两个多重相关变量组的统计分析(2)

本文介绍用最小二乘准则建立多对多线性回归模型 (MLR) ,以及建立主成分回归 (PCR) ,并通过例子比较之。

Prediction Model of Secondary Substances in Anthocyanins Synthesis of Purple Corn

The aim of this study was to assay the polyphenols,flavonoid,polyphenol oxidase and phenylalnine ammonialyase which were relative to the anthocyanins synthesis of purple corn. The optimization of multiple linear regression model of anthocyanins synthesis was y=4.383 86-0.205 45x1＋5.479 638x2＋0.195 575x4. According to standard partial regression coefficient testing,the result indicated that polyphenols content was negatively correlated with anthocyanins and the relative influence to anthocyanins synthesis was-42.7%; flavonoid content and activity of polyphenol oxidase were positively correlated with anthocyanins of purple corn and the relative influence to anthocyanins synthesis were 71.45% and 73.32% respectively. There was no positive correlation between the activity of phenylalnine ammonialyase and anthocyanins of purple corn. The establishment of multiple linear regression model of anthocyanins synthesis was to provide theory foundation of producing anthocyanins in laboratory.

Prediction of Soil Depth from Digital Terrain Data by Integrating Statistical and Visual Approaches

Information about the spatial distribution of soil attributes is indispensable for many land resource management applications; however, the ability of soil maps to supply such information for modern modeling tools is questionable. The objectives of this study were to investigate the possibility of predicting soil depth using some terrain attributes derived from digital elevation models （DEMs） with geographic information systems （GIS） and to suggest an approach to predict other soil attributes. Soil depth was determined at 652 field observations over the A1-Muwaqqar Watershed （70 km2） in Jordan. Terrain attributes derived from 30-m resolution DEMs were utilized to predict soil depth. The results indicated that the use of multiple linear regression models within small watershed subdivisions enabled the prediction of soil depth with a difference of 50 cm for 77% of the field observations. The spatial distribution of the predicted soil depth was visually coincided and had good correlations with the spatial distribution of the classes amalgamating three terrain attributes, slope steepness, slope shape, and compound topographic index. These suggested that the modeling of soil-landscape relationships within small watershed subdivisions using the three terrain attributes was a promising approach to predict other soil attributes.

Quantitative evaluation of urban park cool island factors in mountain city

Evaluating how park characteristics affect the formation of a park cool island(PCI) is the premise of guiding green parks planning in mountain cities.The diurnal variation of PCI intensity was achieved,and correlations between PCI intensity and park characteristics such as park area,landscape shape index(LSI),green ratio and altitude were analyzed,using 3 010 temperature and humidity data from measurements in six parks with typical park characteristics in Chongqing,China.The results indicate that:1) the main factor determining PCI intensity is park area,which leads to obvious cool island effect when it exceeds 14 hm2;2) there is a negative correlation between PCI intensity and LSI,showing that the rounder the park shape is,the better the cool island effect could be achieved;3) regression analysis of humidity and PCI intensity proves that photosynthesis midday depression(PMD) is an important factor causing the low PCI intensity at 13:00;4) the multivariable linear regression model proposed here could effectively well predict the daily PCI intensity in mountain cities.

Damage alarming for bridge expansion joints using novelty detection technique based on long-term monitoring data

Damage alarming and safety evaluation using long-term monitoring data is an area of significant research activity for long-span bridges. In order to extend the research in this field, the damage alarming technique for bridge expansion joints based on long-term monitoring data was developed. The effects of environmental factors on the expansion joint displacement were analyzed. Multiple linear regression models were obtained to describe the correlation between displacements and the dominant environmental factors. The damage alarming index was defined based on the multiple regression models. At last, the X-bar control chart was utilized to detect the abnormal change of the displacements. Analysis results reveal that temperature and traffic condition are the dominant environmental factors to influence the displacement. When the confidence level of X-bar control chart is set to be 0.003, the false-positive indications of damage can be avoided. The damage sensitivity analysis shows that the proper X-bar control chart can detect 0.1 cm damage-induced change of the expansion joint displacement. It is reasonably believed that the proposed technique is robust against false-positive indication of damage and suitable to alarm the possible future damage of the expansion joints.

