### 统计代写|回归分析作业代写Regression Analysis代考|Spatial autocorrelation

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• 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|Defining SA

The presence of nonzero correlation results in one $\mathrm{RV}$, $\mathrm{Y}$, in a pair being dependent on the other $\mathrm{RV}$, X. Its global trend depicting a positive relationship is for larger values of $X$ and $Y$ to tend to coincide, for intermediate values of $X$ and $Y$ to tend to coincide, and for smaller values of $X$ and $Y$ to tend to coincide; values of $\mathrm{X}$ are directly proportional to their corresponding values of $Y$. For an indirect (i.e., negative or inverse) relationship, larger values of $X$ tend to coincide with smaller values of $Y$, intermediate values of $X$ and $Y$ tend to coincide, and smaller values of $X$ tend to coincide with larger values of $Y$; values of $X$ are inversely proportional to their corresponding values of $Y$. A random relationship has values of $X$ and $Y$ haphazardly coinciding according to their relative magnitudes.

Autocorrelation transfers this notion of relationships from two RVs to a single RV; the prefix auto means self. Accordingly, $n$ observations have $\mathrm{n}(\mathrm{n}-1)$ possible pairings, one between each observation and the $(n-1)$

remaining observations; each observation always has a correlation of one with itself, and hence these n self-pairings are of little or no interest in terms of correlation. One relevant question asks whether or not an ordering exists that differentiates between two subsets of these $n(n-1)$ pairings such that the ordered subset contains directly correlated observations, whereas the unordered subset contains uncorrelated observations. For data linked to a map, its spatial ordering of attribute values virtually always yields a collection of correlated observations. Because the ordering involved is spatial, the
SA may be defined generically as the arrangement of attribute values on a map for some RV Y such that a map pattern becomes conspicuous by visual inspection. More specifically, positive SA (PSA)-overwhelmingly the most commonly observed type of SA-may be defined as the tendency for similar $Y$ values to cluster on a map. In other words, larger values of $Y$ tend to be surrounded by larger values of $Y$, intermediate values of $Y$ tend to be surrounded by intermediate values of $Y$, and smaller values of $Y$ tend to be surrounded by smaller values of Y. In contrast, NSA-a rarely observed type of SA-may be defined as the tendency for dissimilar $Y$ values to cluster on a map. In other words, larger values of $Y$ tend to be surrounded by smaller values of $Y$, intermediate values of $Y$ tend to be surrounded by intermediate values of $Y$, and smaller values of Y tend to be surrounded by larger values of Y. The absence of $\mathrm{SA}$ indicates a lack of map pattern and a haphazard mixture of attribute values across a map.

## 统计代写|回归分析作业代写Regression Analysis代考|A mathematical formularization of the first law

The preceding definition of $\mathrm{SA}$ indicates that this concept exists because orderliness, (map) pattern, and systematic concentration, rather than randomness, epitomize real-world geospatial phenomena. Tobler’s $(1969$, P. 7) First Law of Geography captures this notion: “everything is related to everything else, but near things are more related than distant things.” In 2004 the Annals of the American Association of Geographers published commentaries by six prominent geographers (Sui, Barnes, Miller, Phillips, Smith, and Goodchild), together with a reply by Tobler (vol. 94: pp. $269-310$ ) about this notion. Subsequent quantitative SA measurements (e.g., see Section 1.1.3) are mathematical abstractions of this empirical rule.

