## 统计代写|回归分析作业代写Regression Analysis代考|STAT2220

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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|BRM with a Known Dispersion Matrix

It should be stressed that the multivariate model illustrated in Fig. $2.5$ is a special case of the model given in (1.9), which will serve as a basic model for the presentation of the subject matter of this book. Before starting the technical presentation, a formal definition of the $B R M$ is provided.

Definition 2.1 (BRM) $\quad$ Let $\boldsymbol{X}: p \times n, \boldsymbol{A}: p \times q, q \leq p, \boldsymbol{B}: q \times k, \boldsymbol{C}: k \times n$, $r(\boldsymbol{C})+p \leq n$ and $\boldsymbol{\Sigma}: p \times p$ be p.d. Then
$$X=A B C+E$$
defines the $B R M$, where $\boldsymbol{E} \sim N_{p, n}(\mathbf{0}, \boldsymbol{\Sigma}, \boldsymbol{I}), \boldsymbol{A}$ and $\boldsymbol{C}$ are known matrices, and $\boldsymbol{B}$ and $\boldsymbol{\Sigma}$ are unknown parameter matrices.

The condition $r(\boldsymbol{C})+p \leq n$ is an estimability condition when $\boldsymbol{\Sigma}$ is unknown. However, for ease of presentation in this section, it is assumed that the dispersion matrix $\boldsymbol{\Sigma}$ is known. The idea is to give a general overview and leave many details for the subsequent sections.
For the likelihood, $L(\boldsymbol{B})$, we have
$$L(\boldsymbol{B}) \propto|\boldsymbol{\Sigma}|^{-n / 2} e^{-1 / 2 \mathrm{tr}\left[\boldsymbol{\Sigma}^{-1}\left(\boldsymbol{X}_o-\boldsymbol{A B C}\right)\left(\boldsymbol{X}_o-\boldsymbol{A B C}\right)^{\prime}\right] .}$$
From (2.16) it is seen that there exists a design matrix $\boldsymbol{A}$ which describes the expectation of the rows of $\boldsymbol{X}$ (a within-individuals design matrix), as well as a design matrix $\boldsymbol{C}$ which describes the mean of the columns of $\boldsymbol{X}$ (a between-individuals design matrix). It is known that if one pre- and post-multiplies a matrix, a bilinear transformation is performed. Thus, in a comparison of (1.7) and (2.16), instead of a linear model in (1.7), there is a bilinear one in (2.16). The previous techniques used when $R^n$ was decomposed into $\mathcal{C}\left(\boldsymbol{C}^{\prime}\right) \boxplus \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)^{\perp}$ are adopted; i.e. due to bilinearity the tensor product $R^p \otimes R^n$ is decomposed as
$$\left(\mathcal{C}(\boldsymbol{A}) \otimes \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)\right) \boxplus\left(\mathcal{C}(\boldsymbol{A}) \otimes \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)^{\perp}\right) \boxplus\left(\mathcal{C}(\boldsymbol{A})^{\perp} \otimes \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)\right) \boxplus\left(\mathcal{C}(\boldsymbol{A})^{\perp} \otimes \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)^{\perp}\right)$$

## 统计代写|回归分析作业代写Regression Analysis代考|EBRM with a Known Dispersion Matrix

In Sect. $1.5$ two extensions of the $B R M$ were presented, i.e. the $E B R M_B^m$ and $E B R M_W^m$, together with examples of the application of these models. In this section the reader is introduced to the mathematics concerning the $E B R M_B^m$, with $m=3$, which will also be used later when studying the model without a known dispersion matrix. Now (2.16) is formally generalized and the $E B R M_B^m$ is specified in detail.
Definition $2.2\left(E B R M_B^m\right) \quad$ Let $\boldsymbol{X}: p \times n, \boldsymbol{A}i: p \times q_i, q_i \leq p, \boldsymbol{B}_i: q_i \times k_i, \boldsymbol{C}_i$ : $k_i \times n, i=1,2, \ldots, m, r\left(\boldsymbol{C}_1\right)+p \leq n, \mathcal{C}\left(\boldsymbol{C}_i^{\prime}\right) \subseteq \mathcal{C}\left(\boldsymbol{C}{i-1}^{\prime}\right), i=2,3, \ldots, m$, and $\Sigma: p \times p$ be p.d. Then
$$\boldsymbol{X}=\sum_{i=1}^m \boldsymbol{A}i \boldsymbol{B}_i \boldsymbol{C}_i+\boldsymbol{E}$$ defines the $E B R M_B^m$, where $\boldsymbol{E} \sim N{p, n}(\mathbf{0}, \boldsymbol{\Sigma}, \boldsymbol{I}),\left{\boldsymbol{A}_i\right}$ and $\left{\boldsymbol{C}_i\right}$ are known matrices, and $\left{\boldsymbol{B}_i\right}$ and $\boldsymbol{\Sigma}$ are unknown parameter matrices.

In the present book it is usually assumed that $m=2,3$, and in this section $\boldsymbol{\Sigma}$ is supposed to be known. In that case, $r\left(\boldsymbol{C}1\right)+p \leq n, \mathcal{C}\left(\boldsymbol{C}_i^{\prime}\right) \subseteq \mathcal{C}\left(\boldsymbol{C}{i-1}^{\prime}\right), i=$ $2,3, \ldots, m$ are not needed when estimating $\boldsymbol{B}i$. However, since the results from this chapter will be utilized in the next chapter, it is assumed that $\mathcal{C}\left(\boldsymbol{C}_i^{\prime}\right) \subseteq \mathcal{C}\left(\boldsymbol{C}{i-1}^{\prime}\right)$, $i=2,3, \ldots, m$, holds. Thus, the following model will be handled:
$$\boldsymbol{X}=\boldsymbol{A}1 \boldsymbol{B}_1 \boldsymbol{C}_1+\boldsymbol{A}_2 \boldsymbol{B}_2 \boldsymbol{C}_2+\boldsymbol{A}_3 \boldsymbol{B}_3 \boldsymbol{C}_3+\boldsymbol{E}, \quad \boldsymbol{E} \sim N{p, n}(\mathbf{0}, \boldsymbol{\Sigma}, \boldsymbol{I}),$$
where $\mathcal{C}\left(\boldsymbol{C}_3^{\prime}\right) \subseteq \mathcal{C}\left(\boldsymbol{C}_2^{\prime}\right) \subseteq \mathcal{C}\left(\boldsymbol{C}_1^{\prime}\right), \boldsymbol{A}_i: p \times q_i$, the parameter $\boldsymbol{B}_i: p \times q_i$, is unknown, $\boldsymbol{C}_i: k_i \times n$ and the dispersion matrix $\boldsymbol{\Sigma}$ is supposed to be known. It has already been noted in Sect. $1.5$ that without the subspace condition on $\mathcal{C}\left(\boldsymbol{C}_i\right)$, we would have the general “sum of profiles model” (a multivariate seemingly unrelated regression (SUR) model). Later (2.20) is studied when $\mathcal{C}\left(\boldsymbol{A}_3\right) \subseteq \mathcal{C}\left(\boldsymbol{A}_2\right) \subseteq \mathcal{C}\left(\boldsymbol{A}_1\right)$ replaces $\mathcal{C}\left(\boldsymbol{C}_3^{\prime}\right) \subseteq \mathcal{C}\left(\boldsymbol{C}_2^{\prime}\right) \subseteq \mathcal{C}\left(\boldsymbol{C}_1^{\prime}\right)$, i.e. we have an $E B R M_W^3$. Since the model under the assumption $\mathcal{C}\left(\boldsymbol{A}_3\right) \subseteq \mathcal{C}\left(\boldsymbol{A}_2\right) \subseteq \mathcal{C}\left(\boldsymbol{A}_1\right)$ through a reparametrization can be converted to (2.20) and vice versa, i.e. $E B R M_B^3 \rightleftarrows E B R M_W^3$, the models are in some sense equivalent. However, because of non-linearity in estimators of mean parameters, this does not imply that all the results for the models can easily be transferred from one model to the other.

