### 统计代写|回归分析作业代写Regression Analysis代考|MESF and linear regression

statistics-lab™ 为您的留学生涯保驾护航 在代写回归分析Regression Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写回归分析Regression Analysis代写方面经验极为丰富，各种代写回归分析Regression Analysis相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|回归分析作业代写Regression Analysis代考|A theoretical foundation for ESFs

The theoretical foundation for MESF contains two components, one derivable from the general spatial autoregressive model specification and the other derivable from the concept of a random effects term.

The spatial autoregressive response (AR) model (known as the spatial lag model in spatial econometrics) specification, an auto-normal model, may be written as follows, using the spatial linear operator $(\mathbf{I}-\rho \mathbf{C})$ and matrix notation:
$$\mathbf{Y}=(\mathbf{I}-\rho \mathbf{C})^{-1}\left(\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}+\boldsymbol{\varepsilon}\right)$$ where $\boldsymbol{\beta}{\mathbf{X}}$ is a $(\mathrm{p}+1)$-by-1 vector of regression coefficients for $\mathrm{p}$ covariates and the intercept term, $\rho$ is the SA parameter, and $\varepsilon$ is an n-by-1 vector of independent and identically discributed (IID) normal random variables (RVs) with mean zero and constant variance $\sigma^{2}$. The standard maximum likelihood estimation of parameters in Eq. (3.2) involves it being rewritten as the following nonlinear regression specification:

$$(\mathbf{I}-\rho \mathbf{C}) \mathbf{Y}=(\mathbf{I}-\rho \mathbf{C})(\mathbf{I}-\rho \mathbf{C})^{-1}\left(\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}+\boldsymbol{\varepsilon}\right) \Rightarrow \mathbf{Y}=\rho \mathbf{C Y}+\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}+\boldsymbol{\varepsilon}$$
The eigenfunction decomposition of the $S W M C$ is $\mathbf{E} \Lambda \mathbf{E}^{\mathrm{T}}$, where matrix $\mathbf{E}$ is the set of $n$ eigenvectors of SWM $\mathrm{C}$, diagonal matrix $\boldsymbol{\Lambda}$ contains the set of $\mathrm{n}$ eigenvalues of SWM C, with the ordering of entries in these two matrices being the same eigenfunctions, and superscript $T$ denotes the matrix transpose operation. Substituting this decomposition of SWM C into Eq. (3.3) produces.
$$\mathbf{Y}=\rho \mathbf{E} \boldsymbol{A} \mathbf{E}^{\mathrm{T}} \mathbf{Y}+\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}+\boldsymbol{\varepsilon},$$ where $\mathbf{E}^{\mathrm{T}} \mathbf{Y}$ is the ordinary least squares (OLS) estimate of regression coefficients when response variable $\mathbf{Y}$ is regressed on eigenvector matrix $\mathbf{E}$. A stepwise selection procedure (e.g., simultaneous forward-backward) eliminates $j$ eigenvectors for which $\mathbf{E}{j}^{\mathrm{T}} \mathbf{Y} \approx 0$ (i.e., the $\mathrm{SA}$ map patterns for these eigenvectors do not account for any SA in the regression residuals) or for which $\rho \lambda_{j} \approx 0$ (i.e., the map pattern displays a trivial degree of SA), which in practice tends to be a large majority of the eigenvectors, leaving $\mathrm{K}<<\mathrm{n}$ eigenvectors in the model specification:
$$\mathbf{Y}=\mathbf{E}{\mathrm{K}} \boldsymbol{\beta}{\mathrm{E}}+\mathbf{X} \boldsymbol{\beta}_{\mathrm{X}}+\boldsymbol{\xi},$$

