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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

## 计算机代写|深度学习代写deep learning代考|Ordinary Least Squares

A linear regression uses a linear model as shown in Fig. 3.1a. More specifically, the dependent variable can be calculated from a linear combination of the input variables. It is also common to refer to a linear model as Ordinary Least Squares (OLS) linear regression or just Least Squares (LS) regression. For example, a simple linear regression model is given by
$$y_{i}=\beta_{0}+\beta_{1} x_{i}+\epsilon_{i}, \quad i=1, \cdots, n$$
and the goal is to estimate the parameter set $\boldsymbol{\beta}=\left{\beta_{0}, \beta_{1}\right}$ from the training data $\left{x_{i}, y_{i}\right}_{i=1}^{n}$.
In general, a linear regression problem can be represented by
$$y_{i}=\left\langle\boldsymbol{x}{i}, \boldsymbol{\beta}\right\rangle+\epsilon{i}, \quad i=1, \cdots, n$$
where $\left(\boldsymbol{x}{i}, y{i}\right) \in \mathbb{R}^{p} \times \mathbb{R}$ is the $i$-th training data, and $\boldsymbol{\beta} \in \mathbb{R}^{p}$ is referred to as the regression coefficient. This can be represented in matrix form as
$$y=X^{\top} \beta+\epsilon,$$
where
$$\boldsymbol{y}:=\left[\begin{array}{c} y_{1} \ \vdots \ y_{n} \end{array}\right], \boldsymbol{X}:=\left[\boldsymbol{x}{1} \cdots \boldsymbol{x}{n}\right], \quad \boldsymbol{\epsilon}:=\left[\begin{array}{c} \epsilon_{1} \ \vdots \ \epsilon_{n} \end{array}\right] .$$
In this mathematical formulation, $x_{i}$ corresponds to the independent variable, whereas $y_{i}$ is the dependent variable.

## 计算机代写|深度学习代写deep learning代考|Logits and Linear Regression

Similar to the example in Fig. 3.1b, there are many important problems for which the dependent variable has limited values. For example, in binary logistic regression for analyzing smoking behavior, the dependent variable is a dummy variable: coded 0 (did not smoke) or 1 (did smoke). In another example, one is interested in fitting a linear model to the probability of the event. In this case, the dependent variable only takes values between 0 and 1 . In this case, transforming the independent variables does not remedy all of the potential problems. Instead, the key idea of the logistic regression is transforming the dependent variable.

Specifically, we define the term odds:
$$\text { odds }=\frac{q}{1-q}$$
where $q$ is a probability in a range of $0-1$. The odds have a range of $0-\infty$ with values greater than 1 associated with an event being more likely to occur than to not occur and values less than 1 associated with an event that is less likely to occur. Then, the term logit is defined as the log of the odd:
$$\text { logit }:=\log (\text { odds })=\log \left(\frac{q}{1-q}\right) \text {. }$$
This transformation is useful because it creates a variable with a range from $-\infty$ to $\infty$ with zero associated with an event equally likely to occur and not occur. One of the important advantages of this transformation of the dependent variable is that it solves the problem we encountered in fitting a linear model to probabilities. If we transform our probabilities to logits, then the range of the logit is not restricted, so that we can apply a standard linear regression.

# 深度学习代写

## 计算机代写|深度学习代写deep learning代考|Ordinary Least Squares

$$y_{i}=\beta_{0}+\beta_{1} x_{i}+\epsilon_{i}, \quad i=1, \cdots, n$$

$$y_{i}=\langle\boldsymbol{x} i, \boldsymbol{\beta}\rangle+\epsilon i, \quad i=1, \cdots, n$$

$$y=X^{\top} \beta+\epsilon,$$

$$\boldsymbol{y}:=\left[y_{1}: y_{n}\right], \boldsymbol{X}:=[\boldsymbol{x} 1 \cdots \boldsymbol{x} n], \quad \boldsymbol{\epsilon}:=\left[\epsilon_{1} \vdots \epsilon_{n}\right] .$$

## 计算机代写|深度学习代写deep learning代考|Logits and Linear Regression

$$\text { odds }=\frac{q}{1-q}$$

$$\operatorname{logit}:=\log (\text { odds })=\log \left(\frac{q}{1-q}\right) .$$

## 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