Stepwise multiple regressions application in liposome orthogonal experiments

Aim New statistical method was applied in data analysis of orthogonal experiments to optimize the preparation of liposome. Method Particle size, zeta potential, encapsulation efficiency and physical stability of liposomes were selected by orthogonal design as evaluating indicators. Through three statistical methods （direct observation, variance analysis and stepwise multiple regression）, the optimized preparing conditions were acquired and validated by experiment. Results All of the four indicators were different by these analyses. The validation experiments indicated that the optimized conditions by stepwise multiple regressions were better than that by traditional analysis. Conclusion Experiment results suggested that multiple regressions could avoid the weakness of direct observation and variance analysis, but more work should be done in preparing liposomes.

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.

New empirical model to evaluate groundwater flow into circular tunnel using multiple regression analysis

There are various analytical, empirical and numerical methods to calculate groundwater inflow into tun- nels excavated in rocky media. Analytical methods have been widely applied in prediction of groundwa- ter inflow to tunnels due to their simplicity and practical base theory. Investigations show that the real amount of water infiltrating into jointed tunnels is much less than calculated amount using analytical methods and obtained results are very dependent on tunnel＇s geometry and environmental situations. In this study, using multiple regression analysis, a new empirical model for estimation of groundwater seepage into circular tunnels was introduced. Our data was acquired from field surveys and laboratory analysis of core samples. New regression variables were defined after perusing single and two variables relationship between groundwater seepage and other variables. Finally, an appropriate model for estima- tion of leakage was obtained using the stepwise algorithm. Statistics like R, R2, R2e and the histogram of residual values in the model represent a good reputation and fitness for this model to estimate the groundwater seepage into tunnels. The new experimental model was used for the test data and results were satisfactory. Therefore, multiple regression analysis is an effective and efficient way to estimate the groundwater seeoage into tunnels.

Estimating the Texture of Purple Soils Using Vis-NIR Spectroscopy and Optimized Conversion Models

Soil texture is an indicator of soil physical structure which delivers many ecological functions of soils such as thermal regime, plant growth, and soil quality. However, traditional methods for soil texture measurement are time-consuming and labor-intensive. This study attempts to explore an indirect method for rapid estimating the texture of three subgroups of purple soils (i.e. calcareous, neutral, and acidic). 190 topsoil (0 - 10 cm) samples were collected from sloping croplands in Tongnan and Beibei Districts of Chongqing Municipality in China. Vis-NIR spectrum was measured and processed, and stepwise multiple linear regression (SMLR), partial least squares regression (PLSR), and back propagation neural network (BPNN) models were constructed to inform the soil texture. The clay fractions ranged from 4.40% to 27.12% while sand fractions ranged from 0.34% to 36.57%, hereby soil samples encompass three textural classes (i.e. silt, silt loam, and silty clay loam). For the original spectrum, the texture of calcareous and neutral purple soils was not significantly correlated with spectral reflectance and linear models (SMLR and PLSR) exhibited low prediction accuracy. The correlation coefficients and the goodness-of-fits between soil texture and the transformed spectra of all soil groups increased by continuum-removal (CR), first-order differential (R'), and second-order differential (R") transformations. Among them, the R" had the best performance in terms of improving the correlation coefficients and the goodness-of-fits. For the calcareous purple soil, the SMLR exceeds PLSR and BPNN with a higher coefficient of determination (R2) and the ratio of performance to inter-quartile distance (RPIQ) values and lower root mean square error of validation (RMSEV), but for the neutral and acidic purple soils, the PLSR model has a better prediction accuracy. In summary, the linear methods (SMLR and PLSR) are more reliable in estimating the texture of the three purple soil groups when using Vis-NIR spectroscopy inversion.

