### 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Goal of Statistics

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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|多元统计分析代写Multivariate Statistical Analysis代考|Goal of Statistics

A main goal of statistics is to analyze data in order to obtain useful information and make important decisions. In other words, statisticians analyze data to extract useful information from the data in a sample and draw important conclusions about the population. In modern world, many important decisions are based on information from data. With the developments of modern computers and internet, massive data are available and can be easily obtained, but important information in the data may not be easily obtained without using modern statistical methods. Therefore, statistics is becoming one of the most important subjects in the 21 century, and statistical methods are among the most widely used tools in almost every area, including banks, insurance industries, economics, finance, medicine, and engineering. As a New York Times article says (August 5, 2009, For Today’s Graduate, Just One Word: Statistics): “For many different jobs in today’s world, mostly what you do is data analysis (statistics), even for jobs which seem unrelated to statistics … Many today’s decisions in industry and government are based on data analysis results. Statisticians are thus in high demand …”.

Data can be collected in many ways, such as survey, internet, company records and designed experiments. Our goal is to analyze the data to extract as much information as possible and then draw some conclusions about the whole population. For example, if a new drug is found to be effective on 20 randomly selected patients (sample) based on statistical analysis, will this drug also be effective for all patients (population)? If exam scores are found to be related to students’ IQ scores as well as students’ attitude on 50 randomly selected students (sample), is this also true for all students (population)? Such a generalization from sample to population is called statistical inference. Sometimes, however, we may just wish to obtain useful information from the sample, without necessarily making inference about the population, especially if the sample is not a random and representative sample.
In practice, data analysis often consists of two stages:

• exploratory data analysis.formal (or confirmatory) data analysis.
• In exploratory data analyses, data are simply summarized using common statistics (e.g., means, standard deviations, correlations) and are displayed using common graphical tools (e.g., histograms, boxplots, scatterplots). In this stage, we simply present and summarize the data, without trying to generalize the conclusions obtained from summary statistics and graphs to the whole population. In this stage, we do not need to make any distributional assumptions for the data, i.e., we do not need to assume that data follow certain distributions such as the normal distributions. Thus, the conclusions obtained from exploratory analysis do not depend on the validity of any assumptions. Exploratory analysis can reveal important features of the data, which may lead to preliminary conclusions. Exploratory data analysis is an important step in any data analysis and should not be skipped. However, exploratory data analysis is usually followed by a formal or confirmatory analysis, which is used to confirm the preliminary conclusions from the exploratory analysis.
• In formal (or confirmatory) data analysis, we assume models or distributions for the data or population, estimate unknown parameters in the models or distributions, and attempt to make statistical inference so that we may generalize the results based on the sample to the whole population. For example, we may assume that the population follows a normal distribution, and then we use data to estimate the parameters in the normal distribution (mean and variance). Note that the models or distributions are only assumptions, so they may not be true. In other words, the assumed models and distributions should be checked for their validity based on the data. Since the assumed models or distributions rarely hold exactly, formal analysis results should only be viewed as approximate, and it is desirable to use different statistical models or methods to further validate the results.

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

The first step in data analysis should be exploratory analysis, which summarize the data using simple statistics and display the data using graphs. Univariate continuous data are often summarized by simple statistics such as the mean and standard deviation: the mean measures the center of the data while the standard deviation measures the variation of the data. Univariate data can be displayed by graphical tools such as histogram and boxplot: a histogram show the distribution (frequencies) of the data while the boxplot shows five number summaries of the data. It is important to display data using graphs since graphs may show unusual patterns in the data and outliers. These unusual patterns and outliers may make the mean and standard deviation misleading and unreliable. A picture is worth a thousand words! Graphical tools are important components of statistical analysis.

In statistical analysis, choice of statistical methods depends on the types of data in hand. Generally, there are two types of data (or variables):

• continuous data (variables), which take continuous values.
• categorical or discrete data (variables), which take discrete values.

Examples of continuous data include weight, age, income, blood pressure, etc. Examples of categorical data include gender, location, yes/no answers, blood type, etc. Continuous data may be transformed into categorical data by grouping the data based on some threshold values, such as subjects with ages greater than 60 and subjects with ages less than or equal to 60 . Such categorizations of continuous data may simplify analysis but it may also lead to some loss of information. Note that categorical data cannot be converted to continuous data. For a categorical variable, its value may represent a category rather than a numerical value, such as gender (male/female). Statistical methods for analyzing continuous data and categorical data are quite different. In this textbook, we will mostly focus on continuous data, but we will also discuss categorical data.

