土工试验中线性回归应用分析

土工试验数据处理通常是通过繁琐计算与作图来完成,且要求及时、准确。线性回归处理法通过一定的数理关系有效简化数据处理的计算与作图过程。通过大量的剪切、液塑限试验数据处理表明,其结果是准确的、值得信赖的,它通过线性回归简化繁琐计算,使作图也变得简单。本文主要针对土工试验中的线性回归应用进行分析,从大量的剪切、液塑限联合试验中论证其结果的准确性。     

一元线性回归方程有关检验问题的研究

文章从数学角度给出T检验、F检验、相关系数的显著性检验三者一致性证明;明确了决定系数和残差分析在诊断回归效果中的作用。利用三spss软件实例分析,使得一元线性回归问题中的几种检验间的关系及作用进一步明确。     

直线法线式方程在建筑施工放样中的应用

建筑物轴线的放样主要是计算出各轴线的交点的坐标,然后通过全站仪极坐标放样的方法定出轴线交点的位置。由于建筑物坐标系和测量坐标系不同,应先通过坐标转换将建筑物轴线交点转换为测量指标,本文提出无需进行坐标转换,而是通过建立建筑方格网主轴线法线式直线方程,并以此推求出建筑物轴线的法线式直线方程,进而通过解方程组求得交点坐标。     

基于线性回归方法的我国电力市场短期用电需求预测分析

文章采用一元线性回归分析法和趋势比率误差调整法,基于以往五年我国季度月度用电量数据,对未来短期内我国的用电量做出了科学的预测。解决了电力市场短期用电需求预测的实际问题。具有结果误差小,操作简便等优点。     

运用多元一次回归模型编制科研项目预算——以X公司为例探析科研项目预算编制思路

本文针对以X公司预算编制存在的问题,提出了解决方案。依据X公司近五年的财务数据,通过建立多元一次回归模型,选择最相关的研发费用因素来准确的预测出X公司2014年度研发费用总额。     

基于主成分分析的多元线性回归用水量模型研究——以安徽省为例

用水量的准确预测对水资源规划具有重要意义。根据统计资料,选取了八项主要影响用水量变化的指标。按照主成分分析法原理,运用少数综合因子对影响用水量变化的原有八项指标进行了综合和简化,并研究其贡献率及综合效应;分析了用水量增长的特点,选用Logistic方程对综合因子进行回归分析;结合多元线性回归方法,建立了安徽省用水量模型;拟合结果表明,模型具有较高的精度;运用该模型,对安徽省2010年的用水量进行了预测;为水资源规划与管理提供参考依据。     

基于多元线性回归分析的旅游供应链需求预测方法研究

在系统分析旅游行业特点及其影响因素的基础上,提出了有效的旅游需求预测方法,借助旅游供应链理论,从供应链视角出发,分析不同供应链节点对于旅游需求的影响,最后通过具体实例对旅游供应链需求预测模型进行了验证。     

Robust Hierarchical Bayes Small Area Estimation for the Nested Error Linear Regression Model

Standard model‐based small area estimates perform poorly in presence of outliers. Sinha & Rao ( 2009 ) developed robust frequentist predictors of small area means. In this article, we present a robust Bayesian method to handle outliers in unit‐level data by extending the nested error regression model. We consider a finite mixture of normal distributions for the unit‐level error to model outliers and produce noninformative Bayes predictors of small area means. Our modelling approach generalises that of Datta & Ghosh ( 1991 ) under the normality assumption. Application of our method to a data set which is suspected to contain an outlier confirms this suspicion, correctly identifies the suspected outlier and produces robust predictors and posterior standard deviations of the small area means. Evaluation of several procedures including the M‐quantile method of Chambers & Tzavidis ( 2006 ) via simulations shows that our proposed method is as good as other procedures in terms of bias, variability and coverage probability of confidence and credible intervals when there are no outliers. In the presence of outliers, while our method and Sinha–Rao method perform similarly, they improve over the other methods. This superior performance of our procedure shows its dual (Bayes and frequentist) dominance, which should make it attractive to all practitioners, Bayesians and frequentists, of small area estimation.     

