Recognition Method for Change Point of Traffic Flow Linear Regressions

Recognition method of traffic flow change point was put forward based on traffic flow theory and the statistical change point analysis of multiple linear regressions. The method was calibrated and tested with the field data of Liantong Road of Zibo city to verify the validity and the feasibility of the theory. The results show that change point method of multiple linear regression can make out the rule of quantitative changes in traffic flow more accurately than ordinary methods. So, the change point method can be applied to traffic information management system more effectively.

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.

Influencing Factors of Museum Self-Improvement in China: A Multiple Linear Regression Analysis

The purpose of this research is to explore the factors influencing the self-improvement process of museums in China and to conduct empirical analyses based on multiple linear regression models.As core institutions for inheriting and displaying cultural heritage and enhancing public cultural literacy,museums’self-improvement is of great significance in promoting cultural development,optimizing the supply of public cultural services,and enhancing social influence.This paper constructs a multiple linear regression model for the influencing factors of museum self-improvement by integrating several key variables,including emerging cultural and museum business(EF),institutional reform(SR),research and innovation level(RIL),management level(ML),and the museum cultural and creative industry(MCCI).The study employs scientific methods such as literature review,data collection,and data analysis to thoroughly explore the internal logic of museum operations and development.Through multiple linear regression analyses,it quantifies the specific influence and relative importance of each factor on the level of museum self-improvement.The results indicate that the management level(ML)is the dominant factor among the variables studied,exerting the most significant influence on museum self-improvement.Based on these empirical findings,this paper provides an in-depth analysis of the specific factors affecting museum self-improvement in China,offering solid theoretical support and practical guidance for the sustainable development of museums.

Study on Influencing Factors of Tourism Income in Yantai City Based on Multiple Linear Regression Analysis

As one of the first coastal open cities in China,Yantai City is situated in the eastern Shandong Peninsula,bordered by the Yellow Sea and Bohai Sea.With the continuous improvement of tourism infrastructure,public enthusiasm for tourism in Yantai has been growing.To formulate more effective tourism development policies tailored to the local context,this study examines Yantai City using a multiple linear regression model to identify the primary factors influencing domestic tourism income.Based on the findings,this paper proposes scientifically grounded and actionable strategies to further optimize the development of tourism in Yantai City.

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.

Water quality analysis and source apportionment in estuaries along the coast of the Bohai Sea,North China

High-dimensional data(a dataset with many features)were collected from 64 sampling sites to analyze the water quality in estuaries along the coast of the Bohai Sea,North China.The twenty-five water quality parameters analyzed were collected monthly from January 2021 to December 2021.Multivariate statistical techniques,such as the absolute principal component score-multiple linear regression model(APCS-MLR),correlation analysis,and analysis of variance were used to identify and quantify the potential sources or factors affecting water quality and to analyze the spatial-temporal variation in water quality.The water quality indices(WQIs),ranging from 67.96 to 70.67,showed that the water quality was at an intermediate level in the estuaries during both the flood and nonflood seasons.The concentrations of total phosphorus(TP),ammonia N(AN),and organic pollutants were greater in the Haihe River Basin than in the Liaohe River and Huanghe-Huaihe River Basins.The concentration of total nitrogen(TN)in the Haihe River Basin was lower than that in the Liaohe River and Huanghe-Huaihe River Basins.Heavy metal concentrations in the Liaohe River Basin were greater than those in the Haihe River and Huanghe-Huaihe River Basins.The annual mean concentrations of AN in the estuaries of the Haihe,Liaohe,and Huanghe(Yellow)rivers exhibited significant decreasing trends from 2013 to 2022,but no significant decreasing trends were found for permanganate index(COD_(Mn))or the TP.The concentrations of TN and AN were lower in the flood season than in the nonflood season,and the TP concentration was greater in the flood season than in the nonflood season.However,the concentrations of organic pollutants did not exhibit significant differences.Domestic sewage and industrial wastewater,substance exchange between air and water,nonpoint sources from rural and urban areas,and aquaculture wastewater were the major sources or factors responsible for water pollution in the estuaries.

