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# 统计代写|多元统计分析代考MULTIVARIATE STATISTICAL ANALYSIS代考|STAT505 DATA DISPLAYS AND PICTORIAL REPRESENTATIONS

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## 统计代写|多元统计分析代考MULTIVARIATE STATISTICAL ANALYSIS代考|DATA DISPLAYS AND PICTORIAL REPRESENTATIONS

The rapid development of powerful personal computers and workstations has led to a proliferation of sophisticated statistical software for data analysis and graphics. It is often possible, for example, to sit at one’s desk and examine the nature of multidimensional data with clever computer-generated pictures. These pictures are valuable aids in understanding data and of ten prevent many false starts and subsequent inferential problems.

As we shall see in Chapters 8 and 12, there are several techniques that seek to represent $p$-dimensional observations in few dimensions such that the original distances (or similarities) between pairs of observations are (nearly) preserved. In general, if multidimensional observations can be represented in two dimensions, then outliers, relationships, and distinguishable groupings can often be discerned by eye. We shall discuss and illustrate several methods for displaying multivariate data in two dimensions. One good source for more discussion of graphical methods is [12].

## 统计代写|多元统计分析代考MULTIVARIATE STATISTICAL ANALYSIS代考|DISTANCE

Although they may at first appear formidable, most multivariate techniques are based upon the simple concept of distance. Straight-line, or Euclidean, distance should be familiar. If we consider the point $P=\left(x_{1}, x_{2}\right)$ in the plane, the straightline distance, $d(O, P)$, from $P$ to the origin $O=(0,0)$ is, according to the Pythagorean theorem,
$$d(O, P)=\sqrt{x_{1}^{2}+x_{2}^{2}}$$
The situation is illustrated in Figure 1.13. In general, if the point $P$ has $p$ coordinates so that $P=\left(x_{1}, x_{2}, \ldots, x_{p}\right)$, the straight-line distance from $P$ to the origin $O=(0,0, \ldots, 0)$ is
$$d(O, P)=\sqrt{x_{1}^{2}+x_{2}^{2}+\cdots+x_{p}^{2}}$$
(See Chapter 2.) All points $\left(x_{1}, x_{2}, \ldots, x_{p}\right)$ that lie a constant squared distance, such as $c^{2}$, from the origin satisfy the equation
$$d^{2}(O, P)=x_{1}^{2}+x_{2}^{2}+\cdots+x_{p}^{2}=c^{2}$$
Because this is the equation of a hypersphere (a circle if $p=2$ ), points equidistant from the origin lie on a hypersphere.

The straight-line distance between two arbitrary points $P$ and $Q$ with coordinates $P=\left(x_{1}, x_{2}, \ldots, x_{p}\right)$ and $Q=\left(y_{1}, y_{2}, \ldots, y_{p}\right)$ is given by
$$d(P, Q)=\sqrt{\left(x_{1}-y_{1}\right)^{2}+\left(x_{2}-y_{2}\right)^{2}+\cdots+\left(x_{p}-y_{p}\right)^{2}}$$

## 统计代写|多元统计分析代考MULTNARIATE STATISTICAL ANALYSIS代写|DISTANCE

$$d(O, P)=\sqrt{x_{1}^{2}+x_{2}^{2}}$$

$$d(O, P)=\sqrt{x_{1}^{2}+x_{2}^{2}+\cdots+x_{p}^{2}}$$
(见第 2 章。) 所有要点 $\left(x_{1}, x_{2}, \ldots, x_{p}\right)$ 它位于一个恒定的平方距离，例如 $c^{2}$ ，从原点满足方程
$$d^{2}(O, P)=x_{1}^{2}+x_{2}^{2}+\cdots+x_{p}^{2}=c^{2}$$

## 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。