# 回归分析代写

## 统计代写|回归分析作业代写Regression Analysis代考|BRM with a Known Dispersion Matrix

$$X=A B C+E$$

$$L(\boldsymbol{B}) \propto|\boldsymbol{\Sigma}|^{-n / 2} e^{-1 / 2 \operatorname{tr}\left[\boldsymbol{\Sigma}^{-1}\left(\boldsymbol{X}_o-\boldsymbol{A B C}\right)\left(\boldsymbol{X}_o-\boldsymbol{A B C}\right)^{\prime}\right] .}$$

$$\left(\mathcal{C}(\boldsymbol{A}) \otimes \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)\right) \boxplus\left(\mathcal{C}(\boldsymbol{A}) \otimes \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)^{\perp}\right) \boxplus\left(\mathcal{C}(\boldsymbol{A})^{\perp} \otimes \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)\right) \boxplus\left(\mathcal{C}(\boldsymbol{A})^{\perp} \otimes \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)^{\perp}\right)$$

## 统计代写|回归分析作业代写Regression Analysis代考|EBRM with a Known Dispersion Matrix

$$\boldsymbol{X}=\boldsymbol{A} 1 \boldsymbol{B}_1 \boldsymbol{C}_1+\boldsymbol{A}_2 \boldsymbol{B}_2 \boldsymbol{C}_2+\boldsymbol{A}_3 \boldsymbol{B}_3 \boldsymbol{C}_3+\boldsymbol{E}, \quad \boldsymbol{E} \sim N p, n(\mathbf{0}, \boldsymbol{\Sigma}, \boldsymbol{I})$$

## 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。

## 统计代写|回归分析作业代写Regression Analysis代考|STA321

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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Linear Models with a Focus on the Singular Gauss-Markov Model

The inference method adopted in this book is mainly based on the likelihood function. The purpose of this section is to introduce vector space decompositions and show their roles when estimating parameters. In Appendix B, Theorems B.3 and B.11, a few important results about the linear space $\mathcal{C}(\bullet)$, its orthogonal complement $\mathcal{C}(\bullet)^{\perp}$ and projections $\boldsymbol{P}_A=\boldsymbol{A}\left(\boldsymbol{A}^{\prime} \boldsymbol{A}\right)^{-} \boldsymbol{A}^{\prime}$ are presented. Once again the univariate linear model
$$\boldsymbol{x}^{\prime}=\boldsymbol{\beta}^{\prime} \boldsymbol{C}+\boldsymbol{e}^{\prime}, \quad \boldsymbol{e} \sim N_n\left(\mathbf{0}, \sigma^2 \boldsymbol{I}\right) .$$ will be studied. In Example $1.1$ it was noted that $\widehat{\boldsymbol{\mu}}^{\prime}=\widehat{\boldsymbol{\beta}}^{\prime} \boldsymbol{C}$ and the maximum likelihood estimator of $\sigma^2$ equalled $n \widehat{\sigma}^2=\boldsymbol{r}^{\prime} \boldsymbol{r}$, where the “mean” $\widehat{\boldsymbol{\mu}}=\boldsymbol{P}{C^{\prime}} \boldsymbol{x}$ and “residuals” $\boldsymbol{r}=\left(\boldsymbol{I}-\boldsymbol{P}{C^{\prime}}\right) \boldsymbol{x}$. Hence, the estimators and residuals are obtained by projecting $\boldsymbol{x}$ on the column space $\mathcal{C}\left(\boldsymbol{C}^{\prime}\right)$ and on its orthogonal complement $\mathcal{C}\left(\boldsymbol{C}^{\prime}\right)^{\perp}$, respectively. The estimates are obtained by replacing $\boldsymbol{x}$ by $\boldsymbol{x}o$ in the expressions given above. Moreover, under normality, $\widehat{\mu}$ and $r$ are independently distributed and constitute the building blocks of the complete and sufficient statistics. Thus, $\widehat{\mu}$ and $\boldsymbol{r}$ are very fundamental quantities for carrying out inference according to the statistical paradigm, i.e. parameter estimation and model evaluation. Indeed, this is the basic philosophy adopted throughout this book, even if the models presented later become much more complicated. Consequently, the following space decomposition is of interest: $$\mathcal{R}^n=\mathcal{C}\left(\boldsymbol{C}^{\prime}\right) \boxplus \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)^{\perp},$$ where $\boxplus$ denotes the orthogonal sum (see Appendix A, Sect. A.8), which is illustrated in Fig. 2.1. Suppose now that in the model $\boldsymbol{x}^{\prime}=\boldsymbol{\beta}^{\prime} \boldsymbol{C}+\boldsymbol{e}^{\prime}$, the restrictions $$\beta^{\prime} \boldsymbol{G}=\mathbf{0}$$ hold. The restrictions mean that there is some prior information about $\boldsymbol{\beta}$ or some hypothesis has been postulated about the parameters in $\beta$. Then it follows from Sect. $1.3$ that $$\widehat{\boldsymbol{\beta}}^{\prime} \boldsymbol{C}=\boldsymbol{x}^{\prime} \boldsymbol{C}^{\prime} \boldsymbol{G}^o\left(\boldsymbol{G}^{o^{\prime}} \boldsymbol{C} \boldsymbol{C}^{\prime} \boldsymbol{G}^o\right)^{-} \boldsymbol{G}^{o^{\prime}} \boldsymbol{C}=\boldsymbol{x}^{\prime} \boldsymbol{P}{C^{\prime} G^a}$$

## 统计代写|回归分析作业代写Regression Analysis代考|Multivariate Linear Models

In this short section, an MLE for $\boldsymbol{\Sigma}$ is additionally given, for comparisons with the estimator of the variance in univariate linear models (see Fig. 2.5). The purpose of this section is to link univariate linear models with multivariate linear models, which will later be linked to the $B R M$. The multivariate linear model was presented in Sect. $1.4$ and its MLEs were given by
\begin{aligned} \widehat{\boldsymbol{B}}o \boldsymbol{C} & =\boldsymbol{X}_o \boldsymbol{P}{C^{\prime}}, \ n \widehat{\boldsymbol{\Sigma}}o & =\boldsymbol{r}_o \boldsymbol{r}_o^{\prime}, \quad \boldsymbol{r}_o^{\prime}=\left(\boldsymbol{I}-\boldsymbol{P}{C^{\prime}}\right) \boldsymbol{X}_o^{\prime} . \end{aligned}
In comparison with univariate linear models, the only difference when estimating parameters is that instead of $\boldsymbol{x}^{\prime}: 1 \times n$, we have $\boldsymbol{X}: p \times n$. Thus, in some sense, from a mathematical point of view, the treatment of the univariate and multivariate models concerning estimation is the same. Indeed it would be mathematically more correct to say “linear multivariate model” instead of “multivariate linear model”. However, if one considers properties of the estimators, then differences appear. This is mainly due to the difference between the Wishart distribution and the $\chi^2$ distribution (see Appendix A, Sect. A.9, for definitions of the distributions). Moreover, from a practical point of view, since in the multivariate case one is dealing with several variables simultaneously, the data analysis also becomes more complicated. For example, dependencies among the variables have to be taken into account, which of course is not necessary in the univariate case. Obviously there are more questions which are to be considered in the multivariate model. The differences between the univariate linear and multivariate linear models are illustrated in Fig. 2.5.

It is worth noting that any multivariate linear model via a vectorization can be written as a univariate linear model. Consider the multivariate linear model
$$\boldsymbol{X}=\boldsymbol{B} \boldsymbol{C}+\boldsymbol{E}, \quad \boldsymbol{E} \sim N_{p, n}(\mathbf{0}, \boldsymbol{\Sigma}, \boldsymbol{I}), \quad \boldsymbol{\Sigma}>0,$$
which can also be written as follows:
$$\operatorname{vec} \boldsymbol{X}=\left(\boldsymbol{C}^{\prime} \otimes \boldsymbol{I}\right) \operatorname{vec} \boldsymbol{B}+\boldsymbol{e}, \quad \boldsymbol{e} \sim N_{p n}(\mathbf{0}, \boldsymbol{I} \otimes \boldsymbol{\Sigma}), \quad \boldsymbol{\Sigma}>0 .$$
However, stating that any one of the representations given above has some general advantages does not make sense from a statistical point of view. Finally, it is noted that a general inference strategy in multivariate analysis is to take an arbitrary linear combination of $\boldsymbol{X}$, let us say $\boldsymbol{I}^{\prime} \boldsymbol{X}$, leading to a univariate model, and then to try to choose in some sense the best $l$ (e.g. see Rao, 1973, Chapter 8).

