### 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Moving to Higher Dimensions

statistics-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|Summary Statistics

This section focuses on the representation of basic summary statistics (means, covariances and correlations) in matrix notation, since we often apply linear transformations to data. The matrix notation allows us to derive instantaneously the corresponding characteristics of the transformed variables. The Mahalanobis transformation is a prominent example of such linear transformations.

Assume that we have observed $n$ realisations of a $p$-dimensional random variable; we have a data matrix $\mathcal{X}(n \times p)$ :
$$\mathcal{X}=\left(\begin{array}{ccc} x_{11} & \cdots & x_{1 p} \ \vdots & & \vdots \ \vdots & & \vdots \ x_{n 1} & \cdots & x_{n p} \end{array}\right)$$
The rows $x_{i}=\left(x_{i 1}, \ldots, x_{i p}\right) \in \mathbb{R}^{p}$ denote the $i$ th observation of a $p$-dimensional random variable $X \in \mathbb{R}^{p}$.

## 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:
$$(\hat{\alpha}, \hat{\beta})=\arg \min {(\alpha, \beta)} \sum{i=1}^{n}\left(y_{i}-\alpha-\beta x_{i}\right)^{2} .$$
The solution to this task are the estimators:
\begin{aligned} &\hat{\beta}=\frac{s_{X Y}}{s_{X X}} \ &\hat{\alpha}=\bar{y}-\hat{\beta} \bar{x} \end{aligned}
The variance of $\hat{\beta}$ is:
$$\operatorname{Var}(\hat{\beta})=\frac{\sigma^{2}}{n \cdot s_{X X}}$$
The standard error (SE) of the estimator is the square root of (3.31),
$$\operatorname{SE}(\hat{\beta})={\operatorname{Var}(\hat{\beta})}^{1 / 2}=\frac{\sigma}{\left(n \cdot s_{X X}\right)^{1 / 2}}$$
We can use this formula to test the hypothesis that $\beta=0$. In an application the variance $\sigma^{2}$ has to be estimated by an estimator $\hat{\sigma}^{2}$ that will be given below. Under a normality assumption of the errors, the $t$-test for the hypothesis $\beta=0$ works as follows.
One computes the statistic
$$t=\frac{\hat{\beta}}{\operatorname{SE}(\hat{\beta})}$$
and rejects the hypothesis at a $5 \%$ significance level if $|t| \geq t_{0.975 ; n-2}$, where the $97.5 \%$ quantile of the Student’s $t_{n-2}$ distribution is clearly the $95 \%$ critical value for the two-sided test. For $n \geq 30$, this can be replaced by $1.96$, the $97.5 \%$ quantile of the normal distribution. An estimator $\hat{\sigma}^{2}$ of $\sigma^{2}$ will be given in the following.

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Simple Analysis of Variance

In a simple (i.e. one-factorial) analysis of variance (ANOVA), it is assumed that the average values of the response variable $y$ are induced by one simple factor. Suppose that this factor takes on $p$ values and that for each factor level, we have $m=n / p$ observations. The sample is of the form given in Table $3.1$, where all of the observations are independent.
The goal of a simple ANOVA is to analyse the observation structure
$$y_{k l}=\mu_{l}+\varepsilon_{k l} \text { for } k=1, \ldots, m, \text { and } l=1, \ldots, p$$
Each factor has a mean value $\mu \mathrm{l}$. Each observation $y_{k l}$ is assumed to be a sum of the corresponding factor mean value $\mu /$ and a zero mean random error $\varepsilon_{k l}$. The linear

regression model falls into this scheme with $m=1, p=n$ and $\mu_{i}=\alpha+\beta x_{i}$, where $x_{i}$ is the $i$ th level value of the factor.

Example $3.14$ The “classic blue” pullover company analyses the effect of three marketing strategies

2. presence of sales assistant,
3. luxury presentation in shop windows.
All of these strategies are tried in ten different shops. The resulting sale observations are given in Table 3.2.

There are $p=3$ factors and $n=m p=30$ observations in the data. The “classic blue” pullover company wants to know whether all three marketing strategies have the same mean effect or whether there are differences. Having the same effect means that all $\mu_{l}$ in $(3.41$ ) equal one value, $\mu$. The hypothesis to be tested is therefore
$$H_{0}: \mu_{l}=\mu \text { for } I=1, \ldots, p$$

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

X=(X11⋯X1p ⋮⋮ ⋮⋮ Xn1⋯Xnp)

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

(一个^,b^)=参数⁡分钟(一个,b)∑一世=1n(是一世−一个−bX一世)2.

b^=sX是sXX 一个^=是¯−b^X¯

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Simple Analysis of Variance

1. 在当地报纸上刊登广告，
2. 销售助理在场，
3. 橱窗里的奢侈品展示。
所有这些策略都在十个不同的商店中进行了尝试。表 3.2 给出了所得的销售观察结果。

H0:μl=μ 为了 我=1,…,p

## 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。