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.

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.

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.

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.

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.

Predicting urbanization level by main element analysis and multiple linear regression---taking Xiantao district in Hubei Province as an example

In this paper we firstly select main factors relating to urbanization level of Xiantao District in Hubei Province by main element, then, make model of urbanization level by analysis of multiple liner regression, and lastly predict its urbanization level

Prediction of Anti-Inflammatory Activity of a Series of Pyrimidine Derivatives, by Multiple Linear Regression and Artificial Neural Networks

Anti-inflammatory activity of a series of tri-substituted pyrimidine derivatives was predicted using two Quantitative Structure-Activity Relationship models. These relationships were developed from molecular descriptors calculated using the DFT quantum chemistry method using the B3LYP/6-31G(d,p) level of theory and molecular lipophilicity. Thus, the four descriptors which are the dipole moment μD, the energy of the highest occupied molecular orbital EHOMO, the isotropic polarizability α and the ACD/logP lipophilicity were selected for this purpose. The Multiple Linear Regression (MLR) and Artificial Neural Network (ANN) models are respectively accredited with the following statistical indicators: R2=91.28%, R2aj=89.11%, RMCE = 0.2831, R2ext=86.50% and R2=98.22%, R2aj=97.75%, RMCE = 0.1131, R2ext=98.54%. The results obtained with the artificial neural network are better than those of the multiple linear regression. However, these results show that the two models developed have very good predictive performance of anti-inflammatory activity. These two models can therefore be used to predict anti-inflammatory activity of new similar pyrimidine derivatives.

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.

Using Multiple Linear Regression and Artificial Neural Network Techniques for Predicting CCR5 Binding Affinity of Substituted 1-(3, 3-Diphenylpropyl)-Piperidinyl Amides and Ureas

Quantitative structure–activity relationship (QSAR) models were developed to predict for CCR5 binding affinity of substituted 1-(3, 3-diphenylpropyl)-piperidinyl amides and ureas using multiple linear regression (MLR) and artificial neural network (ANN) techniques. A model with four descriptors, including Hydrogen-bonding donors HBD(R7), the partition coefficient between n-octanol and water logP and logP(R1) and Molecular weight MW(R7), showed good statistics both in the regression and artificial neural network with a configuration of (4-3-1) by using Bayesian and Leven-berg-Marquardt Methods. Comparison of the descriptor’s contribution obtained in MLR and ANN analysis shows that the contribution of some of the descriptors to activity may be non-linear.

Research on the Impact of Employment on GDP Based on Multiple Linear Regression Model

In order to study the impact of employed persons in various industries on regional GDP,based on the data of GDP in various regions and employed persons divided by industries in various regions in 2019,the employed persons are divided into seven categories,and the multiple linear regression model of GDP in various regions of China on employed persons in various industries is established by using the methods of multiple linear regression analysis and cluster analysis,It also analyzes the impact of employees in various industries on the GDP of various regions.

Multiple Regression and Big Data Analysis for Predictive Emission Monitoring Systems

Predictive Emission Monitoring Systems (PEMS) offer a cost-effective and environmentally friendly alternative to Continuous Emission Monitoring Systems (CEMS) for monitoring pollution from industrial sources. Multiple regression is one of the fundamental statistical techniques to describe the relationship between dependent and independent variables. This model can be effectively used to develop a PEMS, to estimate the amount of pollution emitted by industrial sources, where the fuel composition and other process-related parameters are available. It often makes them sufficient to predict the emission discharge with acceptable accuracy. In cases where PEMS are accepted as an alternative method to CEMS, which use gas analyzers, they can provide cost savings and substantial benefits for ongoing system support and maintenance. The described mathematical concept is based on the matrix algebra representation in multiple regression involving multiple precision arithmetic techniques. Challenging numerical examples for statistical big data analysis, are investigated. Numerical examples illustrate computational accuracy and efficiency of statistical analysis due to increasing the precision level. The programming language C++ is used for mathematical model implementation. The data for research and development, including the dependent fuel and independent NOx emissions data, were obtained from CEMS software installed on a petrochemical plant.

Influence of confined water on the limit support pressure of tunnel face in weakly water-rich strata

In the process of shield tunneling through soft soil layers,the presence of confined water ahead poses a significant threat to the stability of the tunnel face.Therefore,it is crucial to consider the impact of confined water on the limit support pressure of the tunnel face.This study employed the finite element method(FEM)to analyze the limit support pressure of shield tunnel face instability within a pressurized water-containing layer.Subsequently,a multiple linear regression approach was applied to derive a concise solution formula for the limit support pressure,incorporating various influencing factors.The analysis yields the following conclusions:1)The influence of confined water on the instability mode of the tunnel face in soft soil layers makes the displacement response of the strata not significant when the face is unstable;2)The limit support pressure increases approximately linearly with the pressure head,shield tunnel diameter,and tunnel burial depth.And inversely proportional to the thickness of the impermeable layer,soil cohesion and internal friction angle;3)Through an engineering case study analysis,the results align well with those obtained from traditional theoretical methods,thereby validating the rationality of the equations proposed in this paper.Furthermore,the proposed equations overcome the limitation of traditional theoretical approaches considering the influence of changes in impermeable layer thickness.It can accurately depict the dynamic variation in the required limit support pressure to maintain the stability of the tunnel face during shield tunneling,thus better reflecting engineering reality.

