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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 Gauss-Markov Model and Theorem

While the OLS estimates are best under the assumptions of the classical regression model, including, in particular, the assumption of normality, the OLS estimates still have a good mathematical property when you drop the normality assumption. The Gauss-Markov theorem states that if the data come from the classical regression model, minus the normality assumption, then these estimates are still “good,” in a certain sense.

To be more precise, recall the classical regression model, stated here in terms of simple regression:
$$Y_{i} \mid X_{i}=x_{i} \sim \text { independent } \mathrm{N}\left(\beta_{0}+\beta_{1} x_{i}, \sigma^{2}\right) \text {, for } i=1,2, \ldots, n$$
It is common to write the observable $Y_{i} \mid X_{i}=x_{i}$ as follows:
$$Y_{i}=\beta_{0}+\beta_{1} x_{i}+\left{Y_{i}-\left(\beta_{0}+\beta_{1} x_{i}\right)\right}$$
or as
$$Y_{i}=\beta_{0}+\beta_{1} x_{i}+\varepsilon_{i}$$
where $\varepsilon_{i}=Y_{i}-\left(\beta_{0}+\beta_{1} x_{i}\right)$ is the deviation from the $Y$ value to the conditional mean for observation $i$. These $\varepsilon_{i}$ terms are called “errors,” as noted above, or more specifically as “true errors,” because they involve vertical deviations from the true regression line. Note that the true errors are not observable in practice, because you do not know the true $\beta^{\prime}$ ‘s.
The classical regression model
$$Y_{i} \mid X_{i}=x_{i} \sim_{\text {independent }} \mathrm{N}\left(\beta_{0}+\beta_{1} x_{i}, \sigma^{2}\right) \text {, for } i=1,2, \ldots, n$$
is equivalent to the model
$$Y_{i}=\beta_{0}+\beta_{1} X_{i}+\varepsilon_{i}$$
under the assumptions that
(i) $\mathrm{E}\left(Y_{i} \mid X_{i}=x_{i}\right)=\beta_{0}+\beta_{1} x_{i}$, and (ii) $\varepsilon_{i} \sim \sim_{\text {iid }} \mathrm{N}\left(0, \sigma^{2}\right)$

## 统计代写|回归分析作业代写Regression Analysis代考|The Classical Model and Its Consequences

The classical regression model assumes normality, independence, constant variance, and linearity of the conditional mean function, and is (once again) stated as follows:
$$Y_{i} \mid X_{i}=x_{i} \quad \sim_{\text {independent }} \mathrm{N}\left(\beta_{0}+\beta_{1} x_{i}, \sigma^{2}\right) \text {, for } i=1,2, \ldots, n \text {. }$$
Whether you like it or not, this model is also what your computer assumes when you ask it to analyze your data via standard regression methods. The parameter estimates you get from the computer are best under this model, and the inferences ( $p$-values and confidence intervals) are exactly correct under this model. If the assumptions of the model are not true, then the estimates are not best, and the inferences are incorrect. You might think we are saying that assumptions must be true in order to use statistical methods that make such assumptions, but we are not. As we noted in Chapter 1 , it is not necessarily a problem that any or all of the assumptions of the model are wrong, depending on how badly violated is the assumption. And the easiest way to understand whether an assumption is violated “too badly” is to use simulation.

We have found that students in statistics classes often resist learning simulation. After all, the data that researchers use is usually real, and not simulated, so the students wonder, what is the point of using simulation? Here are some answers:

• Simulation shows you, clearly and concretely, how to interpret the regression analysis of your real (not simulated) data.
• Simulation helps you to understand how a regression model can be useful even when the model is wrong.
• Simulation models help you to understand the meaning of the regression model parameters.
• Simulation models help you to understand the meaning of the regression model assumptions.
• Simulation models help you to understand the meaning of a “research hypothesis.”
• Simulation helps you to understand how to interpret your data in the presence of chance effects.
• Simulation helps you to understand all the commonly misunderstood concepts in statistics, like “unbiasedness,” “standard error,” “p-value,” and “confidence interval.”
• Simulation methods are commonly used in the analysis of real data; examples include the bootstrap and Markov Chain Monte Carlo.

An alternative to using simulation is to use advanced mathematics, typically involving multidimensional calculus. But this is much, much harder than simulation.

# 回归分析代写

## 统计代写|回归分析作业代写Regression Analysis代考|The Gauss-Markov Model and Theorem

$$Y_{i} \mid X_{i}=x_{i} \sim \text { independent } \mathrm{N}\left(\beta_{0}+\beta_{1} x_{i}, \sigma^{2}\right), \text { for } i=1,2, \ldots, n$$

\left 的分隔符缺失或无法识别

$$Y_{i}=\beta_{0}+\beta_{1} x_{i}+\varepsilon_{i}$$

$$Y_{i} \mid X_{i}=x_{i} \sim_{\text {independent }} \mathrm{N}\left(\beta_{0}+\beta_{1} x_{i}, \sigma^{2}\right), \text { for } i=1,2, \ldots, n$$

$$Y_{i}=\beta_{0}+\beta_{1} X_{i}+\varepsilon_{i}$$

$$\text { (i) } \mathrm{E}\left(Y_{i} \mid X_{i}=x_{i}\right)=\beta_{0}+\beta_{1} x_{i} \text { 和 (ii) } \varepsilon_{i} \sim \sim_{\text {iid }} \mathrm{N}\left(0, \sigma^{2}\right)$$

## 统计代写|回归分析作业代写Regression Analysis代考|The Classical Model and Its Consequences

$$Y_{i} \mid X_{i}=x_{i} \quad \sim_{\text {independent }} \mathrm{N}\left(\beta_{0}+\beta_{1} x_{i}, \sigma^{2}\right), \text { for } i=1,2, \ldots, n .$$

• 模拟清晰而具体地向您展示了如何解释真实 (非模拟) 数据的回归分析。
• 模拟可帮助您了解回归模型如何在模型错误的情况下发挥作用。
• 模拟模型帮助您理解回归模型参数的含义。
• 模拟模型可帮助您理解回归模型假设的含义。
• 模拟模型可帮助您理解“研究假设“的含义。
• 模拟可帮助您了解如何在存在机会效应的情况下解释您的数据。
• 模拟可帮助您理解统计中所有常见的误解概念，例如”无偏性”、”标准误差”、”p 值”和”置信区间”。
• 模拟方法常用于真实数据的分析；示例包括 bootstrap 和 Markov Chain Monte Carlo。
吏用模拟的替代方法是使用高级数学，通常涉及多维微积分。但这比模拟要困难得多。

## 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。

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