Calculations of rock matrix modulus based on a linear regression relation

The rock matrix bulk modulus or its inverse, the compressive coefficient, is an important input parameter for fluid substitution by the Biot-Gassmann equation in reservoir prediction. However, it is not easy to accurately estimate the bulk modulus by using conventional methods. In this paper, we present a new linear regression equation for calculating the parameter. In order to get this equation, we first derive a simplified Gassmann equation by using a reasonable assumption in which the compressive coefficient of the saturated pore fluid is much greater than the rock matrix, and, second, we use the Eshelby- Walsh relation to replace the equivalent modulus of a dry rock in the Gassmann equation. Results from the rock physics analysis of rock sample from a carbonate area show that rock matrix compressive coefficients calculated with water-saturated and dry rock samples using the linear regression method are very close （their error is less than 1%）. This means the new method is accurate and reliable.

Study on QSAR of Taxol and its Derivatives Based on Stepwise Multivariate Linear Regression Analysis

Abstract Using the method of stepwise multivariate linear regression (SMLR), the quantitative structure activity relationships (QSAR) of two isomeric series of taxol and its derivatives have been studied. It was found that the molar refractivity of the C3′substituent of the C13 side chain has significant correlation with its activity. We deduce that structural changes in the C3′substituents may be critical to the anticancer function. It would be useful to the design and synthesis of taxol like compounds with improved activities.

Selection of the Linear Regression Model According to the Parameter Estimation

In this paper, based on the theory of parameter estimation, we give a selection method and, in a sense of a good character of the parameter estimation, we think that it is very reasonable. Moreover, we offer a calculation method of selection statistic and an applied example.

Prediction of kiwifruit firmness using fruit mineral nutrient concentration by artificial neural network(ANN) and multiple linear regressions(MLR)

Many properties of fruit are influenced by plant nutrition. Fruit firmness is one of the most important fruit characteristics and determines post-harvest life of the fruit, in recent decades, artificial intelligence systems were employed for developing predictive models to estimate and predict many agriculture processes. In the present study, the predictive capabilities of multiple linear regressions （MLR） and artificial neural networks （ANNs） are evaluated to estimate fruit firmness in six months, including each of nutrients concentrations （nitrogen （N）, potassium （K）, calcium （Ca） and magnesium （Mg）） alone （P1）, com- bination of nutrients concentrations （P2）, nutrient concentration ratios alone （P3）, and combination of nutrient concentrations and nutrient concentration ratios （P4）. The results showed that MLR model estimated fruit firmness more accuracy than ANN model in three datasets （P1, P2 and P4）. However, the application of P3 （N/Ca ratio） as the input dataset in ANN model improved the prediction of fruit firmness than the MLR model. Correlation coefficient and root mean squared error （RMSE） were 0.850 and 0.539 between the measured and the estimated data by the ANN model, respectively. Generally, the ANN model showed greater potential in determining the relationship between 6-mon-fruit firmness and nutrients concentration.

Isolated Area Load Forecasting using Linear Regression Analysis: Practical Approach

This paper presents an analysis to forecast the loads of an isolated area where the history of load is not available or the history may not represent the realistic demand of electricity. The analysis is done through linear regression and based on the identification of factors on which electrical load growth depends. To determine the identification factors, areas are selected whose histories of load growth rate known and the load growth deciding factors are similar to those of the isolated area. The proposed analysis is applied to an isolated area of Bangladesh, called Swandip where a past history of electrical load demand is not available and also there is no possibility of connecting the area with the main land grid system.

FIXED-DESIGN SEMIPARAMETRIC REGRESSION FOR LINEAR TIME SERIES

This article studies parametric component and nonparametric component estimators in a semiparametric regression model with linear time series errors; their r-th mean consistency and complete consistency are obtained under suitable conditions. Finally, the author shows that the usual weight functions based on nearest neighbor methods satisfy the designed assumptions imposed.

A study of the mixed layer of the South China Sea based on the multiple linear regression

Multiple linear regression （MLR） method was applied to quantify the effects of the net heat flux （NHF）, the net freshwater flux （NFF） and the wind stress on the mixed layer depth （MLD） of the South China Sea （SCS） based on the simple ocean data assimilation （SODA） dataset. The spatio-temporal distributions of the MLD, the buoyancy flux （combining the NHF and the NFF） and the wind stress of the SCS were presented. Then using an oceanic vertical mixing model, the MLD after a certain time under the same initial conditions but various pairs of boundary conditions （the three factors） was simulated. Applying the MLR method to the results, regression equations which modeling the relationship between the simulated MLD and the three factors were calculated. The equations indicate that when the NHF was negative, it was the primary driver of the mixed layer deepening; and when the NHF was positive, the wind stress played a more important role than that of the NHF while the NFF had the least effect. When the NHF was positive, the relative quantitative effects of the wind stress, the NHF, and the NFF were about i0, 6 and 2. The above conclusions were applied to explaining the spatio-temporal distributions of the MLD in the SCS and thus proved to be valid.

