回归系数

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

Based on the autoregression equation for the standard variation of the residual errors obtained by ordinary regression analysis, the least square estimates and the maximum likelihood estimates for the regression, the autoregression and the moving average coefficients are derived.

提出一种异方差回归－时序模型，通过建立回归分析残差的标准差自回归方程，给出回归系数、自回归系数和滑动平均系数的最小二乘估计和极大似然估计。

In autoregression models, when the parameter from GED is known, adaptive rejection sampling method is used to estimate parameters; when the parameter from GED is unknown, we have to decide a range, also use the same method to give a reasonable estimate of the parameters.

在自回归模型中，GED分布的参数已知的情况下，基于似然函数的形式用拒绝抽样方法估计自回归系数；GED分布的参数未知时，我们给定参数的范围，用拒绝抽样方法寻找自回归系数合理的估计值。

What is the sampling distribution of a regression coefficient?

分别回答什么是回归系数，什么是回归系数的样本分布？

In the regression add variables and delete the variables of each step, the regression equation of the series solution of regression coefficients, and calculation of regression coefficients significant test statistic.

在逐步回归添加变量和删除变量的每一个步骤，都要解一系列的回归方程，求回归系数，计算回归系数显著性检验的统计量。

The 352 valid samples were analyzed by SPSS. The results showed there was no distinct corresponding relationship between the product attributes and reaction time. The different key attributes from questionnaire importance rating and the shortest reaction time standards were used to regressively analyze the results of customers' overall rating (such as overall satisfaction,objective quality, recommend intention).The results indicated that the coefficiency of regression of the special attributes chosen from reaction time to overall rating was distinct, while the coefficiency of the special attributes chosen from importance rating to overall rating was not. The main conclusions are: 1. Regarded attributes can be obtained by the reaction time of brand performance rating.

本实验的有效样本为352个，通过SPSS软件进行分析统计，数据统计结果显示，在品牌表现评价反应时与其重要性问卷评定结果的相关系数的检验中，并未发现品牌表现评价反应时与品牌属性重要性评定结果之间的显著相关；将由问卷重要性评价最高标准所得到的关键属性与通过品牌表现评价反应时最短的标准所选取的关键属性的品牌表现分别对消费者的总体评价结果（如&总体满意度&、&主观质量&、&推荐意向&）进行回归分析，发现通过品牌表现评价反应时方法选取的特殊关键属性（与问卷重要性评定法选取不一致的关键属性）的品牌表现对总体评价结果的回归系数显著，而重要性评定问卷法选取的特殊关键属性（与品牌表现评价反应时法选取的不一致的关键属性）的品牌表现对总体评价结果回归系数不显著。

Multiple linear regression is the simplest way to build the relationship between the several explanatory variables and response variable. However, MLR often causes the estimated regression coefficients unstable or even unaccessible when the number of explanatory variables is more than that of objects. Especially, the explanatory variables are highly intercorrelated which called multi-collinear data. Therefore, many methods have been developed to analyze multi-collinear data, such as variable selection methods, ridge regression, principal components regression and partial least squares regression.

当要同时建立多个解释变数与反应变数间的关系时，最简单的方式是以复回归来处理，但是当解释变数数目远多於样本数，或者变数之间具有高度相关性时，会使得回归系数的估计变得不稳定甚至无法求得，这样的资料又称为共线性资料，在面临这样的资料时可以利用变数选取的方式降低资料组的维度，或者以脊回归、主成分回归及净最小平方回归等方法来灭种共线性的干扰。

A mathematic model,which deals with the relationship between maximum temperature of thick plate butt multipass welding and weld heat input,interpass temperature,ambient temperature and the distance of measuring points to heat source center,was founded using multivariant nonlinear regression analysis.

采用多元非线性回归的方法，建立了厚板对接多道焊的最高温度与焊接线能量、层间温度、环境温度以及测点到热源中心的距离之间的数学模型。通过相关性检验、线性回归的显著性检验以及回归系数的显著性检验，证明了模型可行；同时分析了回归系数与测点到焊缝中心距离之间的关系。结果表明，它们之间的关系是一种非线性关系，而且呈现出了一定的变化趋势

Results analysis of data indicated a significant positive correlation among the refraction dioptres of myopia and axis length,vitreous length of eye (standardized coefficients are 0.909 and 0.803,respectively). multiple linear regression analysis of the data showed that vitreous length was the main factor to affected the formation and development of myopia diopter.

结果 眼轴长度（标准化回归系数b'j =0.909）及玻璃体腔长度（标准化回归系数b'j =0.893）均与近视屈光度呈显著正相关；用逐步回归多元线性分析法分析玻璃体腔长度、晶体厚度及前房深度各屈光要素，其中玻璃体腔长度对眼轴长度的影响最大。

SPSS 11.5 software package were applied to analyze the data. Results Analysis of data indicated a significant positive correlation among the refraction dioptres of myopia and axis length,vitreous length of eye (standardized coefficients are 0.909 and 0.803,respectively).

结果 眼轴长度（标准化回归系数b'j =0.909）及玻璃体腔长度（标准化回归系数b'j =0.893）均与近视屈光度呈显著正相关；用逐步回归多元线性分析法分析玻璃体腔长度、晶体厚度及前房深度各屈光要素，其中玻璃体腔长度对眼轴长度的影响最大。

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。