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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|Prediction

A major topic within the discipline that has come to be known as “Data Science” is called “Predictive Modeling,” which concerns the use of non-linear (and therefore realistic) regression models. Such models include neural networks, random forests, decision trees, and LOESS. In predictive modeling, your aim is to predict a $Y$, for example, the “Yes/ $\mathrm{No}^{\prime \prime}$ outcome of “will this customer repay the loan,” as a function of various $X$ variables such as $X_1=$ age, $X_2=$ income, $X_3=$ assets, $X_4=$ debt, $X_5=$ credit history, $\ldots, X_k=$ # of children. The goal is to come up with a function $f\left(x_1, \ldots, x_k\right)$ that is as close as possible to $Y \mid X_1=x_1, \ldots, X_k=x_k$.
In theory, the correct solution is to choose $f\left(x_1, \ldots, x_k\right)$ to be the expected value of the conditional distribution of $Y \mid X_1=x_1, \ldots, X_k=x_{k^k}$. It is a mathematical theorem that, if
$$f\left(x_1, \ldots, x_k\right)=\mathrm{E}\left(Y \mid X_1=x_1, \ldots, X_k=x_k\right),$$
then $\mathrm{E}\left{Y-f\left(X_1, \ldots, X_k\right)\right}^2$ is a minimum. Thus the best predictor of $Y$, in the sense of minimizing the average squared deviation from the predictor, is the conditional mean function $f\left(x_1, \ldots, x_k\right)$, which is almost always a non-linear function of $x_1, \ldots, x_k$.
The proof of this theorem is given below the following example.

## 统计代写|回归分析作业代写Regression Analysis代考|Predicting Loan Repayment

Suppose you are a loan officer. A person comes to your office presenting $X_1=31$ years old, $X_2=\$ 60 \mathrm{~K}$income,$X_3=\$0$ assets, $X_4=\$ 100 \mathrm{~K}$debt,$X_5=500$credit score, …, and$X_k=2$children. This person wants a loan. You would like to know whether she or he will be able to repay the loan$(Y=1)$or not$(Y=0)$. Then your best prediction of$Y$is$\mathrm{E}\left(Y \mid X_1=31, \ldots, X_k=2\right)$, which is the average of all potentially observable$Y$‘s for people with exactly the same characteristics as this person. If there were many people who might apply for the loan who shared these exact characteristics, and whose loan-repaying outcomes ( 0 ‘s of 1’s) were observed, then you could appeal to the Law of Large numbers, getting a good estimate of$\mathrm{E}\left(Y \mid X_1=31, \ldots, X_k=2\right)$by averaging the$Y$values (in this case the$Y$values are 0 ‘s and$1^{\prime}$s) for this group of people. The problem with this solution is that there might not be anyone else in the whole world with exactly this same profile ($X_1=31$years old,$X_2=\$60 \mathrm{~K}$ income, $X_3=\$ 0$assets,$X_4=\$100 \mathrm{~K}$ debt, $X_5=500$ credit score, …, $X_k=2$ children). So, while the solution is simple, in theory, you have to use some special methods to estimate $f\left(x_1, \ldots, x_k\right)$. Logistic regression, discussed in Chapter 13 , is one such method. Neural networks and regression trees are other (more flexible) methods; these are discussed in Chapters 17 and $18 .$

Putting aside the issue of how to estimate $f\left(x_1, \ldots, x_k\right)=\mathrm{E}\left(Y \mid X_1=x_1, \ldots, X_k=x_k\right)$, how do you know that $f\left(x_1, \ldots, x_k\right)$ actually is the best predictor of $Y$ ? The answer lies in the famous “Law of Total Expectation,” which is actually a mathematical theorem, not just a mild suggestion or ugly rule of thumb.
Law of Total Expectation
Suppose $(V, W)$ are random variables. Let $\mathrm{E}(W \mid V=v)=f(v)$. Then
$$\mathrm{E}(W)=\mathrm{E}_V{f(V)}$$
In simple, informal words, the Law of Total Expectation states that “the (weighted) average of the within-group averages is equal to the global average.”

It bears repeating that the best way to understand abstract concepts is by using simulation because you can attach actual numbers to everything.

# 回归分析代写

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

$$f\left(x_1, \ldots, x_k\right)=\mathrm{E}\left(Y \mid X_1=x_1, \ldots, X_k=x_k\right),$$

## 统计代写|回归分析作业代写Regression Analysis代考|Predicting Loan Repayment

$$\mathrm{E}(W)=\mathrm{E}_V f(V)$$

## 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