Plasma homocysteine levels are independently associated with alterations of large artery stiffness in men but not in women

Objectives To investigate the associations of the plasma homocysteine levels with the alterations in arterial stiffness in a commu- nity-based cohort. The gender differences in these associations were examined. Methods We evaluated the relationship between plasma homocysteine levels to three measures of vascular ftmction [carotid-femoral pulse wave velocity （CF-PWV）, carotid-ankle PWV （CA-PWV） and heart rate corrected augmentation index （AI）] in 1680 participants （mean age： 61.5 years; 709 men, 971 women） from communities of Beijing, China. Results In univariate analysis, plasma homocysteine levels was positively related to the CF-PWV （r = 0.211, P 〈 0.0001） and CA-PWV （r = 0.148, P 〈 0.0001）, whereas inversely associated with AI （r = -0.052, P = 0.016）. In multiple linear regression models adjusting for covariants, plasma homocysteine remained positively related to the CF-PWV （standardized 13 = 0.065, P = 0.007） in total cases. When the groups of men and women were examined separately, plasma homocysteine remained positively associated with the CF-PWV （standardized β = 0.082, P = 0.023） in men, whereas the relations between homocysteine and any of the arterial stiffness indices were not further present in women. Conclusions In Chinese population, plasma homocysteine levels are independently associated with alterations of large artery stiffness in men but not in women.

A topographical model for precipitation pattern in the Tibetan Plateau

As the highest and most extensive plateau on earth, the Tibetan Plateau has strong thermo- dynamic effect, which not only affects regional climate around the plateau but precipitation patterns of scattered meteorological also temperature and itself. However, due to stations, its spatial precipitation pattern and, especially, the mechanism behind are poorly understood. The availability of spatially consistent satellite-derived precipitation data makes it possible to get accurate precipitation pattern in the plateau, which could help quantitatively explore the effect and mechanism of mass elevation effect on precipitation pattern. This paper made full use of TMPA 3B43 V7 monthly precipitation data to track the trajectory of precipitation and identified four routes （east, southeast, south, west directions） along which moisture-laden air masses move into the plateau. We made the assumption that precipitation pattern is the result interplay of these four moisture- laden air masses transportation routes against the distances from moisture sources and the topographic barriers along the routes. To do so, we developed a multivariate linear regression model with the spatial distribution of annual mean precipitation as the dependent variable and the topographical barriers to these four moisture sources as independent variables. The result shows that our model could explain about 7o% of spatial variation of mean annual precipitation pattern in the plateau; the regression analysis also shows that the southeast moisture source （the Bay of Bengal） contributes the most （32.56%） to the rainfall pattern of the plateau; the east and the south sources have nearly the same contribution, 23.59% and 23.48%, respectively; while the west source contributes the least, only 2o.37%. The findings of this study can greatly improve our understanding of mass elevation effect on spatial precipitation pattern.

Estimation of surface tension of organic compounds using quantitative structure-property relationship

A novel quantitative structure-property relationship （QSPR） model for estimating the solution surface tension of 92 organic compounds at 20℃ was developed based on newly introduced atom-type topological indices. The data set contained non-polar and polar liquids, and saturated and unsaturated compounds. The regression analysis shows that excellent result is obtained with multiple linear regression. The predictive power of the proposed model was discussed using the leave-one-out （LOO） cross-validated （CV） method. The correlation coefficient （R） and the leave-one-out cross-validation correlation coefficient （Rcv） of multiple linear regression model are 0.991 4 and 0.991 3, respectively. The new model gives the average absolute relative deviation of 1.81% for 92 substances. The result demonstrates that novel topological indices based on the equilibrium electro-negativity of atom and the relative bond length are useful model parameters for QSPR analysis of compounds.

