多元方差分析

Function and limit, one-variable calculus and its application, ABC of progression and multiple-variable calculus, determinant, matrix and its calculation, system of linear equations and quadratic form, probability of occurrence, chance variable, law of large numbers and central limit theorem, sample and parametric estimation, variance analysis, regression analysis.

Advanced Mathematics 1 [Course Code 1040008 MAT114] 本课程主要介绍函数和极限，一元微积分和它的应用，ABC 级数和多元微积分，行列式和矩阵的应用，线性方程和二次方程式，事件的概率，偶然性变量，大数定律和中心极限定理，样本和参数估计，方差分析，回归分析。

Traditional multivariable analysis method, for example, principal component analysis method and factor analysis method, are common in calculating the mean vector, the covariance matrix of sample and other variables.

摘要传统的多元统计分析方法，如主成分分析方法和因子分析方法等的共同点是计算样本的均值向量和协方差矩阵，并在这两者的基础上计算其他统计量。

Studying the positive definitiveness of the covariance matrix from discrete data is important to design the sampling plan and provides the base for the data analysis.However, there have been few outcomes about the positive definitiveness of covariance matrix, most of which have been restricted to the Covariance-matrix of continuous sample.

研究离散型样本协方差矩阵的正定性有助于判断是否可以降低样本的维数，有利于优化抽样个数，为抽样调查的优化设计方案提供一定的理论基础；为基于特征根的多元统计分析提供理论指导。

Taken Qinshui Basin as an example a predictive model of gas content is established by multiple stepwise regression analysis, using Langmuir volume and gas saturation as its parameters. The result of multiple correlation coefficient testing, F-testing and t-testing indicates that the model meets the hypothesis testing of linearity and its matching effect is preferable.

以沁水盆地为例，运用多元逐步回归分析方法，建立了以Langmuir体积和含气饱和度为参数的含气量预测模型；复相关系数、F检验、t检验结果表明，该模型满足线性与方差齐性的假设，拟合效果较好。

Balanced and unbalanced designs; multivariate analysis of variance and repeated measurements; linear and nonlinear mixed models.

平衡和非平衡设计；方差反复测量多元分析；线性和非线性混合模型。

Customs of food and life were asked with same questionary.

测定工人血压、身高体重等，用统一的调查表询问饮食习惯、生活习惯等项目，并测定作业环境中苯、甲苯、二甲苯的浓度，对所得数据进行单因素方差分析和多元逐步回归分析。

For these important and practical problems,sample covariance matrix is an important statistic because many important statistics are functionals of it.When we make statistical inferences,such as estimations and/or hypothesis tests,the sample covariance matrices must be investigated.

以上诸多方面在做估计和假设检验过程中，无不用到大维随机矩阵的处理，尤其是大维样本协方差矩阵的相关性质，因为多元分析中许多重要的统计量都可以表示成样本协方差矩阵的函数。

These data were analyzed with analysis of variance and stepwise regression.

单因素方差分析结果表明，接触组的收缩压低于对照组(P 0 1)，而舒张压均高于对照组(P 0 5 )，多元逐步回归的结果显示接触苯的浓度是导致血压升高的主要影响因素之一。

We analyzed primary test factor through multi-element linear regression model. We finally concluded the optimum conditions for tapioca starch micronization.

利用多元线性回归进行方差分析，分析了试验因素对回归方程的影响效应，最后得出优化的木薯淀粉微细化处理条件。

Multiple regression techniques were used to discern whether increasing case number was associated with improved perioperative and 2-year minimum radiographic and clinical outcomes. The 96 cases were divided into 4 equal quartiles of 24 cases/group (i.e., Q1-Q4) and compared using analysis of variance measures.

使用多元回归技术辨别是否随着病例数的增加，初始和2年后围手术期的最小放射线剂量和临床结果有差别。96例患者被分成平均的4组，每组24人（i.e。，Q1-Q4），并使用方差分析的方法进行比较。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。