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.

Estimating cooling loads of Indian residences using building geometry data and multiple linear regression

International Energy Agency(IEA)predicts India’s AC stock will reach 1144 million units by 2050,making it the second largest ACs holder globally.Studies on the effect of building geometry on cooling load reduction are primarily focused on material and envelope specifications.However,studies on building morphological parame-ters in the Indian context are scarce.Therefore,this research quantifies the effect of four morphology predictors,namely,FL(floor number),ESA(exposed surface area),CZB(conditioned zones per building),and CZF(con-ditioned zones per floor)on cooling load in 75 dominant residential built forms of Navi Mumbai.The selected buildings are simulated using the Rhinoceros 6 tool with the energy plus plugin.Despite having the same sim-ulation inputs,envelope parameters,and conditioned volume,the results indicated a 90%variation between the compact and loosely designed forms.Multiple Linear Regression shows that the four predictors explain 78%(R2=0.78)of variation in the cooling load.It is observed that tall buildings show greater efficiency in cooling load reduction due to lesser CZF values.Also,an increase in CZB and a decrease in ESA significantly reduce the mean cooling load due to compactness and wall sharing,respectively.

The Influence of Internet Use on Women’s Depression and Its Countermeasures—Empirical Analysis Based on Data from CFPS

Based on China Family Panel Studies(CFPS)2018 data,the multiple linear regression model is used to analyze the effects of Internet use on women’s depression,and to test the robustness of the regression results.At the same time,the effects of Internet use on mental health of women with different residence,age,marital status and physical health status are analyzed.Then,we can obtain that Internet use has a significant promoting effect on women’s mental health,while the degree of Internet use has a significant inhibitory effect on women’s mental health.In addition,the study found that women’s age,education,place of residence,marital status,length of sleep,working status and physical health status are the main factors affecting the mental health of Chinese women.In the heterogeneity investigation of residence,age,marital status and physical health status,Internet use has a greater negative impact on the Center for Epidemiological Studies Depression Scale(CES-D8)scores of women in rural areas,has a significant positive impact on the mental health of middle-aged and elderly women or women with spouses,and has a positive impact on the mental health of physically unhealthy women.Therefore,in view of women’s mental health needs and the problems existing in the use of the Internet,this paper puts forward some suggestions to further improve the overall mental health level of women.

Statistical Approach to Basketball Players’Skill Level

In basketball, each player’s skill level is the key to a team’s success or failure, the skill level is affected by many personal and environmental factors. A physics-informed AI statistics has become extremely important. In this article, a complex non-linear process is considered by taking into account the average points per game of each player, playing time, shooting percentage, and others. This physics-informed statistics is to construct a multiple linear regression model with physics-informed neural networks. Based on the official data provided by the American Basketball League, and combined with specific methods of R program analysis, the regression model affecting the player’s average points per game is verified, and the key factors affecting the player’s average points per game are finally elucidated. The paper provides a novel window for coaches to make meaningful in-game adjustments to team members.

Diffusion tensor imaging with multiple diffusion-weighted gradient directions

Diffusion tensor MRI （DT-MRI or DTI） is emerging as an important non-invasive technology for elucidating intemal brain structures. It has recently been utilized to diagnose a series of diseases that affect the integrity of neural systems to provide a basis for neuroregenerative studies. Results from the present study suggested that neural tissue is reconstructed with multiple diffusion-weighted gradient directions DTI, which varies from traditional imaging methods that utilize 6 gradient directions. Simultaneously, the diffusion tensor matrix is obtained by multiple linear regressions from an equation of echo signal intensity. The condition number value and standard deviation of fractional anisotropy for each scheme can be used to evaluate image quality. Results demonstrated that increasing gradient direction to some extent resulted in improved effects. Therefore, the traditional 6 and 15 directions should not be considered optimal scan protocols for clinical DTI application. In a scheme with 20 directions, the condition number and standard deviation of fractional anisotropy of the encoding gradients matrix were significantly reduced, and resulted in more clearly and accurately displayed neural tissue. Results demonstrated that the scheme with 20 diffusion gradient directions provided better accuracy of structural renderings and could be an optimal scan protocol for clinical DTI application.

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.

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.