Spatial-temporal Characteristics and Factors Influencing Commuting Activities of Middle-class Residents in Guangzhou City, China

The middle class in metropolitan Chinese cities has become an important social group. With the rapid development of urbanization and constant advancement of suburbanization, the middle class has increasingly come to influence city traffic. Research into middle-class commuting activities thus has practical significance for improving traffic congestion and reducing the commuting burden in metropolitan cities. Based on a dataset formed by 816 completed surveys, this paper analyzes the commuting mode, time and distance of middle-class residents in Guangzhou City using the descriptive statistical method. The results indicate that private cars are the main commuting mode, followed by public transport. Meanwhile, middle-class residents mainly undertake medium-short time and medium-short distance commuting. The study subsequently uses multilevel logistic regression and multiple linear regression models to analyze the factors that influence commuting mode choice, time and distance. The gender, age, number of family cars, housing source and jobs-housing balance are the most important factors influencing commuting mode choice; housing, population density, jobs-housing balance and commuting mode significantly affect commuting time; and transport accessibility, jobs-housing balance and commuting mode are the notable factors affecting commuting distance. Finally, this paper analyzes what is affecting the commuting activities of middle-class residents and determines the differences in commuting activity characteristics and influence factors between middle-class and ordinary residents. Policy suggestions to improve urban planning and urban management are also proposed.

Regression analysis of major parameters affecting the intensity of coal and gas outbursts in laboratory

Estimating the intensity of outbursts of coal and gas is important as the intensity and frequency of outbursts of coal and gas tend to increase in deep mining. Fully understanding the major factors contributing to coal and gas outbursts is significant in the evaluation of the intensity of the outburst. In this paper, we discuss the correlation between these major factors and the intensity of the outburst using Analysis of Variance(ANOVA) and Contingency Table Analysis(CTA). Regression analysis is used to evaluate the impact of these major factors on the intensity of outbursts based on physical experiments. Based on the evaluation, two simple models in terms of multiple linear and nonlinear regression were constructed for the prediction of the intensity of the outburst. The results show that the gas pressure and initial moisture in the coal mass could be the most significant factors compared to the weakest factor-porosity. The P values from Fisher's exact test in CTA are: moisture(0.019), geostress(0.290), porosity(0.650), and gas pressure(0.031). P values from ANOVA are moisture(0.094), geostress(0.077), porosity(0.420), and gas pressure(0.051). Furthermore, the multiple nonlinear regression model(RMSE: 3.870) is more accurate than the linear regression model(RMSE: 4.091).

Characteristics of ventilation coefficient and its impact on urban air pollution

The temporal variation of ventilation coefficient was estimated and a simple model for the prediction of urban ventilation coefficient in Changsha was developed. Firstly, Pearson correlation analysis was used to investigate the relationship between meteorological parameters and mixing layer height during 2005-2009 in Changsha, China. Secondly, the multi-linear regression model between daytime and nighttime was adopted to predict the temporal ventilation coefficient. Thirdly, the validation of the model between the predicted and observed ventilation coefficient in 2010 was conducted. The results showed that ventilation coefficient significantly varied and remained high during daytime, while it stayed relatively constant and low during nighttime. In addition, the diurnal ventilation coefficient was distinctly negatively correlated with PM10 (particle with the diameter less than 10 μm) concentration in Changsha, China. The predicted ventilation coefficient agreed well with the observed values based on the multi-linear regression models during daytime and nighttime. The urban temporal ventilation coefficient could be accurately predicted by some simple meteorological parameters during daytime and nighttime. The ventilation coefficient played an important role in the PM10 concentration level.

Statistical Downscaling Prediction of Summer Precipitation in Southeastern China

A statistical downscaling approach based on multiple-linear-regression(MLR) for the prediction of summer precipitation anomaly in southeastern China was established,which was based on the outputs of seven operational dynamical models of Development of a European Multi-model Ensemble System for Seasonal to Interannual Prediction(DEMETER) and observed data.It was found that the anomaly correlation coefficients(ACCs) spatial pattern of June-July-August(JJA) precipitation over southeastern China between the seven models and the observation were increased significantly;especially in the central and the northeastern areas,the ACCs were all larger than 0.42(above 95% level) and 0.53(above 99% level).Meanwhile,the root-mean-square errors(RMSE) were reduced in each model along with the multi-model ensemble(MME) for some of the stations in the northeastern area;additionally,the value of RMSE difference between before and after downscaling at some stations were larger than 1 mm d-1.Regionally averaged JJA rainfall anomaly temporal series of the downscaling scheme can capture the main characteristics of observation,while the correlation coefficients(CCs) between the temporal variations of the observation and downscaling results varied from 0.52 to 0.69 with corresponding variations from-0.27 to 0.22 for CCs between the observation and outputs of the models.

