assignmentutor-lab™ 为您的留学生涯保驾护航 在代写多元统计分析Multivariate Statistical 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。我们的专家在代写多元统计分析Multivariate Statistical Analysis代写方面经验极为丰富，各种代写多元统计分析Multivariate Statistical 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|多元统计分析代写Multivariate Statistical Analysis代考|Covariance

Covariance is a measure of dependency between random variables. Given two (random) variables $X$ and $Y$ the (theoretical) covariance is defined by:
$$\sigma_{X Y}=\operatorname{Cov}(X, Y)=\mathrm{E}(X Y)-(\mathrm{E} X)(\mathrm{E} Y)$$
The precise definition of expected values is given in Chap. 4. If $X$ and $Y$ are independent of each other, the covariance $\operatorname{Cov}(X, Y)$ is necessarily equal to zero, see Theorem 3.1. The converse is not true. The covariance of $X$ with itself is the variance:
$$\sigma_{X X}=\operatorname{Var}(X)=\operatorname{Cov}(X, X) .$$
If the variable $X$ is $p$-dimensional multivariate, e.g. $X=\left(\begin{array}{c}X_{1} \ \vdots \ X_{p}\end{array}\right)$, then the theoretical covariances among all the elements are put into matrix form, i.e. the covariance matrix:
$$\Sigma=\left(\begin{array}{ccc} \sigma_{X_{1} X_{1}} & \cdots & \sigma_{X_{1} X_{p}} \ \vdots & \ddots & \vdots \ \sigma_{X_{p} X_{1}} & \cdots & \sigma_{X_{p} X_{p}} \end{array}\right)$$
Properties of covariance matrices will be detailed in Chap. 4. Empirical versions of these quantities are:
\begin{aligned} &s_{X Y}=\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right) \ &s_{X X}=\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2} . \end{aligned}

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Linear Model for Two Variables

We have looked several times now at downward and upward-sloping scatterplots. What does the eye define here as a slope? Suppose that we can construct a line corresponding to the general direction of the cloud. The sign of the slope of this line would correspond to the upward and downward directions. Call the variable on the vertical axis $Y$ and the one on the horizontal axis $X$. A slope line is a linear relationship between $X$ and $Y$ :
$$y_{i}=\alpha+\beta x_{i}+\varepsilon_{i}, i=1, \ldots, n$$

Here, $\alpha$ is the intercept and $\beta$ is the slope of the line. The errors (or deviations from the line) are denoted as $\varepsilon_{i}$ and are assumed to have zero mean and finite variance $\sigma^{2}$. The task of finding $(\alpha, \beta)$ in (3.27) is referred to as a linear adjustment.

In Sect. $3.6$ we shall derive estimators for $\alpha$ and $\beta$ more formally, as well as accurately describe what a “good” estimator is. For now, one may try to find a “good” estimator $(\hat{\alpha}, \hat{\beta})$ via graphical techniques. A very common numerical and statistical technique is to use those $\hat{\alpha}$ and $\hat{\beta}$ that minimise:
$$(\hat{\alpha}, \hat{\beta})=\arg \min {(\alpha, \beta)} \sum{i=1}^{n}\left(y_{i}-\alpha-\beta x_{i}\right)^{2}$$

# 多元统计分析代考

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Covariance

$$\sigma_{X Y}=\operatorname{Cov}(X, Y)=\mathrm{E}(X Y)-(\mathrm{E} X)(\mathrm{E} Y)$$

$$\sigma_{X X}=\operatorname{Var}(X)=\operatorname{Cov}(X, X) .$$

$$s_{X Y}=\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right) \quad s_{X X}=\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2} .$$

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Linear Model for Two Variables

$$y_{i}=\alpha+\beta x_{i}+\varepsilon_{i}, i=1, \ldots, n$$

$$(\hat{\alpha}, \hat{\beta})=\arg \min (\alpha, \beta) \sum i=1^{n}\left(y_{i}-\alpha-\beta x_{i}\right)^{2}$$

## 有限元方法代写

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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。

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