Estimating purple-soil moisture content using Vis-NIR spectroscopy

Soil moisture is essential for plant growth in terrestrial ecosystems.This study investigated the visible-near infrared(Vis-NIR)spectra of three subgroups of purple soils(calcareous,neutral,and acidic)from western Chongqing,China,containing different water contents.The relationship between soil moisture and spectral reflectivity(R)was analyzed using four spectral transformations,and estimation models were established for estimating the soil moisture content(SMC)of purple soil based on stepwise multiple linear regression(SMLR)and partial least squares regression(PLSR).We found that soil spectra were similar for different moisture contents,with reflectivity decreasing with increasing moisture content and following the order neutral>calcareous>acidic purple soil(at constant moisture content).Three of the four spectral transformations can highlight spectral sensitivity to SMC and significantly improve the correlation between the reflectance spectra and SMC.SMLR and PLSRmethods provide similar prediction accuracy.The PLSR-based model using a first-order reflectivity differential(R?)is more effective for estimating the SMC,and gave coefficient of determination(v2),root mean square errors of validation(RMSEV),and ratio of performance to inter-quartile distance(RPIQ)values of 0.946,1.347,and 6.328,respectively,for the calcareous purple soil,and 0.944,1.818,and 6.569,respectively,for the acidic purple soil.For neutral purple soil,the best prediction was obtained using the SMLR method with R?transformation,yieldingv2,RMSEV and RPIQ values of 0.973,0.888 and 8.791,respectively.In general,PLSR is more suitable than SMLR for estimating the SMC of purple soil.

Quantifying TiO_2 Abundance of Lunar Soils:Partial Least Squares and Stepwise Multiple Regression Analysis for Determining Causal Effect

Partial least squares （PLS） regression was applied to the Lunar Soft Characterization Consortium （LSCC） dataset for spectral estimation of TiO2. The LSCC dataset was split into a number of subsets including the low-Ti, high-Ti, total mare soils, total highland, Apollo 16, and Apollo 14 soils to investigate the effects of interfering minerals and nonlinearity on the PLS performance. The PLS weight loading vectors were analyzed through stepwise multiple regression analysis （SMRA） to identify mineral species driving and interfering the PLS performance. PLS exhibits high performance for estimating TiO2 for the LSCC low-Ti and high-Ti mare samples and both groups analyzed together. The results suggest that while the dominant TiO2-bearing minerals are few, additional PLS factors are required to compensate the effects on the important PLS factors of minerals that are not highly corrected to TiO2, to accommodate nonlinear relationships between reflectance and TiO2, and to correct inconsistent mineral-TiO2 correlations between the high-Ti and iow-Ti mare samples. Analysis of the LSCC highland soil samples indicates that the Apollo 16 soils are responsible for the large errors of TiO2 estimates when the soils are modeled with other subgroups. For the LSCC Apollo 16 samples, the dominant spectral effects of plagioclase over other dark minerals are primarily responsible for large errors of estimated TiO2. For the Apollo 14 soils, more accurate estimation for TiO2 is attributed to the posi- tive correlation between a major TiOe-bearing component and TiO2, explaining why the Apollo 14 soils follow the regression trend when analyzed with other soils groups.

Establishment and evaluation of operation function model for cascade hydropower station

Toward solving the actual operation problems of cascade hydropower stations under hydrologic uncertainty, this paper presents the process of extraction of statistical characteristics from long-term optimal cascade operation, and proposes a monthly operation function algorithm for the actual operation of cascade hydropower stations through the identification, processing, and screening of available information during long-term optimal operation. Applying the operation function to the cascade hydropower stations on the Jinshajiang-Yangtze River system, the modeled long-term electric generation is shown to have high precision and provide benefits. Through comparison with optimal operation, the simulation results show that the operation function proposed retains the characteristics of optimal operation. Also, the inadequacies and attribution of the algorithm are discussed based on case study, providing decision support and reference information for research on large-scale cascade operation work.

2D-QSARs of 1-Alkoxymethyl-5-alkyl-6-naphthylmethyl Uracils as HEPT Analogues with Anti-HIV-1 Activity

The two-dimensional Quantitative Structure-Activity Relationship （2D-QSAR） models have been developed to estimate and predict the inhibitory activities of a series of HEPT analogues against HIV-1 by using quantum chemical parameters and physicochemical parameters. The best model of three parameters yields r = 0.908, r^2A = 0.800 and s = 0.467 based on stepwise multiple regression （SMR） method. The stability of the model has been verified by t-test, and the results show that the model has perfect robustness. The predictive power of QSAR models has been tested by Leave-One-Out （LOO） and Leave-Group（regularly random set）-Out（LGO） procedure Cross-Validation methodology. The r^2cv of 0.755 and r^2pred of 0.759 were obtained, respectively.

