### 统计代写|回归分析作业代写Regression Analysis代考|STA 321

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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|Introduction to Regression Models

Regression models are used to relate a variable, $Y$, to a single variable $X$, or to multiple variables, $X_{1}, X_{2}, \ldots, X_{k}$.

• How does a person’s choice of toothpaste $(Y)$ relate to the person’s age $\left(X_{1}\right)$ and income $\left(X_{2}\right)$ ?
• How does a person’s cancer remission status $(Y)$ relate to their chemotherapy regimen $(X)$ ?
• How does the number of potholes in a road $(Y)$ relate to the material used in surfacing $\left(X_{1}\right)$ and time since installation $\left(X_{2}\right)$ ?
• How does a person’s ability to repay a loan $(Y)$ relate to the person’s income $\left(X_{1}\right)$, assets $\left(X_{2}\right)$, and debt $\left(X_{3}\right)$ ?
• How does a person’s intent to purchase a technology product $(Y)$ relate to their perceived usefulness $\left(X_{1}\right)$ and perceived ease of use of the product $\left(X_{2}\right)$ ?
• How does today’s return on the S\&P 500 stock index $(Y)$ relate to yesterday’s return $(X)$ ?
• How does a company’s profitability $(Y)$ relate to its investment in quality management $(X)$ ?
Understanding such relationships can help you to predict what an unknown $Y$ will be for a given fixed value of $X$, it can help you to make decisions as to what course of action you should choose, and it can help you to understand the subject that you are studying in a scientific way.

Regression models can help you to forecast the future as well. Forecasting is a special case of prediction: Forecasting means prediction of the future, while prediction includes any type of “what-if” analysis, not only about what might happen in the future, but also about what might have happened in the past under different circumstances.
In some subjects, you learn to make predictions using equations such as
$$Y=f(X),$$
where the function $f$ might be a linear, quadratic, exponential, or logarithmic function; or it might not have any “named” function form at all. In all cases, though, this is a deterministic relationship: Given a particular value, $x$, of the variable $X$, the value of $Y$ is completely determined by $Y=f(x)$.

Notice that there is a distinction between upper-case $X$ and lower-case $x$. The convention followed in this book regarding lower-case and upper-case $Y$ and $X$ is standard: Uppercase refers to the variable in general, which can be many different possible values, while lower-case refers to a specific value of the variable. For example, $X=$ Age can be many different values in general, whereas $X=x$ identifies the subset of people having age $x$, e.g., the subset of people who are 25 years old.

## 统计代写|回归分析作业代写Regression Analysis代考|Randomness of the Measured Area of a Circle as Related to Its Measured Radius

A circle in nature has its radius $(X)$ measured. Suppose the measurement is $X=10$ meters. Still, there are many potentially observable measurements of its area, $Y$, due to imperfections in the circle and imperfections in the measuring device. The regression model states that $Y$ is a random observation from the conditional distribution $p(y \mid X=10)$.

This model is reasonable, because it perfectly matches the reality that there are many potentially observable measurements of the area $Y$, even when the radius $X$ is measured to be precisely 10 meters. Note that this model does not say anything about the mean of the distribution $p(y \mid x)$ : It might be $3.14159265 x^{2}$, but it is more likely not, because of biases in the data-generating process (again, this data-generating process includes imperfections in circles, and also imperfections in the measuring devices).

This model also does not say anything about the nature of the probability distributions $p(y \mid x)$, whether they are discrete, continuous, normal, lognormal, etc., or even whether you have one type of distribution for one $x$ (e.g., normal) and another for a different $x$ (e.g., Poisson). It simply says there is a distribution $p(y \mid x)$ of potential outcomes of $Y$ when $X=x$, and that the number you measure will appear as if produced at random from this distribution, i.e., as if simulated using a random number generator. As such, there is no arguing with the model-the measured data really will look this way (random, variable), hence you may even say that this model is a correct model because it produces data that are random and variable (non-deterministic). Further, because the model is so general, no data can ever contradict, or “reject” it.

Thus, the model $p(y \mid x)$ is correct. It is only when you make assumptions about the nature of $p(y \mid x)$, for example, about the specific distributions (e.g. normal), and about how are distributions related to $x$ (e.g., linearly), that you must consider that the model is wrong in certain ways.

The model $p(y \mid x)$ does not require that the distribution of $Y$ change for different values of $X$. If the distributions $p(y \mid x)$ are the same, for all values $X=x$, then, by definition, $Y$ is independent of $X$. In the example above, one may logically assume that the distributions of $Y$ (measured area) will differ greatly for different $X$ (measured radius), and that $Y$ and $X$ are thus strongly dependent.

The following $\mathrm{R}$ code and resulting graph of Figure $1.1$ illustrate how the distributions of area $(Y)$ might look for circles whose radius $(X)$ is measured to be $9.0$ meters versus circles whose radius is measured to be $10.0$ meters. In this example, we assume that $p(y \mid x)$ is a normal distribution with mean $\pi x^{2}$ meters ${ }^{2}$ and standard deviation of 1 meter $^{2}$.

## 统计代写|回归分析作业代写Regression Analysis代考|Introduction to Regression Models

• 一个人如何选择牙享 $(Y)$ 与人的年龄有关 $\left(X_{1}\right)$ 和收入 $\left(X_{2}\right)$ ?
• 一个人的㾔症缓解状态如何 $(Y)$ 与他们的化疗方案有关 $(X)$ ?
• 道路坑洼的数量是多少 $(Y)$ 与表面处理中使用的材料有关 $\left(X_{1}\right)$ 和安装后的时间 $\left(X_{2}\right)$ ?
• 一个人偿还贷款的能力如何 $(Y)$ 与该人的收入有关 $\left(X_{1}\right)$ ，资产 $\left(X_{2}\right)$ ，和债务 $\left(X_{3}\right)$ ?
• 一个人购买科技产品的意图如何 $(Y)$ 与他们感知的有用性有关 $\left(X_{1}\right)$ 和感知到的产品易用性 $\left(X_{2}\right)$ ?
• 标准普尔 500 股指今天的回报率如何 $(Y)$ 与昨天的回报有关 $(X)$ ?
• 一家公司的盈利能力如何 $(Y)$ 与其在质量管理方面的投资有关 $(X)$ ?
了解这种关系可以帮助您预测末知的 $Y$ 将对于给定的固定值 $X$ ，它可以帮助你决定你应该选择什么样的行 动方案，它可以帮助你以科学的方式理解你正在学习的主题。
回归模型也可以帮助您预测末来。预测是预测的一个特例：预测意味着对末来的预测，而预测包括任何类型的“假 设”分析，不仅是关于末来可能发生的事情，还包括过去在不同情况下可能发生的事情。情况。
在某些科目中，您将学习使用方程式进行预测，例如
$$Y=f(X)$$
函数在哪里 $f$ 可能是线性、二次、指数或对数函数；或者它可能根本没有任何“命名”函数形式。然而，在所有情况 下，这是一种确定性的关系：给定一个特定的值， $x$ ，的变量 $X ，$ 的价值 $Y$ 完全由 $Y=f(x)$.
注意大写之间是有区别的 $X$ 和小写 $x$. 本书中关于小写和大写的约定 $Y$ 和 $X$ 是标准的：大写是指一般的变量，可以 是许多不同的可能值，而小写是指变量的特定值。例如， $X=$ 一般来说，年龄可以是许多不同的值，而 $X=x$ 识别有年龄的人的子集 $x$ ，例如，25 岁的人的子集。

## 广义线性模型代考

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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。