Continuous data are probably most common in practice and thus will be our main focus. For univariate continuous data, the two most important features are

• the center of the data, measured by the sample mean.
• the variation of the data, measured by the sample standard deviation.
The mean and the standard deviation should always be reported in statistical analysis. They give us some idea about the average of the data and the variation in the data- the two most important features of continuous data. Note that the mean and the standard deviation can be very sensitive to outliers and the data distributions, i.e., a few outliers in the data or a severely skewed data distribution can greatly affect the values of the mean and standard deviation and thus may lead to misleading conclusions. Graphical tools such as histograms may reveal outliers and data distributions, so they should be used in data analysis.

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

In practice, data are often collected on more than one variables, and these variables may be associated or correlated, i.e., change in one variable corresponds to changes in other variables. For example, income and education may be correlated, and gender and smoking status may be associated. When variables are associated or correlated, it is desirable to incorporate the association or correlation and analyze the data on these variables simultaneously. In other words, when several variables are associated,

it may be more desirable to use multivariate analysis than univariate analysis, since multivariate analysis uses extra information from the correlation or association. In other words, when analyzing data on one variable from a multivariate dataset, we can borrow information from data on other variables. Note that the term “correlation” is usually used for continuous data while the term “association” may be used for both continuous and discrete data. Data on two or more variables are called multivariate data, and statistical analysis of multivariate data is called multivariate analysis. In multivariate analysis, a key consideration is to incorporate the correlation or association between the variables.

Methods to measure the correlation among continuous data and methods to measure the association among discrete data are quite different. For continuous multivariate data, we usually use correlation matrices while for discrete multivariate data we usually use odds ratio or other measurements, which will be described in details in later chapters. We first focus on multivariate continuous data, where each variable is a continuous variable.

As an example for multivariate continuous data, suppose that a bank or a credit card company wish to classify all customers into two groups: individuals with good credit risks and individuals with bad credit risks. The classification can be based on customers’ education $\left(x_{1}\right)$, income $\left(x_{2}\right)$, age $\left(x_{3}\right)$, and past credit history $\left(x_{4}\right)$. It would be easy to do the classification if we just consider one variable, say income. For example, individuals with high income may be classified as good credit risk, while those with low income may be classified as bad credit risk. However, since these variables $\left(x_{1}, x_{2}, x_{3}, x_{4}\right)$ may be associated, we need to consider all variables simultaneously. The classification based on all variables can be challenging. For example, an individual with high income may have low education and young age. Therefore, special multivariate analysis methods are required to do the classification.

## 统计代写|多元统计分析代写Multivariate Statistical Analysis代考|Goal of Statistics

• 探索性数据分析。正式（或确认）数据分析。
• 在探索性数据分析中，使用常见的统计数据（例如，平均值、标准差、相关性）简单地汇总数据，并使用常见的图形工具（例如，直方图、箱线图、散点图）显示数据。在这个阶段，我们只是简单地呈现和总结数据，而不是试图将总结统计和图表得出的结论推广到整个人群。在这个阶段，我们不需要对数据做任何分布假设，即我们不需要假设数据遵循一定的分布，例如正态分布。因此，探索性分析得出的结论不依赖于任何假设的有效性。探索性分析可以揭示数据的重要特征，从而得出初步结论。探索性数据分析是任何数据分析的重要步骤，不应跳过。但是，探索性数据分析之后通常会进行正式或确认性分析，用于确认探索性分析的初步结论。
• 在正式（或验证性）数据分析中，我们假设数据或总体的模型或分布，估计模型或分布中的未知参数，并尝试进行统计推断，以便我们可以将基于样本的结果推广到整个总体. 例如，我们可以假设总体服从正态分布，然后我们使用数据来估计正态分布中的参数（均值和方差）。请注意，模型或分布只是假设，因此它们可能不正确。换言之，应根据数据检查假设的模型和分布的有效性。由于假设的模型或分布很少完全成立，因此形式分析结果只能视为近似值，

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

• 连续数据（变量），取连续值。
• 采用离散值的分类或离散数据（变量）。

• 数据的中心，由样本均值测量。
• 数据的变化，由样本标准偏差测量。
应始终在统计分析中报告平均值和标准偏差。它们让我们了解数据的平均值和数据的变化——连续数据的两个最重要的特征。请注意，均值和标准差可能对异常值和数据分布非常敏感，即数据中的少数异常值或严重偏斜的数据分布会极大地影响均值和标准差的值，从而可能导致误导结论。直方图等图形工具可能会揭示异常值和数据分布，因此应在数据分析中使用它们。

## 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。