Estimation of thermal decomposition temperatures of organic peroxides by means of novel local and global descriptors

The thermal decomposition temperature is one of the most important parameters to evaluate fire hazard of organic peroxide. A quantitative structure-property relationship model was proposed for estimating the thermal decomposition temperatures of organic peroxides. The entire set of 38 organic peroxides was at random divided into a training set for model development and a prediction set for external model validation. The novel local molecular descriptors of AT1, AT2, AT3, AT4, AT5, AT6 and global molecular descriptor of ATC have been proposed in order to character organic peroxides’ molecular structures. An accurate quantitative structure-property relationship （QSPR） equation is developed for the thermal decomposition temperatures of organic peroxides. The statistical results showed that the QSPR model was obtained using the multiple linear regression （MLR） method with correlation coefficient （R）, standard deviation （S）, leave-one-out validation correlation coefficient （RCV） values of 0.9795, 6.5676 ℃ and 0.9328, respectively. The average absolute relative deviation （AARD） is only 3.86% for the experimental values. Model test by internal leave-one-out cross validation and external validation and molecular descriptor interpretation were discussed. Comparison with literature results demonstrated that novel local and global descriptors were useful molecular descriptors for predicting the thermal decomposition temperatures of organic peroxides.

Analysis of factors affecting individual participation in carbon market

China will set up a national carbon emissions trading market by the end of 2017, which is initially open to individual investors from the initial market for business and institutional investors. In this article, the main influencing factors and mechanism of individual participation in carbon trading market are studied by establishing multiple linear regression model. The study found that age,education level, length of account opening time, and risk attitude are the main factors influencing the participation of individual investors. Environmental awareness and environmental impact are less affected; information transparency and transaction risk also have an impact on the degree of individual investor participation; investment experience does not affect the participation of individual investors in the carbon trading market.

Combined back-analysis method of ground stress based on refined geological modeling

A new back-analysis method of ground stress is proposed with comprehensive consideration of influence of topography, geology and nonlinear physical mechanical properties of rock on ground stress. This method based on non-uniform rational B-spline (NURBS) technology provides the means to build a refined three-dimensional finite element model with more accurate meshing under complex terrain and geological conditions. Meanwhile, this method is a back-analysis of ground stress with combination of multivariable linear regression model and neural network (ANN) model. Firstly, the regression model is used to fit approximately boundary loads. Regarding the regressed loads as mean value, some sets of boundary loads with the same interval are constructed according to the principle of orthogonal design, to calculate the corresponding ground stress at the observation positions using finite element method. The results (boundary loads and the corresponding ground stress) are added to the samples for ANN training. And on this basis, an ANN model is established to implement higher precise back-analysis of initial ground stress. A practical application case shows that the relative error between the inversed ground stress and observed value is mostly less than 10 %, which can meet the need of engineering design and construction requirements.

Updating Methods for Real Time Flood Forecasting： A Comparison through Senegal River Basin Upstream Bakel

Heavy floods occur frequently in the Senegal River Basin, causing catastrophic flooding downstream the river rating station of Bakel. Anticipating the occurrence of such phenomena is the only way to reduce the resulting damages. Flood forecasting is a necessity. Flood forecasting plays also an important role in the implementation of flood management scenarios and in the protection of hydro electric structures. Many methods are applied. The most complete are based on the conservation laws of physics governing the free surface flow. These methods need a complete description of the geometry of the river and their implementation requires also huge investments. In practice the river basin can be considered as a system of inputs-outputs related by a transfer function. In this paper the authors first used a multiple linear regression model with constant parameters estimated by the ordinary least square method to simulate the propagation of the floods in the upstream part of the Senegal river basin. The authors then apply statistical and graphical criteria of goodness-of-fit to test the suitability of this model. Three procedures of parameters updating have then been added to this linear model： the Kalman filter method, the recursive least square method, and the stochastic gradient method The criteria of goodness-of-fit used above have shown that the stochastic gradient method, although more rudimentary, represents better the flood propagation in the head basin of the Senegal river upstream Bakel. This result is particularly interesting because data influenced by Manantali Dam are used.

