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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

## 经济代写|计量经济学代写Econometrics代考|Linear and Nonlinear Regression Functions

The general regression function $x_{t}(\boldsymbol{\beta})$ can be made specific in a very large number of ways. It is worthwhile to consider a number of special cases so as to get some idea of the variety of specific regression functions that are commonly used in practice.
The very simplest regression function is
$$x_{t}(\boldsymbol{\beta})=\beta_{1} \iota_{t}=\beta_{1},$$
where $\iota_{t}$ is the $t^{\text {th }}$ element of an $n$-vector $\iota$, each element of which is 1 . In this case, the model (2.01) says that the conditional mean of $y_{t}$ is simply a constant. While this is a trivial example of a regression function, since $x_{t}(\boldsymbol{\beta})$ is the same for all $t$, it is nevertheless a good example to start with and to keep in mind. All regression functions are simply fancier versions of (2.10). And any regression function that cannot fit the data at least as well as (2.10) should be considered a highly unsatisfactory one.

The next-simplest regression function is the simple linear regression function
$$x_{t}(\boldsymbol{\beta})=\beta_{1}+\beta_{2} z_{t},$$
where $z_{t}$ is a single independent variable. $\Lambda$ ctually, an even simpler model would be one with a single independent variable and no constant term. However, in most applied problems it does not make sense to omit the constant term. Many linear regression functions are used as approximations to unknown conditional mean functions, and such approximations will rarely be accurate if they are constrained to pass through the origin. Equation (2.11) has two parameters, an intercept $\beta_{1}$ and a slope $\beta_{2}$.

## 经济代写|计量经济学代写Econometrics代考|Error Terms

When we specify a regression model, we must specify two things: the regression function $x_{t}(\boldsymbol{\beta})$ and at least some of the properties of the error terms $u_{t}$. We have already seen how important the second of these can be. When we added crrors with constant variance to the multiplicative regression function (2.13), we obtained a genuinely nonlinear regression model. But when we added errors that were proportional to the regression function, as in (2.15), and made use of the approximation $e^{w} \cong 1+w$, which is a very good one when $w$ is small, we obtained a loglinear regression model. It should be clear from this example that how we specify the error terms will have a major effect on the model which is actually estimated.

In (2.01) we specified that the error terms were independent with identical means of zero and variances $\sigma^{2}$, but we did not specify how they were actually distributed. Even these assumptions may often be too strong. They rule out any sort of dependence across observations and any type of variation over time or with the values of any of the independent variables. They also rule out distributions where the tails are so thick that the error terms do not have a finite variance. One such distribution is the Cauchy distribution. A random variable that is distributed as Cauchy not only has no finite variance but no finite mean either. See Chapter 4 and Appendix B.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Linear and Nonlinear Regression Functions

$$x_{t}(\boldsymbol{\beta})=\beta_{1} \iota_{t}=\beta_{1},$$ 都一样 $t$ ，但它仍然是一个很好的例子，可以开始并牢记。所有回归函数都是 (2.10) 的更高级版本。并且任何不能至少与 (2.10) 一样拟合数据的回归函数都应该被认 为是一个非常不令人满意的回归函数。

$$x_{t}(\boldsymbol{\beta})=\beta_{1}+\beta_{2} z_{t},$$

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