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.

A class of estimators of the mean survival time from interval censored data with application to linear regression

A class of estimators of the mean survival time with interval censored data are studied by unbiased transformation method. The estimators are constructed based on the observations to ensure unbiasedness in the sense that the estimators in a certain class have the same expectation as the mean survival time. The estimators have good properties such as strong consistency （with the rate of O（n^-1/1 （log log n）^1/2）） and asymptotic normality. The application to linear regression is considered and the simulation reports are given.

Determination of pKa values of alendronate sodium in aqueous solution by piecewise linear regression based on acid-base potentiometric titration

As a mono-sodium salt form of alendronic acid,alendronate sodium presents multi-level ionization for the dissociation of its four hydroxyl groups.The dissociation constants of alendronate sodium were determined in this work by studying the piecewise linear relationship between volume of titrant and p H value based on acidbase potentiometric titration reaction.The distribution curves of alendronate sodium were drawn according to the determined p Ka values.There were 4 dissociation constants(pKa_1=2.43,pKa_2=7.55,pKa_3=10.80,pKa_4=11.99,respectively) of alendronate sodium,and 12 existing forms,of which 4 could be ignored,existing in different p H environments.

Identification of heavy metal-contaminated Tegillarca granosa using laser-induced breakdown spectroscopy and linear regression for classification

Tegillarca granosa(T.granosa)is susceptible to heavy metals,which may pose a threat to consumer health.Thus,healthy and polluted T.granosa should be distinguished quickly.This study aimed to rapidly identify heavy metal pollution by using laser-induced breakdown spectroscopy(LIBS)coupled with linear regression classification(LRC).Five types of T.granosa were studied,namely,Cd-,Zn-,Pb-contaminated,mixed contaminated,and control samples.Threshold method was applied to extract the significant variables from LIBS spectra.Then,LRC was used to classify the different types of T.granosa.Other classification models and feature selection methods were used for comparison.LRC was the best model,achieving an accuracy of 90.67%.Results indicated that LIBS combined with LRC is effective and feasible for T.granosa heavy metal detection.

Predicting the Acute Toxicity of Aromatic Amines by Linear and Nonlinear Regression Methods

In current paper, a quantitative structure-activity relationship （QSAR） study was performed for the prediction of acute toxicity of aromatic amines. A set of 56 compounds was randomly divided into a training set of 46 compounds and a test set of 10 compounds. The electronic and topological descriptors computed by the Scigress package and Dragon software were used as predictor variables. Multiple linear regression （MLR） and support vector machine （SVM） were utilized to build the linear and nonlinear QSAR models, respectively. The obtained models with five descriptors show strong predictive ability. The linear model fits the training set with R2 = 0.71, with higher SVM values of R2 = 0.77. The validation results obtained from the test set indicate that the SVM model is comparable or superior to that obtained by MLR, both in terms of prediction ability and robustness.

Support Vector Machines for Regression: A Succinct Review of Large-Scale and Linear Programming Formulations

Support Vector-based learning methods are an important part of Computational Intelligence techniques. Recent efforts have been dealing with the problem of learning from very large datasets. This paper reviews the most commonly used formulations of support vector machines for regression (SVRs) aiming to emphasize its usability on large-scale applications. We review the general concept of support vector machines (SVMs), address the state-of-the-art on training methods SVMs, and explain the fundamental principle of SVRs. The most common learning methods for SVRs are introduced and linear programming-based SVR formulations are explained emphasizing its suitability for large-scale learning. Finally, this paper also discusses some open problems and current trends.

Application of Multiple Linear Regression and Manova to Evaluate Health Impacts Due to Changing River Water Quality

Rivers are important systems which provide water to fulfill human needs. However, excessive human uses over the years have led to deterioration in quality of river causing, causing health problems from contaminated water. This study focuses on the application of statistical techniques, Multiple Linear Regression model and MANOVA to assess health impacts due to pollution in Cauvery river stretch in Srirangapatna. In this study, using Multiple Linear Regression, it is found that health impact level is 60.8% dependent on water quality parameters of BOD, COD, TDS, TC and FC. The t-statistics and their associated 2-tailed p-values indicate that COD and TDS produces health impacts compared to BOD, TC and FC, when their effects are put together across all the six sampling stations in Srirangapatna. Further Pearson correlation Matrix shows highly significant positive correlation amongst parameters across all stations indicating possibility of common sources of origin that might be anthropogenic. Also graphs are plotted for individual parameters across all stations and it reveals that COD and TDS values are significant across all sampling stations, though their values are higher in impact stations, causing health impacts.

