functional Additive Models

We consider a functional partially linear additive model that predicts a functional response by a scalar predictor and functional predictors. The B-spline and eigenbasis least squares estimator for both the parametric and the nonparametric components proposed. In the final of this paper, as a result, we got the variance decomposition of the model and establish the asymptotic convergence rate for estimator.

A Recursive Binary Tree Model for the Analysis of the Response to Antiretroviral Therapy of HIV Infected Adults in Burkina Faso

In this paper we aim to analyse temporal variation of CD4 cell counts for HIV-infected individuals under antiretroviral therapy by using statistical methods. This is achieved by resorting to recursive binary regression tree approach [1]?[2]. This approach has made it possible to highlight the existence of several segments of the population of interest described by the interactions between the predictive covariates of the response to the treatment regimen.

Analysis of Alkaline Foam to Water Temperature Model

Factors affecting bath water temperature model include the shape and size of a bath, people’s gesture, volume, individual temperature adaptation as well as body movement in the bath. In addition, the bathroom space, ambient temperature and bath materials will also affect changes of the water temperature to a certain extent. In this paper, the cooling function and linear regression method are used and the MATLAB software is also used to simulate the model of water temperature, alkaline bath foams that obtained can accelerate changes in water temperature.

The Establishment of Mathematical Models for the Composition Analysis and Identification of Ancient Glass Products

Glass is the precious material evidence of the trade of the early Silk Road. The ancient glass was easily affected by the environmental impact and weathering, and the change of composition ratios affected the correct judgment of its category. In this paper, mathematical models and methods such as Chi-square test, weighted average method, principal component analysis, cluster analysis, binary classification model and grey correlation analysis were used comprehensively to analyze the data of sample glass products combined with their categories. The results showed that the weathered high-potassium glass could be divided into 12, 9, 10 and 27, 7, 22 and so on.

Identification of predictive MRI and functional biomarkers in a pediatric piglet traumatic brain injury model

Traumatic brain injury(TBI) at a young age can lead to the development of long-term functional impairments. Severity of injury is well demonstrated to have a strong influence on the extent of functional impairments;however, identification of specific magnetic resonance imaging(MRI) biomarkers that are most reflective of injury severity and functional prognosis remain elusive. Therefore, the objective of this study was to utilize advanced statistical approaches to identify clinically relevant MRI biomarkers and predict functional outcomes using MRI metrics in a translational large animal piglet TBI model. TBI was induced via controlled cortical impact and multiparametric MRI was performed at 24 hours and 12 weeks post-TBI using T1-weighted, T2-weighted, T2-weighted fluid attenuated inversion recovery, diffusion-weighted imaging, and diffusion tensor imaging. Changes in spatiotemporal gait parameters were also assessed using an automated gait mat at 24 hours and 12 weeks post-TBI. Principal component analysis was performed to determine the MRI metrics and spatiotemporal gait parameters that explain the largest sources of variation within the datasets. We found that linear combinations of lesion size and midline shift acquired using T2-weighted imaging explained most of the variability of the data at both 24 hours and 12 weeks post-TBI. In addition, linear combinations of velocity, cadence, and stride length were found to explain most of the gait data variability at 24 hours and 12 weeks post-TBI. Linear regression analysis was performed to determine if MRI metrics are predictive of changes in gait. We found that both lesion size and midline shift are significantly correlated with decreases in stride and step length. These results from this study provide an important first step at identifying relevant MRI and functional biomarkers that are predictive of functional outcomes in a clinically relevant piglet TBI model. This study was approved by the University of Georgia Institutional Animal Care and Use Committee(AUP: A2015 11-001) on December 22, 2015.

A Vehicle Traveling Time Prediction Method Based on Grey Theory and Linear Regression Analysis

Vehicle traveling time prediction is an important part of the research of intelligent transportation system. By now, there have been various kinds of methods for vehicle traveling time prediction. But few consider both aspects of time and space. In this paper, a vehicle traveling time prediction method based on grey theory （GT） and linear regression analysis （LRA） is presented. In aspects of time, we use the history data sequence of bus speed on a certain road to predict the future bus speed on that road by GT. And in aspects of space, we calculate the traffic affecting factors between various roads by LRA. Using these factors we can predict the vehicle＇s speed at the lower road if the vehicle＇s speed at the current road is known. Finally we use time factor and space factor as the weighting factors of the two results predicted by GT and LRA respectively to find the final result, thus calculating the vehicle＇s traveling time. The method also considers such factors as dwell time, thus making the prediction more accurate.

Functional Analysis of Chemometric Data

The objective of this paper is to present a review of different calibration and classification methods for functional data in the context of chemometric applications. In chemometric, it is usual to measure certain parameters in terms of a set of spectrometric curves that are observed in a finite set of points (functional data). Although the predictor variable is clearly functional, this problem is usually solved by using multivariate calibration techniques that consider it as a finite set of variables associated with the observed points (wavelengths or times). But these explicative variables are highly correlated and it is therefore more informative to reconstruct first the true functional form of the predictor curves. Although it has been published in several articles related to the implementation of functional data analysis techniques in chemometric, their power to solve real problems is not yet well known. Because of this the extension of multivariate calibration techniques (linear regression, principal component regression and partial least squares) and classification methods (linear discriminant analysis and logistic regression) to the functional domain and some relevant chemometric applications are reviewed in this paper.

Experimental Study on Anchoring Physical Properties of Different Anchoring Lengths Coupled with Temperature and Pressure

Aiming at deep roadway anchorage solids, laboratory similar model tests were used to reveal the mechanical properties of anchorage solids with different anchorage lengths under the coupling effect of temperature and pressure, and SPSS statistical analysis software was used to conduct linear regression analysis of the ultimate anchorage force obtained from the tests. The results show that: through multiple linear regression analysis, the influence degree of temperature and pressure coupling on the ultimate anchorage force is arranged in order of anchoring length > surrounding rock strength > temperature > side pressure coefficient, and the linear regression equation of the model is obtained. Compared with the linear regression equation of simulation results, the model has a high explanatory ability.

Analysis and Evaluation of Housing Price Factors Using Mathematical Modeling

In recent years,the real estate industry has achieved significant progress,driving the development of related sectors and playing a crucial role in economic growth.However,rapid real estate market expansion has led to challenges,particularly concerning housing prices,which have drawn widespread societal attention.This article explores the theories of housing prices,analyzes factors influencing them,and conducts an empirical investigation of the impact of representative factors on ordinary residential prices.Using regression analysis and the entropy weight method,a mathematical model was developed to examine how various factors affect housing prices.

基于一元线性回归模型的供水网络中水表读数虚高问题研究

为了定量研究供水网络中总表漏水程度和分表读数虚高程度,根据水量平衡分析法的原理,结合大数据分析技术,建立了一元线性回归方程,回归常数代表总表漏水量程度,回归系数代表分表读数虚高程度。通过针对2021年某高校供水管网的实证研究表明,总表日均漏水量为15.5958吨,分表读数虚高率为1.07%。该方法对供水管网漏损率的精准评估等问题的解决提供了新的思路和方法。