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# 澳洲代考|多元统计分析代考Multivariate Statistical Analysis代考|STAT3006

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## 澳洲代考|多元统计分析代考Multivariate Statistical Analysis代考|ASSESSING THE ASSUMPTION OF NORMALITY

Dot diagrams for smaller $n$ and histograms for $n>25$ or so help reveal situations where one tail of a univariate distribution is much longer than the other. If the histogram for a variable $X_{i}$ appears reasonably symmetric, we can check further by counting the number of observations in certain intervals. A univariate normal distribution assigns probability $.683$ to the interval $\left(\mu_{i}-\sqrt{\sigma_{i i}}, \mu_{i}+\sqrt{\sigma_{i i}}\right)$ and probability $.954$ to the interval $\left(\mu_{i}-2 \sqrt{\sigma_{i i}}, \mu_{i}+2 \sqrt{\sigma_{i i}}\right)$. Consequently, with a large sample size $n$, we expect the observed proportion $\hat{p}{i 1}$ of the observations lying in the interval $\left(\bar{x}{i}-\sqrt{s_{i i}}, \bar{x}{i}+\sqrt{s{i i}}\right)$ to be about .683. Similarly, the observed proportion $\hat{p}{i 2}$ of the observations in $\left(\bar{x}{i}-2 \sqrt{s_{i i}}, \bar{x}{i}+2 \sqrt{s{i i}}\right)$ should be about 954 . Using the normal approximation to the sampling distribution of $\hat{p}{i}$ (see [9]), we observe that either $$\left|\hat{p}{i 1}-.683\right|>3 \sqrt{\frac{(.683)(.317)}{n}}=\frac{1.396}{\sqrt{n}}$$
or
$$\left|\hat{p}_{i 2}-.954\right|>3 \sqrt{\frac{(.954)(.046)}{n}}=\frac{.628}{\sqrt{n}}$$
would indicate departures from an assumed normal distribution for the $i$ th characteristic. When the observed proportions are too small, parent distributions with thicker tails than the normal are suggested.

## 澳洲代考|多元统计分析代考Multivariate Statistical Analysis代考|DETECTING OUTLIERS AND CLEANING DATA

Most data sets contain one or a few unusual observations that do not seem to belong to the pattern of variability produced by the other observations. With data on a single characteristic, unusual observations are those that are either very large or very small relative to the others. The situation can be more complicated with multivariate data. Before we address the issue of identifying these outliers, we must emphasize that not all outliers are wrong numbers. They may, justifiably, be part of the group and may lead to a better understanding of the phenomena being studied.
Outliers are best detected visually whenever this is possible. When the number of observations $n$ is large, dot plots are not feasible. When the number of characteristics $p$ is large, the large number of scatter plots $p(p-1) / 2$ may prevent viewing them all. Even so, we suggest first visually inspecting the data whenever possible.

## 澳洲代考|多元统计分析代考MULTIVARIATE STATISTICAL ANALYSIS代考|TRANSFORMATIONS TO NEAR NORMALITY

If normality is not a viable assumption, what is the next step? One alternative is to ignore the findings of a normality check and proceed as if the data were normally distributed. This practice is not recommended, since, in many instances, it could lead to incorrect conclusions. A second alternative is to make nonnormal data more “normal looking” by considering transformations of the data. Normal-theory analyses can then be carried out with the suitably transformed data.

Transformations are nothing more than a reexpression of the data in different units. For example, when a histogram of positive observations exhibits a long right-hand tail, transforming the observations by taking their logarithms or square roots will often markedly improve the symmetry about the mean and the approximation to a normal distribution. It frequently happens that the new units provide more natural expressions of the characteristics being studied.

## 澳洲代考|多元统计分析代考MULTIVARIATE STATISTICAL ANALYSIS代考|ASSESSING THE ASSUMPTION OF NORMALITY

or
$$\left|\hat{p}_{i 2}-.954\right|>3 \sqrt{\frac{(.954)(.046)}{n}}=\frac{.628}{\sqrt{n}}$$

## 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。