# 回归分析代写

## 统计代写|回归分析作业代写Regression Analysis代考|Linear Models with a Focus on the Singular Gauss-Markov Model

$$\boldsymbol{x}^{\prime}=\boldsymbol{\beta}^{\prime} \boldsymbol{C}+\boldsymbol{e}^{\prime}, \quad \boldsymbol{e} \sim N_n\left(\mathbf{0}, \sigma^2 \boldsymbol{I}\right) .$$

$$\mathcal{R}^n=\mathcal{C}\left(\boldsymbol{C}^{\prime}\right) \boxplus \mathcal{C}\left(\boldsymbol{C}^{\prime}\right)^{\perp},$$

$$\beta^{\prime} \boldsymbol{G}=\mathbf{0}$$

$$\widehat{\boldsymbol{\beta}}^{\prime} \boldsymbol{C}=\boldsymbol{x}^{\prime} \boldsymbol{C}^{\prime} \boldsymbol{G}^o\left(\boldsymbol{G}^{o^{\prime}} \boldsymbol{C} \boldsymbol{C}^{\prime} \boldsymbol{G}^o\right)^{-} \boldsymbol{G}^{o^{\prime}} \boldsymbol{C}=\boldsymbol{x}^{\prime} \boldsymbol{P} C^{\prime} G^a$$

## 统计代写|回归分析作业代写Regression Analysis代考|Multivariate Linear Models

$$\widehat{\boldsymbol{B}} o \boldsymbol{C}=\boldsymbol{X}o \boldsymbol{P} C^{\prime}, n \widehat{\boldsymbol{\Sigma}} o \quad=\boldsymbol{r}_o \boldsymbol{r}_o^{\prime}, \quad \boldsymbol{r}_o^{\prime}=\left(\boldsymbol{I}-\boldsymbol{P} C^{\prime}\right) \boldsymbol{X}_o^{\prime} .$$ 与单变量线性模型相比，估计参数时的唯一区别是，而不是 $\boldsymbol{x}^{\prime}: 1 \times n$ ，我们有 $\boldsymbol{X}: p \times n$. 因此，从某 种意义上说，从数学的角度来看，单变量模型和多变量模型在估计方面的处理是相同的。实际上，说 线 性多元模型”而不是“多元线性模型”在数学上更正确。但是，如果考虑估计量的属性，就会出现差异。这主 要是由于 Wishart 分布和 $\chi^2$ 分布（有关分布的定义，请参阅附录 A，第 A.9 节) 。而且，从实际的角度 来看，由于在多变量情况下同时处理多个变量，数据分析也变得更加复杂。例如，必须考虑变量之间的依 赖关系，这在单变量情况下当然是不必要的。显然，多元模型需要考虑的问题更多。单变量线性模型和多 变量线性模型之间的差异如图 $2.5$ 所示。 值得注意的是，任何通过向量化的多元线性模型都可以写成单变量线性模型。考虑多元线性模型 $$\boldsymbol{X}=\boldsymbol{B} \boldsymbol{C}+\boldsymbol{E}, \quad \boldsymbol{E} \sim N{p, n}(\mathbf{0}, \mathbf{\Sigma}, \boldsymbol{I}), \quad \mathbf{\Sigma}>0,$$

$$\operatorname{vec} \boldsymbol{X}=\left(\boldsymbol{C}^{\prime} \otimes \boldsymbol{I}\right) \operatorname{vec} \boldsymbol{B}+\boldsymbol{e}, \quad \boldsymbol{e} \sim N_{p n}(\mathbf{0}, \boldsymbol{I} \otimes \mathbf{\Sigma}), \quad \boldsymbol{\Sigma}>0 .$$

## 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。

## 统计代写|回归分析作业代写Regression Analysis代考|STA4210

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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|How Strong of a Correlation is Considered Good

What is a good correlation? How high should it be? These are commonly asked questions. I have seen several schemes that attempt to classify correlations as strong, medium, and weak.

However, there is only one correct answer. The correlation coefficient should accurately reflect the strength of the relationship. Take a look at the correlation between the height and weight data, $0.705$. It’s not a very strong relationship, but it accurately represents our data.

An accurate representation is the best-case scenario for using a statistic to describe an entire dataset.

The strength of any relationship naturally depends on the specific pair of variables. Some research questions involve weaker relationships than other subject areas. Case in point, humans are hard to predict. Studies that assess relationships involving human behavior tend to have correlations weaker than $+/-0.6$.

However, if you analyze two variables in a physical process, and have very precise measurements, you might expect correlations near $+1$ or $-1$. There is no one-size fits all best answer for how strong a relationship should be. The correct correlation value depends on your study area. We run into this same issue in regression analysis.

## 统计代写|回归分析作业代写Regression Analysis代考|Common Themes with Regression

Understanding correlation is a good place to start learning regression. In fact, there are several themes that I touch upon in this section that show up throughout this book.

For instance, analysts naturally want to fit models that explain more and more of the variability in the data. And, they come up with classification schemes for how well the model fits the data. However, there is a natural amount of variability that the model can’t explain just as there was in the height and weight correlation example. Regression models can be forced to go past this natural boundary, but bad things happen. Throughout this book, be aware of the tension between trying to explain as much variability as possible and ensuring that you don’t go too far. This issue pops up multiple times!

Additionally, for regression analysis, you’ll need to use statistical measures in conjunction with graphs just like we did with correlation. This combination provides you the best understanding of your data and the analytical results.

Wouldn’t it be nice if instead of just describing the strength of the relationship between height and weight, we could define the relationship itself using an equation? Regression analysis does just that by finding the line and corresponding equation that provides the best fit to our dataset. We can use that equation to understand how much weight increases with each additional unit of height and to make predictions for specific heights.

Regression analysis allows us to expand on correlation in other ways. If we have more variables that explain changes in weight, we can include them in the model and potentially improve our predictions. And, if the relationship is curved, we can still fit a regression model to the data.

Additionally, a form of the Pearson correlation coefficient shows up in regression analysis. R-squared is a primary measure of how well a regression model fits the data. This statistic represents the percentage of variation in one variable that other variables explain. For a pair of variables, R-squared is simply the square of the Pearson’s correlation coefficient. For example, squaring the height-weight correlation coefficient of $0.705$ produces an R-squared of $0.497$, or $49.7 \%$. In other words, height explains about half the variability of weight in preteen girls.

But we’re getting ahead of ourselves. I’ll cover R-squared in much more detail in both chapters 2 and 4.

# 回归分析代写

## 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。

## 统计代写|回归分析作业代写Regression Analysis代考|STAT2220

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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Hypothesis Test for Correlations

Correlations have a hypothesis test. As with any hypothesis test, this test takes sample data and evaluates two mutually exclusive statements about the population from which the sample was drawn. For Pearson correlations, the two hypotheses are the following:

• Null hypothesis: There is no linear relationship between the two variables. $\rho=0$.
• Alternative hypothesis: There is a linear relationship between the two variables. $\rho \neq 0$.

A correlation of zero indicates that no linear relationship exists. If your p-value is less than your significance level, the sample contains sufficient evidence to reject the null hypothesis and conclude that the correlation does not equal zero. In other words, the sample data support the notion that the relationship exists in the population.

Now that we have seen a range of positive and negative relationships, let’s see how our correlation of $0.705$ fits in. We know that it’s a positive relationship. As height increases, weight tends to increase. Regarding the strength of the relationship, the graph shows that it’s not a very strong relationship where the data points tightly hug a line. However, it’s not an entirely amorphous blob with a very low correlation. It’s somewhere in between. That description matches our moderate correlation of $0.705$.

For the hypothesis test, our p-value equals $0.000$. This p-value is less than any reasonable significance level. Consequently, we can reject the null hypothesis and conclude that the relationship is statistically significant. The sample data provide sufficient evidence to conclude that the relationship between height and weight exists in the population of preteen girls.

## 统计代写|回归分析作业代写Regression Analysis代考|Correlation Does Not Imply Causation

I’m sure you’ve heard this expression before, and it is a crucial warning. Correlation between two variables indicates that changes in one variable are associated with changes in the other variable. However, correlation does not mean that the changes in one variable actually cause the changes in the other variable.