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 BAYES ESTIMATION FOR ESTIMABLE FUNCTION OF REGRESSION COEFFICIENT IN A MULTIPLE LINEAR REGRESSION MODEL

In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.

Alcoholism Detection by Wavelet Energy Entropy and Linear Regression Classifier

Alcoholism is an unhealthy lifestyle associated with alcohol dependence.Not only does drinking for a long time leads to poor mental health and loss of self-control,but alcohol seeps into the bloodstream and shortens the lifespan of the body’s internal organs.Alcoholics often think of alcohol as an everyday drink and see it as a way to reduce stress in their lives because they cannot see the damage in their bodies and they believe it does not affect their physical health.As their drinking increases,they become dependent on alcohol and it affects their daily lives.Therefore,it is important to recognize the dangers of alcohol abuse and to stop drinking as soon as possible.To assist physicians in the diagnosis of patients with alcoholism,we provide a novel alcohol detection system by extracting image features of wavelet energy entropy from magnetic resonance imaging(MRI)combined with a linear regression classifier.Compared with the latest method,the 10-fold cross-validation experiment showed excellent results,including sensitivity 91.54±1.47%,specificity 93.66±1.34%,Precision 93.45±1.27%,accuracy 92.61±0.81%,F1 score 92.48±0.83%and MCC 85.26±1.62%.

Hole Cleaning Prediction in Foam Drilling Using Artificial Neural Network and Multiple Linear Regression

Foam drilling is increasingly used to develop low pressure reservoirs or highly depleted mature reservoirs because of minimizing the formation damage and potential hazardous drilling problems. Prediction of the cuttings concentration in the wellbore annulus as a function of operational drilling parameters such as wellbore geometry, pumping rate, drilling fluid rheology and density and maximum drilling rate is very important for optimizing these parameters. This paper describes a simple and more reliable artificial neural network (ANN) method and multiple linear regression (MLR) to predict cuttings concentration during foam drilling operation. This model is applicable for various borehole conditions using some critical parameters associated with foam velocity, foam quality, hole geometry, subsurface condition (pressure and temperature) and pipe rotation. The average absolute percent relative error (AAPE) between the experimental cuttings concentration and ANN model is less than 6%, and using MLR, AAPE is less than 9%. A comparison of the ANN and mechanistic model was done. The AAPE values for all datasets in this study were 3.2%, 8.5% and 10.3% for ANN model, MLR model and mechanistic model respectively. The results show high ability of ANN in prediction with respect to statistical methods.

Finite Element Analysis and Linear Regression of Maximum Temperature for Inner Wall of Chimney Foundation

The uniform design method was adopted and the twenty-four groups of different geometric and physical pa-rameters were chosen. The finite element model was built. Comparisons between the simulation results and the test re-sults prove that the simulation results are correct. The distribution of the temperature field of the chimney foundationwas analyzed. The multivariate linear regression of the hightest tomperature was performed on the inner wall of thechimney foundation by the numerical calculated results. The fitting property of the highest temperature with six influ-ence factors was obtained. A simple method for the calculation of the temperature field of the chimney foundation wasprovided.

Statistical analysis of nitrogen use efficiency in Northeast China using multiple linear regression and Random Forest

Understanding the spatial-temporal dynamics of crop nitrogen(N)use efficiency(NUE)and the relationship with explanatory environmental variables can support land-use management and policymaking.Nevertheless,the application of statistical models for evaluating the explanatory variables of space-time variation in crop NUE is still under-researched.In this study,stepwise multiple linear regression(SMLR)and Random Forest(RF)were used to evaluate the spatial and temporal variation of NUE indicators(i.e.,partial factor productivity of N(PFPN);partial nutrient balance of N(PNBN))at county scale in Northeast China(Heilongjiang,Liaoning and Jilin provinces)from 1990 to 2015.Explanatory variables included agricultural management practices,topography,climate,economy,soil and crop types.Results revealed that the PFPN was higher in the northern parts and lower in the center of the Northeast China and PNBN increased from southern to northern parts during the 1990–2015 period.The NUE indicators decreased with time in most counties during the study period.The model efficiency coefficients of the SMLR and RF models were 0.44 and 0.84 for PFPN,and 0.67 and 0.89 for PNBN,respectively.The RF model had higher relative importance of soil and climatic covariates and lower relative importance of crop covariates compared to the SMLR model.The planting area index of vegetables and beans,soil clay content,saturated water content,enhanced vegetation index in November&December,soil bulk density,and annual minimum temperature were the main explanatory variables for both NUE indicators.This is the first study to show the quantitative relative importance of explanatory variables for NUE at a county level in Northeast China using RF and SMLR.This novel study gives reference measurements to improve crop NUE which is one of the most effective means of managing N for sustainable development,ensuring food security,alleviating environmental degradation and increasing farmer’s profitability.