Predicting Surface Roughness and Moisture of Bare Soils Using Multi- band Spectral Reflectance Under Field Conditions

Soil surface roughness, denoted by the root mean square height(RMSH), and soil moisture(SM) are critical factors that affect the accuracy of quantitative remote sensing research due to their combined influence on spectral reflectance(SR). In regards to this issue, three SM levels and four RMSH levels were artificially designed in this study; a total of 12 plots was used, each plot had a size of 3 m × 3 m. Eight spectral observations were conducted from 14 to 30 October 2017 to investigate the correlation between RMSH, SM, and SR. On this basis, 6 commonly used bands of optical satellite sensors were selected in this study, which are red(675 nm), green(555 nm), blue(485 nm), near infrared(845 nm), shortwave infrared 1(1600 nm), and shortwave infrared 2(2200 nm). A negative correlation was found between SR and RMSH, and between SR and SM. The bands with higher coefficient of determination R^2 values were selected for stepwise multiple nonlinear regression analysis. Four characterized bands(i.e., blue, green, near infrared, and shortwave infrared 2) were chosen as the independent variables to estimate SM with R^2 and root mean square error(RMSE) values equal to 0.62 and 2.6%, respectively. Similarly, the four bands(green, red, near infrared, and shortwave infrared 1) were used to estimate RMSH with R^2 and RMSE values equal to 0.48 and 0.69 cm, respectively. These results indicate that the method used is not only suitable for estimating SM but can also be extended to the prediction of RMSH. Finally, the evaluation approach presented in this paper highly restores the real situation of the natural farmland surface on the one hand, and obtains high precision values of SM and RMSH on the other. The method can be further applied to the prediction of farmland SM and RMSH based on satellite and unmanned aerial vehicle(UAV) optical imagery.

Critical Thinking and Its Relevant Factors among Undergraduates

To explore the present status of Critical thinking and its relevant factors among undergraduates.A stratified random sampling was used to select 1013 undergraduates from 7 full-time colleges in Guangdong province.They were investigated with California Critical Thinking Disposition Inventory-Chinese Version(CTDI-CV)and a Self-Compiled Personal General Information Questionnaire.(1)The total score of CTDI-CV was(254.16±38.80).The undergraduates in the four levels of critical thinking of comprehensive strong,relatively strong,contradictory scope and serious opposition accounted for 1.78%,5.31%,87.4%and 5.51%of this group,respectively.(2)Multiple stepwise linear regression showed that the total score of CTDI-CV was positively correlated with the following 10 factors such as grade,family economic status,part-time experience,the teaching method used most commonly,like reading logic books,like reading reviews or essays,father’s warmth,mother’s warmth,openness and responsibility(β=.142 to.701,all P<.05).The following 5 factors such as father’s negation,father’s overprotection,mother’s negation,mother’s overprotection and neuroticism were negatively correlated with the total score of CTDI-CV(β=-.381 to-.616,all P<0.05).The overall level of critical thinking among undergraduates is relatively low.College Students’critical thinking may be related to many factors such as family rearing,school education and personal characteristics.

Incorporation of source contributions to improve the accuracy of soil heavy metal mapping using small sample sizes at a county scale

Estimating heavy metal(HM) distribution with high precision is the key to effectively preventing Chinese medicinal plants from being polluted by the native soil. A total of 44 surface soil samples were gathered to detect the concentrations of eight HMs(As, Hg, Cu, Cr, Ni, Zn, Pb, and Cd) in the herb growing area of Luanping County, northeastern Hebei Province, China. An absolute principal component score-multiple linear regression(APCS-MLR) model was used to quantify pollution source contributions to soil HMs. Furthermore, the source contribution rates and environmental data of each sampling point were simultaneously incorporated into a stepwise linear regression model to identify the crucial indicators for predicting soil HM spatial distributions. Results showed that 88% of Cu, 72% of Cr, and 72% of Ni came from natural sources;50% of Zn, 49% of Pb, and 59% of Cd were mainly caused by agricultural activities;and 44% of As and 56% of Hg originated from industrial activities. When three-type(natural, agricultural, and industrial) source contribution rates and environmental data were simultaneously incorporated into the stepwise linear regression model, the fitting accuracy was significantly improved and the model could explain 31%–86% of the total variance in soil HM concentrations. This study introduced three-type source contributions of each sampling point based on APCS-MLR analysis as new covariates to improve soil HM estimation precision, thus providing a new approach for predicting the spatial distribution of HMs using small sample sizes at the county scale.