Sometimes it is clear that there is a causal relationship. For the height and weight data, it makes sense that adding more vertical structure to a body causes the total mass to increase. Or, increasing the wattage of lightbulbs causes the light output to increase.

However, in other cases, a causal relationship is not possible. For example, ice cream sales and shark attacks are positively correlated. Clearly, selling more ice cream does not cause shark attacks (or vice versa). Instead, a third variable, outdoor temperatures, causes changes in the other two variables. Higher temperatures increase both sales of ice cream and the number of swimmers in the ocean, which creates the apparent relationship between ice cream sales and shark attacks.
In statistics, you typically need to perform a randomized, controlled experiment to determine that a relationship is causal rather than merely correlation.

# 回归分析代写

## 统计代写|回归分析作业代写Regression Analysis代考|Hypothesis Test for Correlations

• 零假设：两个变量之间不存在线性关系。r=0.
• 备择假设：两个变量之间存在线性关系。r≠0.

## 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。

## 统计代写|回归分析作业代写Regression Analysis代考|STA321

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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Interpret the Pearson’s Correlation Coefficient

What do the correlation and p-value mean? We’ll interpret the output soon. First, let’s look at a range of possible correlation values so we can understand how our height and weight example fits in.

Pearson’s correlation coefficient is represented by the Greek letter rho ( $\rho$ ) for the population parameter and $r$ for a sample statistic. This coefficient is a single number that measures both the strength and direction of the linear relationship between two continuous variables. Values can range from $-1$ to $+1$.

• Strength: The greater the absolute value of the coefficient, the stronger the relationship.
• The extreme values of $-1$ and 1 indicate a perfectly linear relationship where a change in one variable is accompanied by a perfectly consistent change in the other. For these relationships, all of the data points fall on a line. In practice, you won’t see either type of perfect relationship. A coefficient of zero represents no linear relationship. As one variable increases, there is no tendency in the other variable to either increase or decrease.
• When the value is in-between 0 and $+1 /-1$, there is a relationship, but the points don’t all fall on a line. As $r$

approaches $-1$ or 1 , the strength of the relationship increases and the data points tend to fall closer to a line.

• Direction: The coefficient sign represents the direction of the relationship.
• Positive coefficients indicate that when the value of one variable increases, the value of the other variable also tends to increase. Positive relationships produce an upward slope on a scatterplot.
• Negative coefficients represent cases when the value of one variable increases, the value of the other variable tends to decrease. Negative relationships produce a downward slope.
Examples of Positive and Negative Correlations
An example of a positive correlation is the relationship between the speed of a wind turbine and the amount of energy it produces. As the turbine speed increases, electricity production also increases.

An example of a negative correlation is the relationship between outdoor temperature and heating costs. As the temperature increases, heating costs decrease.

## 统计代写|回归分析作业代写Regression Analysis代考|Discussion about the Correlation Scatterplots

For the scatterplots above, I created one positive relationship between the variables and one negative relationship between the variables. Then, I varied only the amount of dispersion between the data points and the line that defines the relationship. That process illustrates how correlation measures the strength of the relationship. The stronger the relationship, the closer the data points fall to the line. I didn’t include plots for weaker correlations that are closer to zero than $0.6$ and $-0.6$ because they start to look like blobs of dots and it’s hard to see the relationship.

A common misinterpretation is that a negative correlation coefficient indicates there is no relationship between a pair of variables. After all, a negative correlation sounds suspiciously like no relationship. However, the scatterplots for the negative correlations display real relationships. For negative relationships, high values of one variable are associated with low values of another variable. For example, there is a negative correlation between school absences and grades. As the number of absences increases, the grades decrease.

Earlier I mentioned how crucial it is to graph your data to understand them better. However, a quantitative assessment of the relationship does have an advantage. Graphs are a great way to visualize the data, but the scaling can exaggerate or weaken the appearance of a relationship. Additionally, the automatic scaling in most statistical software tends to make all data look similar.

Fortunately, Pearson’s correlation coefficient is unaffected by scaling issues. Consequently, a statistical assessment is better for determining the precise strength of the relationship.

Graphs and the relevant statistical measures often work better in tandem.

## 统计代写|回归分析作业代写Regression Analysis代考|Interpret the Pearson’s Correlation Coefficient

• 强度：系数的绝对值越大，关系越强。
• 的极值−1和 1 表示完全线性关系，其中一个变量的变化伴随着另一个变量的完全一致的变化。对于这些关系，所有数据点都落在一条线上。实际上，您不会看到任何一种完美关系。系数为零表示没有线性关系。当一个变量增加时，另一个变量没有增加或减少的趋势。
• 当值介于 0 和+1/−1，有关系，但点并不都落在一条线上。作为r

• 方向：系数符号代表关系的方向。
• 正系数表示当一个变量的值增加时，另一个变量的值也有增加的趋势。正相关在散点图上产生向上的斜率。
• 负系数表示当一个变量的值增加时，另一个变量的值趋于减小的情况。负面关系产生向下的斜率。
正相关和负相关
的示例 正相关的示例是风力涡轮机的速度与其产生的能量之间的关系。随着涡轮速度的增加，发电量也增加。

## 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。

## 统计代写|回归分析作业代写Regression Analysis代考|STAT5110

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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|One-sided hypothesis tests

While most tests on statistical significance are based on two-sided tests, the more appropriate test may be one-sided. This should be used when it is clear, theoretically, that an $\mathrm{X}$ variable could affect the outcome only in one direction. For example, we can be pretty certain that, on average and holding all the other factors constant, Blacks will get paid less than Whites and older people would be paid more than younger people at least for the age range of our data ( 38 to 46). Thus, we can form a hypothesis test on whether the coefficient on the variable, black, is negative and that on the variable, ageyears, is positive. Making the test one-sided makes it easier to reject the null hypothesis (which may not be a good thing).
For ageyears, the hypotheses would be:

• $\quad \mathrm{H}_0: \beta_i \leq 0$.
• $\quad \mathrm{H}_1: \beta_i>0$.
In contrast with the procedures for the two-sided test in Figure 5.3, the rejection region for this onesided test will be entirely in the right tail of the $t$-distribution. To find the critical value that defines the rejection region for a hypothesis test, based on having a 5\% significance level, in Excel:
• Use the command T.INV (one-tail test) – this is a left-tail test, so you may have to reverse the sign.
• Plug in $0.05$ for a $5 \%$ level of significance (or $0.01$ for a hypothesis test based on a $1 \%$ level of significance).
• Plug in “degrees of freedom” $=2762$.
• It should give you $t_f=-1.6454$.
• Reverse the sign to $t_c=1.6454$, since it is a right-tailed test and the $t$-distribution is symmetric.
You would then compare the $t$-stat on the coefficient estimate on the variable, ageyears, with that critical value of 1.6454. The graphical representation of this test is Figure 5.4. The $t$-stat on ageyears is $1.95$ (from Tables $5.1$ and 5.2), so it now lies in the rejection region, and we can reject the null hypothesis that the true coefficient on ageyears is less than or equal to zero and accept the alternative hypothesis that age is positively related to income, holding the other factors constant.
• Pretty much all researchers (me included, including in the last sub-section) make the wrong official interpretation of two-sided tests. We would take, say the coefficient estimate and $t$-stat $(-3.13)$ on black from Tables $5.1$ and $5.2$ and conclude: “being Black is associated with significantly lower income than non-Hispanic Whites (the reference group).” But, the proper interpretation is “being Black is associated with significantly different income from non-Hispanic Whites.”
• The reason why people make this incorrect interpretation and why it is okay is that, if it passes a two-sided test, then it would pass the one-sided test in its direction as well. This is because the rejection region for a one-sided test would be larger in the relevant direction than for a two-sided test. So, the two-sided test is, in fact, a stricter test.

## 统计代写|回归分析作业代写Regression Analysis代考|Confidence intervals

Confidence intervals indicate the interval which you can be fairly “confident” that the value of the true coefficient lies in. Assuming that the sample is randomly drawn from the population of interest, a 95\% confidence interval (the standard percentage) is the one in which you can be $95 \%$ confident that the true coefficient estimate lies in that interval. This does not mean that we can be $95 \%$ confident that the true causal effect lies in that interval, as this requires that the coefficient estimate is unbiased as an estimate of the causal effect.

