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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|线性回归代写linear regression代考|One Way Block Designs

Suppose there are $b$ blocks and $n=k b$. The one way Anova design randomly assigns $b$ of the units to each of the $k$ treatments. Blocking places a constraint on the randomization, since within each block of units, exactly one unit is randomly assignèd tó éach ô the $k$ tréatments.

Hence a one way Anova design would use the $R$ command sample(n) and the first $b$ units would be assigned to treatment 1 , the second $b$ units to treatment $2, \ldots$, and the last $b$ units would be assigned to treatment $k$.
For the completely randomized block designs, described below, the command sample(k) is done $b$ times: once for each block. The $i$ th command is for the units of the $i$ th block. If $k=5$ and the sample(b) command yields $\begin{array}{lllll}2 & 5 & 3 & 1 & 4\end{array}$, then the $2 \mathrm{nd}$ unit in the $i$ th block is assigned to treatment 1 , the 5 th unit to treatment 2, the 3rd unit to treatment 3 , the 1 st unit to treatment 4 , and the 4 th unit to treatment 5 .

Remark 7.1. Blocking and randomization often makes the iid error assumption hold to a useful approximation.

For example, if grain is planted in $n$ plots of land, yields tend to be similar (correlated) in adjacent identically treated plots, but the yields from all of the plots vary greatly, and the errors are not iid. If there are 4 treatments and blocks of 4 adjacent plots, then randomized blocking makes the errors approximately iid.

Definition 7.2. For the one way block design or completely randomized block design (CRR $\overline{\mathbf{B}} \mathbf{D})$, there is a factor $A$ with $k$ levels and there are blocks. The CRBD model is
$$Y_{i j}=\mu_{i j}+e_{i j}=\mu+\tau_i+\beta_j+e_{i j}$$
where $\tau_i$ is the $i$ th treatment effect and $\sum_{i=1}^k \tau_i=0, \beta_j$ is the $j$ th block effect and $\sum_{j=1}^b \beta_j=0$. The indices $i=1, \ldots, k$ and $j=1, \ldots, b$.

## 统计代写|线性回归代写linear regression代考|Blocking with the K Way Anova Design

Blocking is used to reduce the MSE so that inference such as tests and confidence intervals are more precise. Below is a partial ANOVA table for a $k$ way Anova design with one block where the degrees of freedom are left blank. For $A$, use $H_0: \mu_{10 \cdots 0}=\cdots=\mu_{l_1 0 \cdots 0}$. The other main effects have similar null hypotheses. For interaction, use $H_0:$ no interaction.

These models get complex rapidly as $k$ and the number of levels $l_i$ increase. As $k$ increases, there are a large number of models to consider. For experiments, usually the 3 way and higher order interactions are not significant. Hence a full model that includes the blocks, all $k$ main effects, and all $\left(\begin{array}{l}k \ 2\end{array}\right)$ two way interactions is a useful starting point for response, residual, and transformation plots. The higher order interactions can be treated as potential terms and checked for significance. As a rule of thumb, significant interactions tend to involve significant main effects.

The following example has one block and 3 factors. Hence there are 3 two way interactions and 1 three way interaction.

Example 7.4. Snedecor and Cochran (1967, pp. 361-364) describe a block design (2 levels) with three factors: food supplements Lysine (4 levels), Methionine (3 levels), and Protein (2 levels). Male pigs were fed the supplements in a $4 \times 3 \times 2$ factorial arrangement and the response was average daily weight gain. The ANOVA table is shown on the following page. The model could be described as $Y_{i j k l}=\mu_{i j k l}+e_{i j k l}$ for $i=1,2,3,4 ; j=1,2,3 ; k=1,2$; and $l=1,2$ where $i, j, k$ are for L,M,P and $l$ is for block. Note that $\mu_{i 000}$ is the mean corresponding to the $i$ th level of $\mathrm{L}$.

# 线性回归代写

## 统计代写|线性回归代写linear -regression代考|单向块设计

7.1.

7.2.

$$Y_{i j}=\mu_{i j}+e_{i j}=\mu+\tau_i+\beta_j+e_{i j}$$
，其中$\tau_i$是$i$第一个处理效果，$\sum_{i=1}^k \tau_i=0, \beta_j$是$j$第一个块效果和$\sum_{j=1}^b \beta_j=0$。索引$i=1, \ldots, k$和$j=1, \ldots, b$。

## 统计代写|线性回归代写线性回归代考|用K – Way Anova设计阻塞

Snedecor和Cochran(1967，第361-364页)描述了一个包含三个因素的块设计(2个水平):食物补充剂赖氨酸(4个水平)，蛋氨酸(3个水平)和蛋白质(2个水平)。公猪以$4 \times 3 \times 2$析因的方式饲喂，反应为平均日增重。方差分析表如下页所示。该模型可以描述为$i=1,2,3,4 ; j=1,2,3 ; k=1,2$的$Y_{i j k l}=\mu_{i j k l}+e_{i j k l}$;和$l=1,2$，其中$i, j, k$代表L,M,P, $l$代表块。请注意，$\mu_{i 000}$是$\mathrm{L}$的$i$第th级对应的平均值

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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