### 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Data Analysis Strategies and Statistical Thinking

statistics-lab™ 为您的留学生涯保驾护航 在代写多元统计分析Multivariate Statistical Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写多元统计分析Multivariate Statistical Analysis代写方面经验极为丰富，各种代写多元统计分析Multivariate Statistical Analysis相关的作业也就用不着说。

• 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|多元统计分析代写Multivariate Statistical Analysis代考|Data Analysis Strategies and Statistical Thinking

The main goal of statistics is to learn from data in order for us to make good decisions and to understand real world problems. In data analysis, the most important skill for a statistician is to develop the ability of statistical thinking: how to obtain good data, how to choose appropriate methods to analyze the data, and how to interpret analysis results and draw reliable conclusions. It takes time to develop such skills since real understanding of statistical methods is harder than one may imagine. Statistical thinking is different from mathematical thinking, since mathematics often involves either black or white (i.e., right or wrong) while statistics may involve many grey areas which may not be as simple as either right or wrong. Therefore, in statistics sometimes it may be more important to understand the concepts, models, and methods than to do mathematical derivations or proofs. Statistics is becoming one of the most important subjects in modern world since many important decisions in almost all fields in modern world are based on information from data, obtained via data analysis. As Samuel Wells wrote “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”.

In data analysis, it is desirable to follow certain procedures. These procedures are reflections of statistical thinking. Specifically, a good statistical analysis should consist of the following steps:

1. objectives.
2. data collection.
3. exploratory analysis.
4. confirmatory analysis.
5. interpretation of results.
6. conclusions.
Before collecting data, we should be clear about the study objectives, which allow us to decide how to collect data. Once the objectives are clear, the next step is to decide how to collect data. Getting good data is an important step, since there is not much

The main goal of statistics is to learn from data in order for us to make good decisions and to understand real world problems. In data analysis, the most important skill for a statistician is to develop the ability of statistical thinking: how to obtain good data, how to choose appropriate methods to analyze the data, and how to interpret analysis results and draw reliable conclusions. It takes time to develop such skills since real understanding of statistical methods is harder than one may imagine. Statistical thinking is different from mathematical thinking, since mathematics often involves either black or white (i.e., right or wrong) while statistics may involve many grey areas which may not be as simple as either right or wrong. Therefore, in statistics sometimes it may be more important to understand the concepts, models, and methods than to do mathematical derivations or proofs. Statistics is becoming one of the most important subjects in modern world since many important decisions in almost all fields in modern world are based on information from data, obtained via data analysis. As Samuel Wells wrote “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”.

In data analysis, it is desirable to follow certain procedures. These procedures are reflections of statistical thinking. Specifically, a good statistical analysis should consist of the following steps:

1. objectives.
2. data collection.
3. exploratory analysis.
4. confirmatory analysis.
5. interpretation of results.
6. conclusions.
Before collecting data, we should be clear about the study objectives, which allow us to decide how to collect data. Once the objectives are clear, the next step is to decide how to collect data. Getting good data is an important step, since there is not much statistics can do if the data is poorly collected. There are generally two ways to collect data: designed experiments or observation studies (e.g., sample surveys). Designed experiments often involve randomization which allows us to make causal inference. Observational studies such as sample surveys allow us to find associations. Nowadays, there are many other ways that massive data are automatically generated, such as data from internet and records from business transactions. A good understanding of how the data are generated can help us to make reliable conclusions from data analysis.

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Outline

The topics for multivariate analysis can be quite extensive, since many statistical models and methods involving more than one variables may be viewed as multivariate analysis in a general sense. In some classic textbooks, multivariate analysis focuses mostly on models and methods for multivariate normal distributions with i.i.d. data. Such a focus allows theoretical developments since multivariate normal distributions have many nice properties and have elegant mathematical expressions. In practice, however, real data are highly complex. The multivariate normal distribution assumption may not hold for some real world problems. This book focuses more on how to analyze data from real world problems. In practice, the data may not follow normal distributions, may be discrete, and may not be independent. We select the topics

which are among the most commonly used in practice. Due to space limitation, some topics, which may also be important in practice, have to be omitted.