The formula for a confidence interval for the true population value of a coefficient, $\beta$, in a given model is:
$$\hat{\beta} \pm t_c \times \operatorname{SE}(\hat{\beta}) \text { or }\left[\hat{\beta}-t_c \times \operatorname{SE}(\hat{\beta}), \hat{\beta}+t_c \times \operatorname{SE}(\hat{\beta})\right]$$
where

• $\alpha=$ the significance level;
• $t_c=$ the critical value from the Student’s t-distribution giving $\alpha / 2$ in each tail, based on degrees of freedom $=n-K-1$ ( $n=$ # observations; $K=$ # explanatory variables);
• $\mathrm{SE}(\hat{\beta})=$ standard error on the coefficient estimate for $\beta$.
This means that:
$$\operatorname{Pr}\left[\beta \text { is in }\left(\hat{\beta}-t_c \times \operatorname{SE}(\hat{\beta}), \hat{\beta}+t_c \times \operatorname{SE}(\hat{\beta})\right]=1-\alpha\right.$$
To determine the critical $t$ value, use the same method as outlined above (in Section 5.2.4). So, from Table 5.1, the $95 \%$ confidence interval for the coefficient estimate on ageyears would be:
$$752.8 \pm 1.9608 \times 386.2=(-4.4,1510.1)$$
Note that the interval includes zero. In fact there is a relationship between statistical significance (for two-sided hypothesis tests) and confidence intervals:
• $\quad$ Significant at the $5 \%$ level $(p<0.05)] \leftrightarrow[95 \%$ confidence interval does not include 0$]$
• $\quad$ Insignificant at the $5 \%$ level ( $p>0.05)] \leftrightarrow[95 \%$ confidence interval includes 0$]$
In Tables $5.1$ and $5.2$, the $95 \%$ confidence intervals for $e d u c$, afqt, and the other variables with estimates with $\mathrm{p}<0.05$ do not include zero.

## 统计代写|回归分析作业代写Regression Analysis代考|One-sided hypothesis tests

• $\mathrm{H}_0: \beta_i \leq 0$.
• $\mathrm{H}_1: \beta_i>0$.
与图 $5.3$ 中双侧测试的程序相反，此单侧测试的拒绝区域将完全位于右尾 $t$-分配。要根据 $5 \%$ 的显着 性水平在 Excel 中查找定义假设检验拒绝区域的临界值:
• 使用命令 T.INV (单尾测试) 一一这是一个左尾测试，因此您可能需要反转符号。
• 揷入 $0.05$ 为一个 $5 \%$ 显着性水平（或 $0.01$ 对于基于 $\mathrm{a}$ 的假设检验 $1 \%$ 显着性水平）。
• 揷入 “自由度” $=2762$.
• 它应该给你 $t_f=-1.6454$.
• 将符号反转为 $t_c=1.6454$ ，因为它是右尾测试，并且 $t$-分布是对称的。
然后你会比较 $t$-统计变量 ageyears 的系数估计值，临界值为 1.6454。该测试的图形表示如图 $5.4$ 所示。这 $t$-关于年龄的统计是 $1.95$ (来自表格 $5.1$ 和 5.2)，所以它现在位于拒绝域，我们可以拒绝 ageyears 的真实系数小于或等于零的原假设，并接受年龄与收入正相关的备择假设，同时保留其他 因素持续的。
• 几乎所有研究人员 (包括我在内，包括在最后一个小节中) 都对双侧测试做出了错误的官方解释。 我们会乎取，比如说系数估计和 $t$-统计 $(-3.13)$ 来自表的黑色 $5.1$ 和 $5.2$ 并得出结论： 与与非西班牙㾔 白人 (参照组) 相比，身为黑人的收入明显较低。”但是，正确的解释是“作为黑人与非西班牙鸼白 人的收入有很大不同”。
• 人们之所以会做出这种不正确的解释，为什么还可以，是因为如果它通过了一个双面的测试，那么 它在它的方向上也通过了一个单向的测试。这是因为单侧测试的拒绝区域在相关方向上比双侧测试 的更大。所以，双面测试实际上是一个更严格的测试。

## 统计代写|回归分析作业代写Regression Analysis代考|Confidence intervals

$$\hat{\beta} \pm t_c \times \mathrm{SE}(\hat{\beta}) \text { or }\left[\hat{\beta}-t_c \times \mathrm{SE}(\hat{\beta}), \hat{\beta}+t_c \times \mathrm{SE}(\hat{\beta})\right]$$

• $\alpha=$ 显着性水平；
• $t_c=$ 学生 $\mathrm{t}$ 分布给出的临界值 $\alpha / 2$ 在每条尾巴上，基于自由度 $=n-K-1(n=#$ 观察; $K=$ # 解释变量)；
• $\operatorname{SE}(\hat{\beta})=$ 系数估计的标准误差 $\beta$. 这意味着:
$$\operatorname{Pr}\left[\beta \text { is in }\left(\hat{\beta}-t_c \times \operatorname{SE}(\hat{\beta}), \hat{\beta}+t_c \times \operatorname{SE}(\hat{\beta})\right]=1-\alpha\right.$$
确定关键 $t$ 值，使用与上述相同的方法（在第 5.2.4 节中）。因此，从表 $5.1$ 中，95\%ageyears 系 数估计的置信区间为:
$$752.8 \pm 1.9608 \times 386.2=(-4.4,1510.1)$$
请注意，区间包括零。事实上，统计显着性（对于双侧假设检验）和置信区间之间存在关系：
• 显着于 $5 \%$ 等级 $(p<0.05)] \leftrightarrow[95 \%$ 置信区间不包括 0
• 微不足道的 $5 \%$ 等级 $(p>0.05)] \leftrightarrow[95 \%$ 置信区间包括 0 $]$
在表格中 $5.1$ 和 $5.2$ ，这 $95 \%$ 的置信区间 $e d u c$ 、afqt 和其他具有估计值的变量p $<0.05$ 不包括 零。

## 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。

## 统计代写|回归分析作业代写Regression Analysis代考|AH7722

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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Setting up the problem for hypothesis tests

Let’s say that you want to explore the theory that the anti-bullying campaigns that today’s teenagers are exposed to affect their empathy. In particular, you want to test whether current teenagers have a different level of empathy from the historical population of teenagers. Suppose you have a random sample of 25 teenagers. And, let’s say that there is a questionnaire with a multitude of questions that are combined to give a standardized score on empathy that has, in the historic population of teenagers, a normal distribution with a mean of 100 and a standard deviation of 15 . From your sample of current teenagers, let’s say that you find that their average empathy score is a little higher than the historical average, with an average of 104 . So, you want to conduct a hypothesis test to see whether there is evidence confirming the contention that current teenagers do indeed have a different level of empathy from the historical teenage average. (Note that I am initially testing for a different level and not a higher level of empathy. We will consider directional hypothesis testing later on.)

The test is really about how certain we can be to rule out randomness giving you the sample statistic that is different from 100 , the historical mean. Randomness pervades our life. Randomness in getting the right coach can dictate the difference between making it or not in professional sports. For a student growing up in poverty, randomness in the teacher she gets could determine academic and financial success in life. Randomness on questions you are guessing on when taking the SAT could determine whether you get into your desired college, which could change the course of your life. Randomness could mean the difference between life and death on the battlefield. And, randomness can determine who you marry.

In statistics, randomness in outcomes can affect the empirical relationships between variables. The more observations there are, randomness will tend to have a smaller role in those relationships, and we can better gauge whether any relationships observed are real (whether large, small, or zero). And,randomness dictates the sample that you get when you draw from a larger population. The higher mean level of empathy in the sample of current teenagers means that either:

• They do have the same mean empathy level as the historical population of teenagers, and it was random variation that caused this sample of 25 teenagers to have a mean level of empathy that is 4 points off from the population mean of 100 ; or
• Current teenagers indeed have a different mean empathy level from the historical population of teenagers.