基于多元线性回归的上海市生产性服务业和汽车产业发展的关联分析

生产性服务业是上海市“十二五”重点发展产业,“十二五”期间是上海市汽车产业的关键时期,发展基于汽车行业的生产性服务业将有效促进上海市两大关键产业的发展.从上海市生产性服务业和汽车产业发展的实践出发,基于生产性服务业和汽车行业的关联性概念模型,应用多元线性回归技术,通过对上海市生产性服务业、汽车产业及其外部环境因素的多元线性回归,论文研究了上海市生产性服务业、汽车产业和外部环境的数量关联及其含义.     

识别概念的参数关系说质疑

经济计量学联立方程模型识别概念的参数关系说有两种形式的表述。本文利用线性方程组的求解理论,揭示了参数关系说识别概念的内涵。对于其表述1,我们指出了它叙述的不够准确与不够直观,并在文中给出了相应的建议;对于其表述2,则通过反例证明了它概念上的内在矛盾性。     

Expected Precision of Estimation and Probability of Ruling Out a Hypothesis Based on a Confidence Interval

Interval estimation is an important objective of most experimental and observational studies. Knowing at the design stage of the study how wide the confidence interval (CI) is expected to be and where its limits are expected to fall can be very informative. Asymptotic distribution of the confidence limits can also be used to answer complex questions of power analysis by computing power as probability that a CI will exclude a given parameter value. The CI‐based approach to power and methods of calculating the expected size and location of asymptotic CIs as a measure of expected precision of estimation are reviewed in the present paper. The theory is illustrated with commonly used estimators, including unadjusted risk differences, odds ratios and rate ratios, as well as more complex estimators based on multivariable linear, logistic and Cox regression models. It is noted that in applications with the non‐linear models, some care must be exercised when selecting the appropriate variance expression. In particular, the well‐known ‘short‐cut’ variance formula for the Cox model can be very inaccurate under unequal allocation of subjects to comparison groups. A more accurate expression is derived analytically and validated in simulations. Applications with ‘exact’ CIs are also considered.     

SPSS相关分析与线性回归分析在我国物流业增加值分析中的应用

物流业增加值是反映物流业发展状况的核心指标,是衡量相关企业经营业绩及经济发展水平的重要依据．图而对其进行分析并在此基础上得出的结论具有重要的现实意义。文章以中国物流与采购网公布的有关统计数据为依托．通过SPSS相关分析及线性回归分析,对反映物流业发展状况的物流业增加值、物流固定资产投资、社会物流费用等指标的相互关系进行探讨．得出了一些对于物流业增加值的分析及预测有较强实际意义的结论,可供有关部门参考。     

城市燃气企业运行成本分析模型构建研究

本文将城市燃气企业配气运行成本划分为人工成本、总折旧费和运营成本三类,将通过分析企业职工总数和固定资产原值情况,间接研究企业所有人工成本和折旧费情况,而直接对企业运营成本进行研究。通过相关性分析与多元线性回归理论构建了城市燃气企业运行成本分析模型,并进行了实例应用研究。此外,具体阐述了城市燃气企业运行成本分析的重要意义。     

线性合同招标中投标人数的博弈模型研究

在线性合同的假设前提下，论文通过建立模型，求解博弈的贝叶斯均衡得到了风险中性的理性招标人的最优合同形式以及投标人的最优报价策略。最后，论文通过引入招标成本函数，进一步提出了对于招标人控制投标人数从而达到自身目标最优的策略。     

Methods for the Analysis of Explanatory Linear Regression Models with Missing Data Not at Random