## 统计代写|回归分析作业代写Regression Analysis代考|The fundamental theorem of MESF

A statement of the fundamental theorem of MESF appears in Section 2.1.3. It is based upon several theorems in matrix algebra, including the fundarnental theorem of principal components analysis (see Tatsuoka, 1988, p. 146), which may be translated as follows:
Given a modified $n-b y-n S W M\left(I-11^{T} / n\right) C\left(I-11^{T} / n\right)$ for a given geographic land scape, we can derive a set of orthogonal and uncorrelated variables $\boldsymbol{E}{\imath}, \boldsymbol{E}{2}, \ldots, \boldsymbol{E}{n}$ by a set of linear transformations corresponding to the principal-axes rotation [i.e, the rigid rotation whose transformation matrix $E$ has the n eigervectors of matrix $\left.\left(I-11^{\top} / n\right) C\left(I-11^{T} / n\right)\right]$ as its columns. The $S A$ measures of this new set of variables are given by the diagonal matrix $\left.\left(|^{\top} \mathrm{C}\right]\right) \Lambda=\left[n / \mathbf{1}^{\top} C 1 \mathbf{E}^{\top}\left(I-11^{\top} / n\right)\right.$ $C\left(I-11^{\top} / n\right) E$, whose diagonal elements are the n MCs of the corresponding map patterns produced by the n eigenvectors of matrix $\boldsymbol{E}$. Orthogonality results from the matrix $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathrm{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)$ being symmetric (if $\mathbf{C}$ is a symmetric matrix, then $\mathbf{A C A}{ }^{T}$ is a symmetric matrix). Uncorrelatedness results from the pre- and postmultiplication of matrix $\mathbf{C}$ by the projection matrix $\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right)$, resulting in a single eigenvector proportional to the $n-b y-1$ vector 1 , and hence the $n-1$ other eigenvectors having elements that sum to zero; the numerator of the Pearson product moment correlation coefficient for a pair of different eigenvectors has a cross-product term (e.g., XY) of zero (orthogonality) and a product of two means (each being a sum of the elements of an eigenvector, with at least one of these sums equal to zero) of zero (Griffith $2000 \mathrm{~b}, \mathrm{p} .105$ ). Tiefelsdorf and Boots (1995; Section 2.1.2) prove that the MC for a given eigenvector $\mathbf{E}{j}$ is given by $\left(\mathrm{n} / \mathbf{1}^{\mathrm{T}} \mathrm{C} 1\right) \lambda_{\mathrm{j}}$. The rank ordering of the $\mathrm{R}$ ayleigh quotients
$$\left(n / 1^{\mathrm{T}} \mathrm{C} 1\right) \mathbf{E}^{\mathrm{T}}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathrm{C}\left(\mathbf{I}-11^{\mathrm{T}} / \mathrm{n}\right) \mathbf{E} /\left(\mathbf{E}^{\mathrm{T}} \mathbf{E}\right)=\left(\mathrm{n} / \mathbf{1}^{\mathrm{T}} \mathrm{C} 1\right) \boldsymbol{\Lambda}$$
produces the sequential ordering from the maximum possible level of positive SA (PSA) to the maximum possible level of negative SA (NSA; see de Jong, Sprenger, \& van Veen, 1984).

Because one eigenvector element corresponds to each of the $\mathrm{n}$ areal units in a geographic landscape, a map can portray the geographic distribution of each set of eigenvector elements. Consequently, a map of the $\mathrm{ESF}{\mathbf{K}} \boldsymbol{\beta}{\mathbf{E}}$ fumishes a visualization of SA; as such, it supplements the Moran scatterplot graphic tool. Furthermore, because each eigenvector is an n-by-1 variate, eigenvectors can be treated like covariates and included in a linear regression analysis.

## 统计代写|回归分析作业代写Regression Analysis代考|Map pattern and SA: Heterogeneity in map-wide trends

SA may be interpreted in a number of different ways, one of which is map pattern (Griffith, 1992). Pattern refers to some discernible real-world regularity that contains elements recurring in a predictable manner. Map pattern refers to this regularity and repetitiveness occurring in two dimensions and is the basis for spatial interpolation (prediction linking to kriging in geostatistics). SA makes map pattern possible by organizing attribute values on a map in such a way that for PSA, for example, relatively high values cluster together in a geographic landscape, as do relatively intermediate, and relatively low, values. This geographic organization can yield global gradients across, as well as large regional or small local clusters in, a geographic landscape; in general, neighborhood subsets of georeferenced attribute values are similar or dissimilar (NSA). These are the components of map pattern depicted by the modified SWM eigenvectors with, respectively, large, moderate, or small but not close to zero, eigenvalues. In other words, map pattern has to do with the geographic arrangement of attribute values of a map, with the nature and degree of (dis)similarities of nearby values relating to $\mathrm{SA}$.
Heterogeneity refers to a collection of diverse elements, elements that are nonuniform in the composition of their attribute values. In terms of statistical properties, these elements are not IID (see Section 3.1). In classical linear regression, a response variable $Y$ often is considered heterogeneous in its individual observation means, resulting in the term $\mathbf{X} \boldsymbol{\beta}{\mathbf{X}}$ being included in a linear regression specification. This specification strategy seeks to account for heterogeneity with the regression mean, rendering residuals that are IID and hence homogeneous. If $X \equiv 1$, then the mean of $Y$ for each areal unit is the constant $\beta{0}$; this is the special case of a homogeneous $Y$. In the presence of $\mathrm{SA}$, the residuals still have a mean of zero, but now heterogeneity persists through their variances being unequal; this outcome is one consequence of variance inflation by SA. Eq. (3.4) highlights how MESF addresses this problem by replacing the constant mean with a variable mean:
$$\mathbf{Y}=\mathrm{E}{\mathrm{K}} \boldsymbol{\beta}{\mathrm{E}}+\mathbf{X} \boldsymbol{\beta}{\mathrm{X}}+\boldsymbol{\xi}=\left(\mathbf{1} \boldsymbol{\beta}{0}+\mathrm{E}{\mathrm{K}} \boldsymbol{\beta}{\mathrm{E}}\right)+\mathbf{X}{\mathrm{P}} \boldsymbol{\beta}{\mathrm{X}}+\boldsymbol{\xi}$$