Chapters 2 to 4 may be viewed as exploratory multivariate analysis for continuous data. The goal is to reduce the dimension of multivariate data or to classify multivariate observations. Distributional assumptions may not be required, although in some cases we may assume multivariate normal distributions for inference. Chapter 5 considers statistical inference for multivariate normal distributions, including hypothesis testing for the mean vector and covariance matrix, which is often a major focus in classical textbooks. Chapter 6 reviews methods for multivariate discrete data, including inference for contingency tables. Chapter 7 briefly introduces Copula models, which are useful models for non-normal multivariate data. Chapters 8 to 10 briefly review linear and generalized linear regression models, with MANOVA models being viewed as special linear models. Chapter 11 shows models for dependent data, especial models for repeated measurements and longitudinal data. In Chapter 12 , we discuss how to handle missing data in multivariate datasets since missing data are very common in practice and they can have substantial effects on analysis results. Chapter 13 briefly describes robust methods for multivariate analysis with outliers, which is an important topic since outliers are not easily detected in multivariate datasets but can have serious impact on analysis results. In Chapter 14 , we briefly describe some general methods which are useful in multivariate analysis.

The focus of this book is on conceptual understanding of the models and methods for multivariate data, rather than tedious mathematical derivations or proofs. Extensive real data examples are presented in R. Students completing this course should be ready to perform statistical analysis of multivariate data from real world problems.

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|The Basic Idea

In practice, a dataset may contain many variables, such as exam scores on algebra, calculus, geometry, violin, piano, and guitar. Some of these variables may be highly correlated, such as scores on violin, piano, and guitar. When analyzing such multivariate data, it is difficult to graphically display the data. Moreover, if we have to assume parametric distributions for these variables for statistical inference, there may be too many parameters to be estimated or there may be multi-collinearity problems. For example, if we assume a multivariate normal distribution for 6 variables, the covariance matrix will contain 21 parameters. That is, the covariance matrix will be of high dimension, so it is likely to be singular or ill behaved. When the sample size is not large, these parameters may be poorly estimated. Therefore, it is important to reduce the number of variables if the loss of information is not much. This dimension reduction is possible because, if some variables are highly correlated, they may be replaced by fewer new variables without much loss of information.

For example, if we have exam scores on six courses (variables): algebra, calculus, geometry, violin, piano, and guitar, we can use a new variable called mathematics skills to represent the first three variables and use another new variable called music skills to represent the last three variables. These two new variables, mathematics skills and music skills, retain most information in the original six variables. Moreover, these two new variables are uncorrelated and can be obtained by linear combinations of the original six variables. Therefore, we have reduced the number of variables from 6 to 2, without much loss of information. The scores of the original six variables can be converted scores of the two new variables, and we can plot the scores of the two new variables to check the normal assumption and possible outliers. That is the basic idea of dimension reduction (the dimension of the original data space is 6 , while the dimension of the new data space is 2 ), and the idea behind principal components analysis. The two new variables are called principal components.

Much information in the data or variables can be measured by the variability (or variance) of the data or variables. In other words, if the values of the data are all the same, there will be little information in the data. The basic idea of principal components analysis (PCA) is to explain the variability in the original set of correlated variables through a smaller set of uncorrelated new variables. These new variables are obtained by certain linear combinations of the original variables, and they are called the principal components $(P C s)$. That is, the goal of PCA is to reduce the number of original variables while maintain most of the information (variation) in the original data, i.e., it is a dimension-reduction method. Since the PCs are linear combinations of the original variables, normality and outliers in the original data should still be present in the “new data” of the PCs (called $P C$ scores), so we can check multivariate normality of the original data or check outliers in the original data based on the $\mathrm{PC}$ scores, which is easier since the new data have a lower dimension.

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Data Analysis Strategies and Statistical Thinking

1. 目标。
2. 数据采集​​。
3. 探索性分析。
4. 验证性分析。
5. 结果的解释。
6. 结论。
在收集数据之前，我们应该明确研究目标，以便我们决定如何收集数据。一旦目标明确，下一步就是决定如何收集数据。获得好的数据是重要的一步，因为没有太多

1. 目标。
2. 数据采集​​。
3. 探索性分析。
4. 验证性分析。
5. 结果的解释。
6. 结论。
在收集数据之前，我们应该明确研究目标，以便我们决定如何收集数据。一旦目标明确，下一步就是决定如何收集数据。获得好的数据是重要的一步，因为如果数据收集得不好，就没有太多的统计数据可以做。通常有两种收集数据的方法：设计实验或观察研究（例如，抽样调查）。设计的实验通常涉及随机化，这使我们能够做出因果推断。抽样调查等观察性研究使我们能够找到关联。如今，海量数据的自动生成方式还有很多，例如来自互联网的数据和来自商业交易的记录。很好地理解数据是如何产生的，可以帮助我们从数据分析中得出可靠的结论。

## 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。