Variable Rate Technology and Cotton Yield Response in Texas

Variable Rate Technology （VRT） takes within-field variability into consideration and aims to match resource application to crop requirement. Even though Texas is the most important cotton producing state in the US, the rate of VRT adoption is very low here. Hence, analyzing the factors influencing the adoption and providing a regional estimate of the impact of VRT adoption on cotton yield is very important. This study used the 2009 Southern Cotton Precision Farming Survey to analyze the farm and farmer characteristics affecting the adoption of VRT among Texas cotton farmers and to empirically estimate the impact of adoption of VRT on cotton yield in Texas. A two-stage least square procedure with a logistic regression model in the first stage and a multiple linear regression model in the second stage was used to analyze the data. The study revealed that there are significant regional differences in adoption pattern within the state of Texas; and the farmers from the coastal region, where there is higher within-field variability, were more likely to adopt VRT compared to other regions. Younger farmers, farmers managing larger farms, and farmers who use computers for farming operations were more likely to adopt VRT. The results also showed that, on an average, the adoption of VRT does not lead to significant yield improvements for cotton in Texas. Since the impact of VRT adoption on yield is not significant, the source of economic advantage of VRT adoption in Texas may be the reduction of input cost.

Board of Directors, Independent Directors and Audit Fees： Based on the Empirical Data of the GEM of China

As one of the alternative variables of audit quality, audit fees have been researched widely in the Mainboard of China stock market, but empirical research based on the GEM （Growth Enterprise Market） of China is very few. From the perspective of GEM of China, this article observes and studies the impact of corporate governance structure represented by board of directors and independent directors on audit fees. This article selects the data of 348 listed companies in the GEM of China in 2012, proves that there is a positive correlation between the number of meetings, independent directors＇ salaries and audit fees through the use of multiple linear regression model, and accordingly proposed suggestions that improve the corporate governance structure of the GEM of China.

A new group contribution-based method for estimation of flash point temperature of alkanes

Flash point is a primary property used to determine the fire and explosion hazards of a liquid. New group contribution-based models were presented for estimation of the flash point of alkanes by the use of multiple linear regression(MLR)and artificial neural network(ANN). This simple linear model shows a low average relative deviation(AARD) of 2.8% for a data set including 50(40 for training set and 10 for validation set) flash points. Furthermore, the predictive ability of the model was evaluated using LOO cross validation. The results demonstrate ANN model is clearly superior both in fitness and in prediction performance.ANN model has only the average absolute deviation of 2.9 K and the average relative deviation of 0.72%.

Bayesian Variable Selection via Perfect Gibbs Coupler Using Approximate Bounds

Variable selection is one of the most fundamental problems in regression analysis. By sampling from the posterior distributions of candidate models, Bayesian variable selection via MCMC （Markov chain Monte-Carlo） is effective to overcome the computational burden of all-subset variable selection approaches. However, the convergence of the MCMC is often hard to determine and one is often not sure about if obtained samples are unbiased. This complication has limited the application of Bayesian variable selection in practice. Based on the idea of CFTP （coupling from the past）, perfect sampling schemes have been developed to obtain independent samples from the posterior distribution for a variety of problems. Here the authors propose an efficient and effective perfect sampling algorithm for Bayesian variable selection of linear regression models, which independently and identically sample from the posterior distribution of the model space and can efficiently handle thousands of variables. The effectiveness of the authors＇ algorithm is illustrated by three simulation studies, which have up to thousands of variables, the authors＇ method is further illustrated in SNPs （single nucleotide polymorphisms） association study among RA （rheumatoid arthritis） patients.