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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|The Assumptions of the Classical Regression Model

A definitive source for the definition of a statistical model is the article “What is a Statistical Model?” by Peter McCullagh (2002), who defines a statistical model as “… a set of probability distributions on the sample space …” Translating, a statistical model is simply an assumption that your sample data are produced randomly by a particular probabilistic process that lies in a prescribed set of possible probabilistic processes. This “prescribed set of possible probabilistic processes” is what is meant by a “statistical model.”

For a simple example, one often refers to the “normal model” in statistics. This model does not prescribe a particular normal distribution as the model for the DGP; instead, it states that the data are randomly generated from a particular normal distribution within the general class of $\mathrm{N}\left(\mu, \sigma^2\right)$ distributions.

There are several assumptions that you make when you analyze the data using regression models. The first and most important assumption is that the data are produced probabilistically, which is specifically stated as $Y \mid X=x \sim p(y \mid x)$. Different types of regression models then make further assumptions regarding the prescribed sets of distributions, and regarding the prescribed way that these distributions are related to $x$. The assumptions are important because they determine the adequacy of the model.

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

Statistical models, including regression models, are statements about how the potentially observable data are produced, in general. They are quantifications of your subject matter theory. If you are writing a research paper in a scientific discipline, you will typically explain all this theory in words that state how and why such generalities occur. Your statistical model is simply a concise, mathematical and probabilistic summary of all that general theory. Your research hypotheses, which are also statements about how your data will appear (or might have appeared), are also defined in terms of your statistical model for your data-generating process.

Usually, you do not see any “randomness” assumption explicitly stated in research articles or other texts. Instead, the assumption is implicit, which you will often see stated in a model form such as
$$Y=\beta_0+\beta_1 X+\varepsilon$$
Implicit in that model formulation is that $\varepsilon$ is random. This assumption is necessary because the data $Y$ are not a deterministic function of $X$. If your relationships are in fact deterministic, then stop reading this book immediately! You should read a book on differential equations instead.

Anticipating multiple regression, where there is one or more $X$ variables, we introduce the boldface term $X$ to denote a set of possible $X$ variables: $X=\left(X_1, X_2, \ldots, X_k\right)$.

It may be the case that $Y$ is independent of $X$, in which case $Y \mid X=x \sim p(y)$, a distribution that is the same, no matter what is $x$. This violates no assumption of the regression model. In fact, many research hypotheses involve a question as to whether $Y$ is related to $X$ at all; these hypotheses are evaluated by estimating both the unrestricted model $Y \mid X=x \sim p(y \mid x)$ and the restricted model $Y \mid X=x \sim p(y)$, and then by comparing the results.

Note that the randomness assumption by itself makes no assumption about distributions (Poisson, normal, lognormal, or otherwise); and it makes no assumptions about the functional relationships between $Y$ and $X$ (linear, quadratic, logarithmic, or otherwise). As such, the model is a valid and correct model: Statistical data really do look as if generated from distributions, simply because they exhibit variability.

Also, notice that there is no assumption here concerning how the $\boldsymbol{X}$ data are generated, or even that they are random at all. We will generally assume the $X$ data are random, and as mentioned above, the randomness of $X$ is sometimes important, as is discussed in later chapters.

# 回归分析代写

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## 统计代写|回归分析作业代写回归分析代考|随机性

$$Y=\beta_0+\beta_1 X+\varepsilon$$

## 有限元方法代写

assignmentutor™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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师