## 统计代写|回归分析作业代写Regression Analysis代考|Standard errors

Let’s consider the case with several explanatory variables from the income model we have been working with. Tables $5.1$ and $5.2$ show the results of a model with a dependent variable of 2003 income, as reported in the 2004 survey, using the original data set income_data. Table $5.1$ shows the output from Stata, while Table $5.2$ shows the $\mathrm{R}$ output. Note that there are differences in the output that is produced, with Stata giving a more complete picture (in my mind).

From Table 5.1, the top panels have overall regression statistics – the top-left three numbers (under SS) are ExSS, RSS, and TSS. The $R^2$, in the top-right panel, is $0.210$. In the bottom panel of the table, the variables used in the model are listed. The variable definitions are:

• income (the dependent variable) $=$ the person’s income in 2003;
• $\quad e d u c=$ years-of-schooling completed;
• $\quad a f q t=\mathrm{AFQT}$ percentile;
• agcycars – age in 2003;
• black $=1$ if the respondent is Black; $=0$ otherwise;
• hisp $=1$ if the respondent is Hispanic; $=0$ otherwise;
• mom_hs $=1$ if the respondent’s mother completed at least 12 years-of-schooling; $=0$ otherwise;
• dad_hs $=1$ if the respondent’s father completed at least 12 years-of-schooling; $=0$ otherwise;
• dad_coll $=1$ if the respondent’s father completed at least 16 years-of-schooling; $=0$ otherwise.
Note that the variables for highest-grade-completed of the mother was missing for 808 respondents (6.4\% of the initial 12,686 respondents), and the highest-grade-completed of the father was missing for 1806 respondents (14.2\%). For the sake of keeping the observations for this exercise, I did the technically incorrect thing of merely giving these observations 11 years-of-schooling (meaning, they would have a 0 for the educational variables of having a high school diploma or college degree). In Section $12.2$, I discuss a better option for dealing with missing data.

## 统计代写|回归分析作业代写Regression Analysis代考|Setting up the problem for hypothesis tests

• 他们确实与历史上的青少年人口具有相同的平均同理心水平，正是随机变化导致这 25 名青少年的平均同理心水平比人口平均值 100 低 4 个点；或者
• 当前的青少年确实与历史上的青少年群体具有不同的平均同理心水平。

## 统计代写|回归分析作业代写Regression Analysis代考|Standard errors

• 收入（因变量）=该人 2003 年的收入；
• 和d在C=完成学业年限；
• 一个Fq吨=一个F问吨百分位数；
• agcycars——2003 年的年龄；
• 黑色的=1如果受访者是黑人；=0否则;
• 他的=1如果受访者是西班牙裔；=0否则;
• 妈妈_hs=1如果受访者的母亲完成了至少 12 年的学校教育；=0否则;
• 爸爸_hs=1如果受访者的父亲完成了至少 12 年的学校教育；=0否则;
• 爸爸_coll=1如果受访者的父亲完成了至少 16 年的学校教育；=0否则。
请注意，808 名受访者（最初 12,686 名受访者中的 6.4%）缺少母亲完成最高年级的变量，1806 名受访者（14.2%）缺少父亲完成最高年级的变量。为了保留这个练习的观察结果，我做了技术上不正确的事情，只给这些观察结果 11 年的学校教育（意思是，对于拥有高中文凭或大学学位的教育变量，它们的值为 0） . 在节12.2，我讨论了处理缺失数据的更好选择。

## 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。

## 统计代写|回归分析作业代写Regression Analysis代考|ST503

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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Case studies to understand “holding other factors constant”

Let’s say you want to test whether adding cinnamon to your chocolate-chip cookies makes them tastier. There are two simple methods to make a control and treatment group:
(A) Make two separate batches from scratch, one with cinnamon (the treatment batch) and one without cinnamon (the control batch).
(B) Make one batch, divide the batch in two, and add cinnamon to one (the treatment batch) and not the other (the control batch).
Which method is better? Why?
I would choose method B. When comparing the treatment to the control batch, we would want nothing else to be different between the two batches other than the inclusion of cinnamon. That is, we want to hold constant all other factors that could vary with whether cinnamon is added. In method A, when building two different batches from scratch, there might be slight variations in the amount of butter, sugar, chocolate, and other things that affect the taste of the cookies. In method B, since it comes from the same batch, the other ingredients, if mixed well, are in the same proportions, so they are being held constant. Thus, unless you are a well-experienced cookie maker and can get the ingredients nearly exactly the same in both batches (with method A), method B should be more reliable than method A because it does a better job at holding the other factors constant.

Let’s say that we are interested in determining how the amount of water affects the production from lemon trees. Consider these details:

• On Day 1, you plant 50 baby lemon trees that appear to be the same.
• Half are planted in the good-soil part of the yard.
• Half are planted in the bad-soil part of the yard.
• Upon planting the trees, you randomly assign each tree 1 of 10 different amounts of water that the tree is then given weekly for 5 years – each of the 10 water amounts will be given to 5 trees.
• Assume that trees are covered when it rains so that the only water they receive is what you give it.

## 统计代写|回归分析作业代写Regression Analysis代考|Using behind-the-curtains scenes

Figures $4.3 \mathrm{a}$ and $4.3 \mathrm{~b}$ provide a flow chart to demonstrate a different approach to understanding “holding other factors constant” (and to demonstrate what a coefficient estimate represents). In Figure 4.3a, we start in the box at the top right, marked with as Box A. This is a Simple Regression Model, regressing income on educ (a simpler variable name for years-of-schooling). The question is, “What does the estimate on $\operatorname{educ}\left(\beta_1\right)$ capture?”

In the box marked $\mathrm{B}, \mathrm{I}$ list four things that tend to move with one additional year of schooling. That is, if we were to compare people with, say, 14 years-of-schooling (two years of college) to those with 13 years-of-schooling, we would expect to see these four factors, on average, to be different for the two sets of people. Let’s assume for the sake of the story here that this is a complete list of things that tend to change with an additional year of schooling, even though we know that there are other factors we’ve discussed earlier. The variables for these four factors are $Z_1$ to $Z_4$, and we will say that the average changes in factors $Z_1$ to $Z_4$ associated with one more year of schooling are, correspondingly, values $a_1$ to $a_4$. So, the $Z$ ‘s are variables, and the a’s are changes in the value of the $Z$ variables.

Note that the list of factors that move with an additional year of schooling includes both things that result from more schooling (greater workplace skills and more network connections) and factors that preceded a person’s education (innate intelligence and motivation)

All four of these factors that are associated with years-of-schooling probably have some effect on income, and we will say that if we had a model estimating the simultaneous effects of these factors $\left(Z_1\right.$ to $Z_4$ ) on income (as in Box C), we would obtain coefficients $\delta_1$ to $\delta_4$, which are also shown in the arrows (marked by the circled C) from the four factors in Box B to income. I call this a “notional model” in Box C because it is going on behind the curtains and probably cannot be estimated given that most of the factors are unobservable/non-quantifiable.
(As with the domino example, and elsewhere in the book, think of the arrows as the effect of a one-unit increase in one variable on the variable it is pointing to. If multiple arrows are going towards one variable, then it is the causal effect of one variable, holding the other variables constant.)
We now can see how $\beta$ is determined. In Box D,
$$\begin{array}{r} \beta_1=a_1 \delta_1+a_2 \delta_2+a_3 \delta_3+a_4 \delta_4 \ \text { M1 } \quad \text { M2 } \text { M3 M M4 } \end{array}$$

## 统计代写|回归分析作业代写Regression Analysis代考|Case studies to understand “holding other factors constant”

(A) 从头开始​​制作两个单独的批次，一批有肉桂（治疗批次），另一批没有肉桂（控制批次）。
(B) 制作一批，将这批分成两批，将肉桂添加到一批（处理批）中，而不是另一批（控制批）。

• 在第 1 天，您种植了 50 棵看起来相同的小柠檬树。
• 一半种植在院子里的好土部分。
• 一半种植在院子里的坏土部分。
• 种植树木后，您随机为每棵树分配 10 种不同水量中的 1 种，然后每周为这棵树提供 5 年——这 10 种水量中的每一种将提供给 5 棵树。
• 假设下雨时树木被遮盖，那么它们唯一吸收的水就是您给它的水。

## 统计代写|回归分析作业代写Regression Analysis代考|Using behind-the-curtains scenes

（与多米诺骨牌示例以及本书其他地方一样，将箭头视为一个变量增加一个单位对其指向的变量的影响。如果多个箭头指向一个变量，则它是一个变量的因果效应，保持其他变量不变。）

b1=一个1d1+一个2d2+一个3d3+一个4d4  M1  M2  M3 M M4

## 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。

## 统计代写|线性回归分析代写linear regression analysis代考|STA4210

statistics-lab™ 为您的留学生涯保驾护航 在代写线性回归分析linear 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。我们的专家在代写线性回归分析linear regression analysis代写方面经验极为丰富，各种代写线性回归分析linear 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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|线性回归分析代写linear regression analysis代考|MEAN AND VARIANCE OF QUADRATIC FORMS

Quadratic forms play a major role in this book. In particular, we will frequently need to find the expected value of a quadratic form using the following theorem.