Pedotransfer functions for predicting bulk density of coastal soils in East China

Soil bulk density(BD) is an important physical property and an essential factor for weight-to-volume conversion. However, BD is often missing from soil databases because its direct measurement is labor-intensive, time-consuming, and sometimes impractical, particularly on a large scale. Therefore, pedotransfer functions(PTFs) have been developed over several decades to predict BD. Here, six previously revised PTFs(including five basic functions and stepwise multiple linear regression(SMLR)) and two new PTFs, partial least squares regression(PLSR) and support vector machine regression(SVMR), were used to develop BD-predicting PTFs for coastal soils in East China. Predictor variables included soil organic carbon(SOC) and particle size distribution(PSD). To compare the robustness and reliability of the PTFs used, the calibration and prediction processes were performed 1 000 times using the calibration and validation sets divided by a random sampling algorithm. The results showed that SOC was the most important predictor, and the revised PTFs performed reasonably although only SOC was included. The PSD data were useful for a better prediction of BD, and sand and clay fractions were the second and third most important properties for predicting BD. Compared to the other PTFs, the PLSR was shown to be slightly better for the study area(the average adjusted coefficient of determination for prediction was 0.581). These results suggest that PLSR with SOC and PSD data can be used to fill in the missing BD data in coastal soil databases and provide important information to estimate coastal carbon storage, which will further improve our understanding of sea-land interactions under the conditions of ongoing global warming.

Estimation of photolysis half-lives of dyes in a continuous-flow system with the aid of quantitative structure-property relationship

In this paper the photolysis half-lives of the model dyes in water solutions and under ultraviolet （UV） radiation were determined by using a continuous-flow spectrophotometric method. A quantitative structure- property relationship （QSPR） study was carried out using 21 descriptors based on different chemometric tools including stepwise multiple linear regression （MLR） and partial least squares （PLS） for the prediction of the photolysis half-life （t1/2） of dyes. For the selection of test set compounds, a K-means clustering technique was used to classify the entire data set, so that all clusters were properly represented in both training and test sets. The QSPR results obtained with these models show that in MLR-derived model, photolysis half-lives of dyes depended strongly on energy of the highest occupied molecular orbital （EHoMO）, largest electron density of an atom in the molecule （ED^＋） and lipophilicity （logP）. While in the model derived from PLS, besides aforementioned EHOMO and ED^＋ descriptors, the molecular surface area （Sm）, molecular weight （M-W）, electronegativity （X）, energy of the second highest occupied molecular orbital （EHoMO- 1） and dipole moment （μ） had dominant effects on logt1/2 values of dyes. These were applicable for all classes of studied dyes （including monoazo, disazo, oxazine, sulfo- nephthaleins and derivatives of fluorescein）. The results were also assessed for their consistency with findings from other similar studies.

Quantitative structure–biodegradability relationships for biokinetic parameter of polycyclic aromatic hydrocarbons

Prediction of the biodegradability of organic pollutants is an ecologically desirable and economically feasible tool for estimating the environmental fate of chemicals. In this paper,stepwise multiple linear regression analysis method was applied to establish quantitative structure biodegradability relationship（QSBR） between the chemical structure and a novel biodegradation activity index（qmax） of 20 polycyclic aromatic hydrocarbons（PAHs）. The frequency B3LYP/6-311＋G（2df,p） calculations showed no imaginary values, implying that all the structures are minima on the potential energy surface. After eliminating the parameters which had low related coefficient with qmax, the major descriptors influencing the biodegradation activity were screened to be Freq, D, MR, EHOMOand To IE. The evaluation of the developed QSBR mode, using a leave-one-out cross-validation procedure, showed that the relationships are significant and the model had good robustness and predictive ability. The results would be helpful for understanding the mechanisms governing biodegradation at the molecular level.