Since the work of Little and Rubin (1987) not substantial advances in the analysisof explanatory regression models for incomplete data with missing not at randomhave been achieved, mainly due to the difficulty of verifying the randomness ofthe unknown data. In practice, the analysis of nonrandom missing data is donewith techniques designed for datasets with random or completely random missingdata, as complete case analysis, mean imputation, regression imputation, maximumlikelihood or multiple imputation. However, the data conditions required to minimizethe bias derived from an incorrect analysis have not been fully determined. In thepresent work, several Monte Carlo simulations have been carried out to establishthe best strategy of analysis for random missing data applicable in datasets withnonrandom missing data. The factors involved in simulations are sample size,percentage of missing data, predictive power of the imputation model and existenceof interaction between predictors. The results show that the smallest bias is obtainedwith maximum likelihood and multiple imputation techniques, although with lowpercentages of missing data, absence of interaction and high predictive power ofthe imputation model (frequent data structures in research on child and adolescentpsychopathology) acceptable results are obtained with the simplest regression imputation.     

Some Decompositions of OLSEs and BLUEs Under a Partitioned Linear Model

We consider in this paper a partitioned linear model { y , X ₁ β ₁ + X ₂ β ₂ , σ ² σ } and two corresponding small models { y , X ₁ β ₁ , σ ² σ } and { y , X ₂ β ₂ , σ ² σ } . We derive necessary and sufficient conditions for (i) the ordinary least squares estimator under the full model to be the sum of the ordinary least squares estimators under the two small models; (ii) the best linear unbiased estimator under the full model to be the sum of the best linear unbiased estimators under the two small models; (iii) the best linear unbiased estimator under the full model to be the sum of the ordinary least squares estimators under the two small models. The proofs of the main results in this paper also demonstrate how to use the matrix rank method for characterizing various equalities of estimators under general linear models.     

Estimating the Size of a Criminal Population from Police Records Using the Truncated Poisson Regression Model

The truncated Poisson regression model is used to arrive at point and interval estimates of the size of two offender populations, i.e. drunk drivers and persons who illegally possess firearms. The dependent capture–recapture variables are constructed from Dutch police records and are counts of individual arrests for both violations. The population size estimates are derived assuming that each count is a realization of a Poisson distribution, and that the Poisson parameters are related to covariates through the truncated Poisson regression model. These assumptions are discussed in detail, and the tenability of the second assumption is assessed by evaluating the marginal residuals and performing tests on overdispersion. For the firearms example, the second assumption seems to hold well, but for the drunk drivers example there is some overdispersion. It is concluded that the method is useful, provided it is used with care.     

Cross Validation Calibration Based Shrinkage – Revisited for the Construction of Prognostic Indices

The use of shrinkage methods for the construction of prognostic indices has been paid increasing attention in the literature on medical statistics in the last years. One approach for the construction of a shrinkage factor is cross validation calibration as suggested by van H ouwelingen and le C essie (1990). We investigate this approach in more detail. First we try to clarify why shrinkage factors constructed by cross validation calibration tend to be smaller than 1. Second we explain why use of this shrinkage factor can result in an improvement of the average prediction error. Third we investigate the possible gain for constellations relevant in medical research by means of a simulation study, focusing on the dilemma, that the improvement on average has to be paid by distinct deteriorations for some patients. Finally we conclude that it is necessary to rethink the choice of loss functions in constructing prognostic indices before recommendations about the use of shrinkage methods can be made.     

The Three Basic Types of Residuals for a Linear Model

We consider residuals for the linear model with a general covariance structure. In contrast to the situation where observations are independent there are several alternative definitions. We draw attention to three quite distinct types of residuals: the marginal residuals, the model‐specified residuals and the full‐conditional residuals. We adopt a very broad perspective including linear mixed models, time series and smoothers as well as models for spatial and multivariate data. We concentrate on defining these different residual types and discussing their interrelationships. The full‐conditional residuals are seen to play several important roles.     

基于历史数据的江苏省基尼系数变化趋势预报——采用多层递阶方法对江苏区域经济差异的模型分析

区域经济差异是客观存在的。对其认识有助于了解区域经济发展的现状,而经济系统是一个复杂的系统,其数学模型难于事先确定,用自适用控制理论中的多层递阶方法修正参数可对经济系统进行较准确的预测与控制。文章试图通过多层递阶方法对江苏省经济差异进行预测,提高预测的准确性。