THEOREM 1.5 Let $\mathbf{X}=\left(X_i\right)$ be an $n \times 1$ vector of random variables, and let $\mathbf{A}$ be an $n \times n$ symmetric matrix. If $E[\mathbf{X}]=\boldsymbol{\mu}$ and $\operatorname{Var}[\mathbf{X}]=\mathbf{\Sigma}=\left(\sigma_{i j}\right)$, then
$$E\left[\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right]=\operatorname{tr}(\mathbf{A} \Sigma)+\mu^{\prime} \mathbf{A} \boldsymbol{\mu}$$
Proof.
\begin{aligned} E\left[\mathbf{X}^{\prime} \mathbf{A X}\right] &=\operatorname{tr}\left(E\left[\mathbf{X}^{\prime} \mathbf{A X}\right]\right) \ &=E\left[\operatorname{tr}\left(\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right)\right] \ &=E\left[\operatorname{tr}\left(\mathbf{A} \mathbf{X} \mathbf{X}^{\prime}\right)\right] \quad \text { [by A.1.2] } \ &=\operatorname{tr}\left(E\left[\mathbf{A X} \mathbf{X}^{\prime}\right]\right) \ &=\operatorname{tr}\left(\mathbf{A} E\left[\mathbf{X} \mathbf{X}^{\prime}\right]\right) \ &=\operatorname{tr}\left[\mathbf{A}\left(\operatorname{Var}[\mathbf{X}]+\mu \boldsymbol{\mu}^{\prime}\right)\right] \quad[\text { by }(1.5)] \ &=\operatorname{tr}(\mathbf{A} \mathbf{\Sigma})+\operatorname{tr}\left(\mathbf{\Lambda} \mu \boldsymbol{\mu}^{\prime}\right) \ &=\operatorname{tr}(\mathbf{A} \mathbf{\Sigma})+\boldsymbol{\mu}^{\prime} \mathbf{A} \boldsymbol{\mu} \quad[\text { by A.1.2] } \end{aligned}
We can deduce two special cases. First, by setting $\mathbf{Y}=\mathbf{X}-\mathbf{b}$ and noting that $\operatorname{Var}[\mathbf{Y}]=\operatorname{Var}[\mathbf{X}]$ (by Example 1.4), we have
$$E\left[(\mathbf{X}-\mathbf{b})^{\prime} \mathbf{A}(\mathbf{X}-\mathbf{b})\right]=\operatorname{tr}(\mathbf{A} \mathbf{\Sigma})+(\boldsymbol{\mu}-\mathbf{b})^{\prime} \mathbf{A}(\boldsymbol{\mu}-\mathbf{b})$$

Second, if $\boldsymbol{\Sigma}=\sigma^2 \mathbf{I}n$ (a common situation in this book), then $\operatorname{tr}(\mathbf{A} \boldsymbol{\Sigma})=$ $\sigma^2 \operatorname{tr}(\mathbf{A})$. Thus in this case we have the simple rule $$\left.E\left[\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right]=\sigma^2 \text { (sum of coefficients of } X_i^2\right)+\left(\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right){\mathbf{X}=\mu} \text {. }$$
EXAMPLE $1.8$ If $X_1, X_2, \ldots, X_n$ are independently and identically distributed with mean $\mu$ and variance $\sigma^2$, then we can use equation (1.12) to find the expected value of
$$Q=\left(X_1-X_2\right)^2+\left(X_2-X_3\right)^2+\cdots+\left(X_{n-1}-X_n\right)^2 .$$
To do so, we first write
$$Q=\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}=2 \sum_{i=1}^n X_i^2-X_1^2-X_n^2-2 \sum_{i=1}^{n-1} X_i X_{i+1} .$$

## 统计代写|线性回归分析代写linear regression analysis代考|MOMENT GENERATING FUNCTIONS AND INDEPENDENCE

If $\mathbf{X}$ and $\mathbf{t}$ are $n \times 1$ vectors of random variables and constants, respectively, then the moment generating function (m.g.f.) of $\mathbf{X}$ is defined to be
$$M_{\mathbf{X}}(\mathrm{t})=E\left[\exp \left(\mathrm{t}^{\prime} \mathbf{X}\right)\right] .$$
A key result about m.g.f.’s is that if $M_{\mathbf{x}}(\mathbf{t})$ exists for all $|\mathbf{t}| \leq t_0\left(t_0>0\right)$ (i.e., in an interval containing the origin), then it determines the distribution uniquely. Fortunately, most of the common distributions have m.g.f.’s, one important exception being the $t$-distribution (with some of its moments being infinite, including the Cauchy distribution with 1 degree of freedom). We give an example where this uniqueness is usefully exploited. It is assumed that the reader is familiar with the m.g.f. of $\chi_r^2$ : namely, $(1-2 t)^{-r / 2}$.

EXAMPLE $1.10$ Suppose that $Q_i \sim \chi_{r_i}^2$ for $i=1,2$, and $Q=Q_1-Q_2$ is statistically independent of $Q_2$. We now show that $Q \sim \chi_r^2$, where $r=r_1-r_2$. Writing
\begin{aligned} (1-2 t)^{-r_1 / 2} &=E\left[\exp \left(t Q_1\right)\right] \ &=E\left[\exp \left(t Q+t Q_2\right)\right] \ &=E[\exp (t Q)] E\left[\exp \left(t Q_2\right)\right] \ &=E[\exp (t Q)](1-2 t)^{-1 / 2}, \end{aligned}
we have
$$E[\exp (t Q)]=(1-2 t)^{-\left(r_1-r_2\right) / 2}$$
which is the m.g.f. of $\chi_r^2$.
Moment generating functions also provide a convenient method for proving results about statistical independence. For example, if $M_{\mathbf{X}}(\mathrm{t})$ exists and
$$M_{\mathbf{X}}(\mathrm{t})=M_{\mathbf{X}}\left(t_1, \ldots, t_r, 0, \ldots, 0\right) M_{\mathbf{x}}\left(0, \ldots, 0, t_{r+1}, \ldots, t_n\right)$$ then $\mathbf{X}1=\left(X_1, \ldots, X_r\right)^{\prime}$ and $\mathbf{X}_2=\left(X{r+1}, \ldots, X_n\right)^{\prime}$ are statistically independent. An equivalent result is that $\mathbf{X}1$ and $\mathbf{X}_2$ are independent if and only if we have the factorization $$M{\mathbf{X}}(t)=a\left(t_1, \ldots, t_r\right) b\left(t_{r+1}, \ldots, t_n\right)$$
for some functions $a(\cdot)$ and $b(\cdot)$.