## 统计代写|回归分析作业代写Regression Analysis代考|A theoretical foundation for ESFs

MESF 的理论基础包含两个组成部分，一个来自一般空间自回归模型规范，另一个来自随机效应项的概念。

## 统计代写|回归分析作业代写Regression Analysis代考|The fundamental theorem of MESF

MESF 基本定理的陈述出现在第 2.1.3 节。它基于矩阵代数中的几个定理，包括主成分分析的基本定理（参见 Tatsuoka, 1988, p. 146），可以翻译如下
：n−b是−n小号在米(一世−11吨/n)C(一世−11吨/n)对于给定的地理景观，我们可以推导出一组正交且不相关的变量和一世,和2,…,和n通过一组对应于主轴旋转的线性变换[即，其变换矩阵的刚性旋转和具有矩阵的 n 个 eigervectors(一世−11⊤/n)C(一世−11吨/n)]作为它的列。这小号一种这组新变量的度量由对角矩阵给出(|⊤C])Λ=[n/1⊤C1和⊤(一世−11⊤/n) C(一世−11⊤/n)和, 其对角元素是矩阵的 n 个特征向量产生的对应地图图案的 n 个 MC和. 矩阵的正交性结果(一世−11吨/n)C(一世−11吨/n)是对称的（如果C是一个对称矩阵，那么一种C一种吨是一个对称矩阵）。矩阵的前乘和后乘导致不相关性C由投影矩阵(一世−11吨/n)，产生一个与n−b是−1向量 1 ，因此n−1其他元素之和为零的特征向量；一对不同特征向量的 Pearson 积矩相关系数的分子具有一个为零的叉积项（例如 XY）（正交性）和两个均值的乘积（每个均值是一个特征向量的元素之和，其中这些总和中至少有一个等于零）的零（格里菲斯2000 b,p.105）。Tiefelsdorf 和 Boots（1995；第 2.1.2 节）证明给定特征向量的 MC和j是（谁）给的(n/1吨C1)λj. 的排名顺序R艾莉商数
(n/1吨C1)和吨(一世−11吨/n)C(一世−11吨/n)和/(和吨和)=(n/1吨C1)Λ

## 统计代写|回归分析作业代写Regression Analysis代考|Map pattern and SA: Heterogeneity in map-wide trends

SA 可以用多种不同的方式来解释，其中一种是地图模式（Griffith，1992）。模式是指一些可识别的现实世界规律，其中包含以可预测方式重复出现的元素。地图模式是指这种在二维中出现的规律性和重复性，是空间插值（与地质统计学中的克里金法相关的预测）的基础。SA 通过组织地图上的属性值使地图模式成为可能，例如，对于 PSA，相对较高的值在地理景观中聚集在一起，相对中等和相对较低的值也是如此。这种地理组织可以产生跨越地理景观的全球梯度，以及地理景观中的大型区域或小型局部集群；一般来说，地理参考属性值的邻域子集相似或不同 (NSA)。这些是修改后的 SWM 特征向量所描绘的地图图案的组成部分，分别具有大、中等或小但不接近于零的特征值。换句话说，地图模式与地图属性值的地理排列有关，与附近值的性质和（不）相似程度有关小号一种.

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。