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.

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 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.

Further Exploring Linear Concentration Addition and Independent Action for Predicting Non-interactive Mixture Toxicity

Since it is unrealistic to do an experimental mixture assessment on every possible combination, mathematical model plays an important role in predicting the mixture toxicity. The present study is devoted to the further application of linear concentration addition（CA）-based model（LCA） and independent action（IA）-based model（LIA） to predict the non-interactive mixture toxicity. The 26 mixtures including 312 data points were used to evaluate the predictive powers of LCA and LIA models. The models were internally validated using the leave-one-out cross-validation and y-randomization test, and the external validations were evaluated by the test tests. Both LCA and LIA models agree well with the experimental values for all mixture toxicity, and present high internally（R2 and Q2 〉 0.98） and externally（Q2F1, Q2F2, and Q2F3 〉 0.99） predictive power. The use of LCA and LIA led to improved predictions compared to the estimates based on the CA and IA models. Both LCA and LIA were found to be appropriate methods for modeling toxicity of non-interactive chemical mixtures.

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.

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.

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.

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%.

Prediction of mode I fracture toughness of rock using linear multiple regression and gene expression programming

Prediction of mode I fracture toughness(KIC) of rock is of significant importance in rock engineering analyses. In this study, linear multiple regression(LMR) and gene expression programming(GEP)methods were used to provide a reliable relationship to determine mode I fracture toughness of rock. The presented model was developed based on 60 datasets taken from the previous literature. To predict fracture parameters, three mechanical parameters of rock mass including uniaxial compressive strength(UCS), Brazilian tensile strength(BTS), and elastic modulus(E) have been selected as the input parameters. A cluster of data was collected and divided into two random groups of training and testing datasets.Then, different statistical linear and artificial intelligence based nonlinear analyses were conducted on the training data to provide a reliable prediction model of KIC. These two predictive methods were then evaluated based on the testing data. To evaluate the efficiency of the proposed models for predicting the mode I fracture toughness of rock, various statistical indices including coefficient of determination(R2),root mean square error(RMSE), and mean absolute error(MAE) were utilized herein. In the case of testing datasets, the values of R2, RMSE, and MAE for the GEP model were 0.87, 0.188, and 0.156,respectively, while they were 0.74, 0.473, and 0.223, respectively, for the LMR model. The results indicated that the selected GEP model delivered superior performance with a higher R2value and lower errors.

Gamma generalized linear model to investigate the effects of climate variables on the area burned by forest fire in northeast China

The purpose of this study was to determine a suitable model for investigating the effects of climate factors on the area burned by forest fire in the Tahe forest region, Daxing＇an Mountains, in northeast China. The response variables were the area burned by lightning- caused fire, human-caused fire, and total burned area. The predictor variables were nine climate variables collected from the local weather station. Three regression models were utilized, including multiple linear regression, log- linear model （log-transformation on both response and predictor variables）, and gamma-generalized linear model. The goodness-of-fit of the models were compared based on model fitting statistics such as R2, AIC, and RMSE. The results revealed that the gamma-generalized linear model was generally superior to both multiple linear regressionmodel and log-linear model for fitting the fire data. Further, the best models were selected based on the criteria that the climate variables were statistically significant at at = 0.05. The gamma best models indicated that maximum wind speed, precipitation, and days that rainfall greater than 0.1 mm had significant impacts on the area burned by the lightning-caused fire, while the mean temperature and minimum relative humidity were the .main drivers of the burned area caused by human activities. Overall, the total burned area by forest fire was significantly influenced by days that rainfall greater than 0.1 mm and minimum rela- tive humidity, indicating that the moisture condition of forest stands determine the burned area by forest fire.

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.

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.

STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.