## 统计代写|线性回归分析代写linear regression analysis代考|MEAN AND VARIANCE OF QUADRATIC FORMS

$$E\left[\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right]=\operatorname{tr}(\mathbf{A} \Sigma)+\mu^{\prime} \mathbf{A} \boldsymbol{\mu}$$

$$\left.E\left[\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right]=\operatorname{tr}\left(E\left[\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right]\right) \quad=E\left[\operatorname{tr}\left(\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right)\right]=E\left[\operatorname{tr}\left(\mathbf{A} \mathbf{X} \mathbf{X}^{\prime}\right)\right] \quad \text { [by A.1.2 }\right] \quad=\operatorname{tr}(E[\mathbf{A}$$

$$E\left[(\mathbf{X}-\mathbf{b})^{\prime} \mathbf{A}(\mathbf{X}-\mathbf{b})\right]=\operatorname{tr}(\mathbf{A} \boldsymbol{\Sigma})+(\boldsymbol{\mu}-\mathbf{b})^{\prime} \mathbf{A}(\boldsymbol{\mu}-\mathbf{b})$$

$$E\left[\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right]=\sigma^2\left(\text { sum of coefficients of } X_i^2\right)+\left(\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}\right) \mathbf{X}=\mu .$$

$$Q=\left(X_1-X_2\right)^2+\left(X_2-X_3\right)^2+\cdots+\left(X_{n-1}-X_n\right)^2 .$$

$$Q=\mathbf{X}^{\prime} \mathbf{A} \mathbf{X}=2 \sum_{i=1}^n X_i^2-X_1^2-X_n^2-2 \sum_{i=1}^{n-1} X_i X_{i+1}$$

## 统计代写|线性回归分析代写linear regression analysis代考|MOMENT GENERATING FUNCTIONS AND INDEPENDENCE

$$M_{\mathbf{X}}(\mathrm{t})=E\left[\exp \left(\mathrm{t}^{\prime} \mathbf{X}\right)\right] .$$

$$(1-2 t)^{-r_1 / 2}=E\left[\exp \left(t Q_1\right)\right] \quad=E\left[\exp \left(t Q+t Q_2\right)\right]=E[\exp (t Q)] E\left[\exp \left(t Q_2\right)\right] \quad=E[\exp$$

$$E[\exp (t Q)]=(1-2 t)^{-\left(r_1-r_2\right) / 2}$$

$$M_{\mathbf{X}}(\mathrm{t})=M_{\mathbf{X}}\left(t_1, \ldots, t_r, 0, \ldots, 0\right) M_{\mathbf{x}}\left(0, \ldots, 0, t_{r+1}, \ldots, t_n\right)$$

## 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。

## 统计代写|线性回归分析代写linear regression analysis代考|STAT2220

statistics-lab™ 为您的留学生涯保驾护航 在代写线性回归分析linear 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。我们的专家在代写线性回归分析linear regression analysis代写方面经验极为丰富，各种代写线性回归分析linear 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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|线性回归分析代写linear regression analysis代考|LINEAR REGRESSION MODELS

If we denote the response variable by $Y$ and the explanatory variables by $X_1, X_2, \ldots, X_K$, then a general model relating these variables is
$$E\left[Y \mid X_1=x_1, X_2=x_2, \ldots, X_K=x_K\right]=\phi\left(x_1, x_2, \ldots, x_K\right)$$
although, for brevity, we will usually drop the conditioning part and write $E[Y]$. In this book we direct our attention to the important class of linear models, that is,
$$\phi\left(x_1, x_2, \ldots, x_K\right)=\beta_0+\beta_1 x_1+\cdots+\beta_K x_K,$$
which is linear in the parameters $\beta_j$. This restriction to linearity is not as restrictive as one might think. For example, many functions of several variables are approximately linear over sufficiently small regions, or they may be made linear by a suitable transformation. Using logarithms for the gravitational model, we get the straight line
$$\log F=\log \alpha-\beta \log d .$$
For the linear model, the $x_i$ could be functions of other variables $z$, $w$, etc.; for example, $x_1=\sin z, x_2=\log w$, and $x_3=z w$. We can also have $x_i=x^i$, which leads to a polynomial model; the linearity refers to the parameters, not the variables. Note that “categorical” models can be included under our umbrella by using dummy (indicator) $x$-variables. For example, suppose that we wish to compare the means of two populations, say, $\mu_i=E\leftU_i\right$. Then we can combine the data into the single model
\begin{aligned} E[Y] &=\mu_1+\left(\mu_2-\mu_1\right) x \ &=\beta_0+\beta_1 x \end{aligned}
where $x=0$ when $Y$ is a $U_1$ observation and $x=1$ when $Y$ is a $U_2$ observation. Here $\mu_1=\beta_0$ and $\mu_2=\beta_0+\beta_1$, the difference being $\beta_1$. We can extend this idea to the case of comparing $m$ means using $m-1$ dummy variables.

## 统计代写|线性回归分析代写linear regression analysis代考|EXPECTATION AND COVARIANCE OPERATORS

In this book we focus on vectors and matrices, so we first need to generalize the ideas of expectation, covariance, and variance, which we do in this section.
Let $Z_{i j}(i=1,2, \ldots, m ; j=1,2, \ldots, n)$ be a set of random variables with expected values $E\left[Z_{i j}\right]$. Expressing both the random variables and their expectations in matrix form, we can define the general expectation operator of the matrix $\mathbf{Z}=\left(Z_{i j}\right)$ as follows:
Definition $1.1$
$$E[\mathbf{Z}]=\left(E\left[Z_{i j}\right]\right) .$$
THEOREM 1.1 If $\mathbf{A}=\left(a_{i j}\right), \mathbf{B}=\left(b_{i j}\right)$, and $\mathbf{C}=\left(c_{i j}\right)$ are $l \times m, n \times p$, and $l \times p$ matrices, respectively, of constants, then
$$E[\mathbf{A Z B}+\mathbf{C}]=\mathbf{A} E[\mathbf{Z}] \mathbf{B}+\mathbf{C} .$$
Proof. Let $\mathbf{W}=\mathbf{A Z B}+\mathbf{C}$; then $W_{i j}=\sum_{r=1}^m \sum_{s=1}^n a_{i r} Z_{r s} b_{s j}+c_{i j}$ and
\begin{aligned} E[\mathbf{A Z B}+\mathbf{C}] &=\left(E\left[W_{i j}\right]\right)=\left(\sum_r \sum_s a_{i r} E\left[Z_{r s}\right] b_{s j}+c_{i j}\right) \ &=\left((\mathbf{A E}[\mathbf{Z}] \mathbf{B}){i j}\right)+\left(c{i j}\right) \ &=\mathbf{A E}[\mathbf{Z}] \mathbf{B}+\mathbf{C} . \end{aligned}
In this proof we note that $l, m, n$, and $p$ are any positive integers, and the matrices of constants can take any values. For example, if $\mathbf{X}$ is an $m \times 1$ vector, then $E[\mathbf{A X}]=\mathbf{A} E[\mathbf{X}]$. Using similar algebra, we can prove that if $\mathbf{A}$ and $\mathbf{B}$ are $m \times n$ matrices of constants, and $\mathbf{X}$ and $\mathbf{Y}$ are $n \times 1$ vectors of random variables, then
$$E[\mathbf{A X}+\mathbf{B} \mathbf{Y}]=\mathbf{A} E[\mathbf{X}]+\mathbf{B} E[\mathbf{Y}]$$
In a similar manner we can generalize the notions of covariance and variance for vectors. If $\mathbf{X}$ and $\mathbf{Y}$ are $m \times 1$ and $n \times 1$ vectors of random variables, then we define the generalized covariance operator Cov as follows.

## 统计代写|线性回归分析代写linear regression analysis代考|LINEAR REGRESSION MODELS

$$E\left[Y \mid X_1=x_1, X_2=x_2, \ldots, X_K=x_K\right]=\phi\left(x_1, x_2, \ldots, x_K\right)$$

$$\phi\left(x_1, x_2, \ldots, x_K\right)=\beta_0+\beta_1 x_1+\cdots+\beta_K x_K,$$

$$\log F=\log \alpha-\beta \log d .$$

## 统计代写|线性回归分析代写linear regression analysis代考|EXPECTATION AND COVARIANCE OPERATORS

$$E[\mathbf{Z}]=\left(E\left[Z_{i j}\right]\right) .$$

$$E[\mathbf{A Z B}+\mathbf{C}]=\mathbf{A} E[\mathbf{Z}] \mathbf{B}+\mathbf{C} .$$

$$E[\mathbf{A Z B}+\mathbf{C}]=\left(E\left[W_{i j}\right]\right)=\left(\sum_r \sum_s a_{i r} E\left[Z_{r s}\right] b_{s j}+c_{i j}\right) \quad=((\mathbf{A E}[\mathbf{Z}] \mathbf{B}) i j)+(c i j)=\mathbf{A} \mathbf{E}$$

$$E[\mathbf{A X}+\mathbf{B Y}]=\mathbf{A} E[\mathbf{X}]+\mathbf{B} E[\mathbf{Y}]$$

## 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。