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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• 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|Logarithmic Transformation of the Y data

If you transform the $Y$ variable to $f(Y)$ but not the $X$ variable, then you think the model
$$f(Y)=\beta_0+\beta_1 X+\varepsilon$$
is better than the model $Y=\beta_0+\beta_1 X+\varepsilon$. As with transformation of $X$, in order to use this model successfully, you must understand what this model states in the original (untransformed) $(X, Y)$ data. Here,
$$Y=f^{-1}\left{\beta_0+\beta_1 X+\varepsilon\right},$$
where $f^{-1}$ is the inverse function (not the inverse of the function). You find the inverse function simply by solving the model equation $\left(f(Y)=\beta_0+\beta_1 X+\varepsilon\right)$ for $Y$.

For example, if $f(Y)=\ln (Y)$, then $Y=f^{-1}{f(Y)}=\exp {f(Y)}$, and the model in terms of the original units is then
$$Y=\exp \left(\beta_0+\beta_1 X+\varepsilon\right),$$
or equivalently,
$$Y=\exp \left(\beta_0\right) \times \exp \left(\beta_1 X\right) \times \exp (\varepsilon)$$
Notice now that the error term is multiplicative, rather than additive. Along with Jensen’s inequality, the multiplicative error implies that the function $\exp \left(\beta_0\right) \times \exp \left(\beta_1 X\right)$ is not the conditional mean. To see why not, note that
\begin{aligned} \mathrm{E}(Y \mid X=x) &=\exp \left(\beta_0\right) \times \exp \left(\beta_1 x\right) \times \mathrm{E}{\exp (\varepsilon \mid X=x)} \ &=\exp \left(\beta_0\right) \times \exp \left(\beta_1 x\right) \times \mathrm{E}{\exp (\varepsilon)} \end{aligned}
But, since $\exp (\cdot)$ is a convex function, $\mathrm{E}{\exp (\varepsilon)}>\exp {\mathrm{E}(\varepsilon)}=\exp (0)=1$, so that $\mathrm{E}(Y \mid X=x)>\exp \left(\beta_0\right) \times \exp \left(\beta_1 x\right)$. Thus, the back-transformed function, $\exp \left(\beta_0\right) \times \exp \left(\beta_1 x\right)$, is no longer the mean function of the untransformed data.

## 统计代写|回归分析作业代写Regression Analysis代考|An Example Where the Inverse Transformation $1 / Y$ Is Needed

Professor Smith collected data on the time it took various computers to perform the same task. He needed to run a massive simulation in a short period of time to meet a deadline for revising a manuscript, so he asked $n=18$ graduate students to run some code overnight and send him the results when it was done. Since this was a Monte Carlo simulation, all 18 results were slightly different due to randomness. He then collated all 18 results to get a much larger simulation size and hence more accurate estimates. This allowed him to perform a simulation overnight that otherwise would have taken days to complete.

He was curious as to what factors affected the time it takes for a computer to complete the simulation, so he also had the students record their computer’s RAM (in gigabytes) and processor speed (in Gigahertz, or $\mathrm{GHz}$ ).

One model he used was $Y=\beta_0+\beta_1 X+\varepsilon$, where $Y=$ time to complete job, and $X=$ Gigabytes RAM (or GB in the code below). However, the results were unsatisfactory: Linearity, constant variance, and normality were clearly violated. He tried using the log-transform on $Y$, but the results were still not ideal. He then realized that the variable “time to finish the job” could be more directly related to computer performance in its inverse transform. After all, time, measured in hours, can be understood as hours per job: If a computer took 2 hours to complete the task, then it took 2 hours per 1 job. But the inverse of $Y$ in this example is more directly related to performance: $1 / Y=1 / 2=0.50$ jobs per hour. Another computer that took 20 minutes ( $1 / 3$ hour) to complete the one job would be able to complete $1 /(1 / 3)=3.0$ jobs per hour. Higher jobs per hour clearly indicates a better computer.

With ratio data, the units of measurement are $(a$ per $b)$, and the inverse transformation often makes sense simply because the measurements become $(b$ per $a$ ), which is just as easy to interpret. For example, a car that gets 30 miles per gallon of gasoline equivalently can be stated to take $(1 / 30)$ gallons per mile. You could use either measure in a statistical analysis, without question from any critical reviewer-miles per gallon and gallons per mile convey the same information. Which form to use? Simply choose the form that least violates the model assumptions.

The following code replicates the analyses shown in Figure $5.6$, for these data, but using the $W=1 / Y$ transformation, which he called “speed”, because higher values indicate a speedier computer.

# 回归分析代写

## 统计代写|回归分析作业代写Regression Analysis代考|Logarithmic Transformation of the Y data

$$f(Y)=\beta_0+\beta_1 X+\varepsilon$$

$\backslash 1$ eft 的分隔符缺失或无法识别

$$Y=\exp \left(\beta_0+\beta_1 X+\varepsilon\right),$$

$$Y=\exp \left(\beta_0\right) \times \exp \left(\beta_1 X\right) \times \exp (\varepsilon)$$

$$\mathrm{E}(Y \mid X=x)=\exp \left(\beta_0\right) \times \exp \left(\beta_1 x\right) \times \operatorname{Eexp}(\varepsilon \mid X=x) \quad=\exp \left(\beta_0\right) \times \exp \left(\beta_1 x\right) \times \operatorname{Eexp}(\varepsilon)$$

## 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