## 统计代写|回归分析作业代写Regression Analysis代考|Quantifying spatial relationships

A spatial weights matrix (SWM) is an n-by-n nonnegative (i.e., all of its entries are zero or positive) matrix, say C, describing the geographic relationship structure latent in a georeferenced dataset containing n observations (areal units or point locations in the case of georeferenced data), and has $\mathrm{n}(\mathrm{n}-1) / 2$ potential pairwise, symmetric relationship designations; without invoking symmetry, it has $n(n-1)$ potential relationship designations. Classical statistics assumes that these pairwise relationship designations do not exist (i.e., observation independence). Time-series analyses assume that $(n-1)$ of these pairwise relationship designations are nonzero and asymmetric (dependence is one-directional in time), with perhaps several additional relationship designations to capture seasonality effects. Spatial data mostly assume that between $n-1$ and $3(n-2)$ of these pairwise relationship designations are nonzero and symmetric, with asymmetric relationships usually specified from symmetric ones. The relationship definition rule (often called the neighbor or adjacency rule) is that correlation between attribute values exists for areal unit polygons sharing a common nonzero length boundary (i.e., the rook definition, using a chess move analogy). One extension of this definition is to nonzero length (i.e., point contacts) shared boundaries (i.e., the queen definition, using a chess move analogy). This latter extension tends to increase the number of designated pairwise correlations for administrative polygon surface partitionings by roughly $10 \%$; its asymptotic upper bound is a doubling of pairwise relationships (i.e., the regular square lattice case) for this near-planar situation, which still constitutes a very small percentage of the $n(n-1) / 2$ possible relationshipr. A third extension is to $k>1$ nearest neighbors, which fails to guarantee a connected dual graph structure and for which $\mathrm{k}$ is sufficiently small that it still constitutes a very small percentage of the $n(n-1)$ possible relationships. In all of these specifications of matrix $C$, if areal units $i$ and $j$ are designated polygons/locations with correlated attribute values, then $c_{i j}=1$; otherwise, $c_{i j}=0$. Frequently, matrix $C$ is converted to its often asymmetric row-standardized counterpart, matrix $W$, for which $w_{i j}=c_{i j} / \sum_{j=1}^{n} c_{i j} ; \sum_{j=1}^{n} w_{i j}=1$.

Yet another specification involves inverse distance (i.e., power or negative exponential) between polygon centroids or other points of privilege (e.g., administrative centers, such as capital cities or county seats) within areal unit polygons; these interpoint distances almost always are standardized (i.e., converted to matrix W), perhaps with a carefully chosen power or exponent parameter that essentially equates them to their shared common

boundary topological structure counterpart. Tiefelsdorf, Griffith, and Boots (1999) discuss other schemes defining a SWM that lies between matrices $\mathbf{C}$ and W.

These nearest neighbor and distance-based specifications allow spatial researchers to posit geographic relationship structures for nonpolygon point observations. By generating Thiessen polygon surface partitionings, these researchers also can posit geographic relationships based upon common boundary rules. Eigenvalues of matrices $C$ and $W$, a topic treated in a number of ensuing sections, furnish a quantitative gauge for comparing competing SWMs.

The purpose of a SWM is to define the set of directly correlated observations within a $R V$, enabling the quantification of $S A$ for a georeferenced attribute. It captures the geometric arrangement of attribute values on a map, often in topological terms.

## 统计代写|回归分析作业代写Regression Analysis代考|Defining SA

SA 可以一般地定义为一些 RV Y 的地图上的属性值的排列，使得地图图案通过视觉检查变得明显。更具体地说，阳性 SA（PSA）——绝大多数是最常见的 SA 类型——可以定义为相似的趋势是在地图上聚类的值。换句话说，较大的值是往往被较大的值包围是, 的中间值是往往被中间值包围是, 和较小的值是倾向于被较小的 Y 值包围。相比之下，NSA（一种很少观察到的 SA 类型）可以定义为不相似的趋势是在地图上聚类的值。换句话说，较大的值是往往被较小的值包围是, 的中间值是往往被中间值包围是, 较小的 Y 值往往被较大的 Y 值包围。小号一种表示缺乏地图模式和地图上属性值的随意混合。

## 统计代写|回归分析作业代写Regression Analysis代考|Quantifying spatial relationships

SWM 的目的是定义一组直接相关的观测值R在, 使量化小号一种对于地理参考属性。它通常以拓扑术语捕获地图上属性值的几何排列。

## 广义线性模型代考

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## 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。