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统计代写|实验设计作业代写experimental design代考|ASSESSING THE TREATMENT MEANS

Posted on 2022年5月2日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

statistics-lab™ 为您的留学生涯保驾护航在代写实验设计experimental designatistical Modelling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。我们的专家在代写实验设计experimental design代写方面经验极为丰富，各种代写实验设计experimental design相关的作业也就用不着说。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|ASSESSING THE TREATMENT MEANS

In the last chapter we desoribed the linear model for a simple experiment, found estimates of the parameters, and described a test for the hypothesis that there $1 s$ no overall treatment effect. In this chapter we cover the next step of examining more closely the pattern of differences among the treatment means. There are a number of approaches, One extreme is to test only the hypotheses framed before the experiment was carried out, but this approach wastes much of the information from the experiment. On the other hand, to carry out conventional hypothesis tests on every effect that looks interesting can be very misleading, for reasons which we now examine.
There are three main difflculties. First, two tests based on the same experiment are unlikely to be independent. Tests will usually involve the same estimate of variance, and if this estimate happens to be too small, every test will be too significant. Further, any comparisons involving the same means will be affected the same way by chance differences between estimate and parameter. As an example consider a case where there are three treatments assessing a new drug. Treatment “A” is the placebo, treatment ” $B^{H}$ the drug administered in one big dose and treatment “C” the orug administered in two half doses. If chance variation happens to make the number of cures on the experimental units using the placebo (A) rather low, the differences between $A$ and $B$, and $A$ and $C$ will both be overstated in the same way. Therefore two significant t-tests, one between $A$ and $B$, the other between $A$ and $C$, cannot be taken as independent corroboration of the effectiveness of the drug.

统计代写|实验设计作业代写experimental design代考|SPECIFIC HYPOTHESES

Any experiment should be designed to answer specif ic questions. If these questions are stated clearly it will be possible to construct a single linear function of the treatment means which answers each question. It can be a difficult for the statistician to discover what these questions are, but this type of problem is beyond the scope of this book. We will present some examples.
Example 6.2+1 Drug comparison example
In the drug comparison experiment mentioned in Section 1 one question might be, is the drug effective? Rather than doing two separate

tests ( $A \vee B$ and A $\vee$ C), a single test of $A$ against the average of $B$ and $C$ gives an unambiguous answer which uses all the relevant data. That is use
$\bar{y}{A}-\left(\bar{y}{B}+\bar{y}{C}\right) / 2$ with variance $\left[1 / r{A}+\left(1 / r_{B}+1 / r_{B}\right) / 4\right] \sigma^{2}$
Having decided that the drug has an effect the next question may be, how much better is two half doses than one complete dose. This will be estimated by the difference between treatment means for $B$ and C. For inferences remember that $\sigma^{2}$ is estimated by $s^{2}$, and this appears with its degrees of freedom in the ANOVA table.

统计代写|实验设计作业代写experimental design代考|Exper imentwise Error Rate

The above are examples of inferences to answer specific questions. Each individual inference will be correot, but there are several inferences being made on each experiment. If all four suggested comparisons were made on the fertilizer experiment, the probability of making at least one type I error will be much higher than the signif icance level of an individual test. If the traditional $5 \%$ level is used, and there are no treatment effeots at all, and the individual tests were independent, the number of significant results from the experiment would be a binomial random variable with $n=4$ and $p=.05$. The probability of no significant results will be $(1-0.05)^{4}$, so that the probability of at least one will be $1-(1-0.05)^{4}=$ 0.185. If one really wanted to have the error rate per experiment equal to $0.05$ each individual test would have to use a significance level, $p$, satisfying
$$
\begin{aligned}
1-(1-p)^{4} &=0.05 \
\text { or } & p=0.013
\end{aligned}
$$

Unfortunately, the underlying assumptions are false because, as we noted in Section 1, each inference is not independent. The correlation between test statistics will usually be positive because each depends on the same variance estimate, and so the probability of all four being nonsignificant w1ll be greater than that calculated above and so the value of p given above will be too low. If the error rate per experiment is important, the above procedure at least provides a lower bound. Usually though it is suffleient to be suspicious of experiments producing many significant results, particularly if the var fance estimate $1 s$ based on rather few degrees of freedom and is smaller than is usually found in similar experiments. Experimenters should not necessarily be congratulated on obtaining many significant results.

In section 1, another source of dependence was mentioned. This results from the same treatment means being used in different conparisons. If the questions being asked are themselves not independent, the inferences cannot be either. However, it is possible to design a treatment structure so that independent questions can be assessed independently. This will be the topic of the next section.

实验设计代考

统计代写|实验设计作业代写experimental design代考|ASSESSING THE TREATMENT MEANS

在上一章中，我们为一个简单的实验解构了线性模型，找到了参数的估计值，并描述了对假设的检验1s没有整体治疗效果。在本章中，我们将讨论更仔细地研究治疗手段之间差异模式的下一步。有许多方法，一个极端是只测试在进行实验之前构建的假设，但是这种方法浪费了实验中的大部分信息。另一方面，对每一个看起来很有趣的效应进行传统的假设检验可能会产生很大的误导性，原因我们现在要研究。
主要有三个难点。首先，基于同一实验的两个测试不太可能是独立的。测试通常会涉及相同的方差估计，如果这个估计恰好太小，每个测试都会太显着。此外，任何涉及相同均值的比较都会受到估计值和参数之间的偶然差异的相同影响。作为一个例子，考虑一个案例，其中有三种治疗方法来评估一种新药。治疗“A”是安慰剂，治疗“乙H药物以大剂量给药，治疗“C” orug 以两个半剂量给药。如果偶然变化恰好使使用安慰剂 (A) 的实验单位的治愈次数相当低，则一种和乙，和一种和C两者都会以同样的方式被夸大。因此，两个显着的 t 检验，一个介于一种和乙, 另一个之间一种和C，不能作为药物有效性的独立佐证。

统计代写|实验设计作业代写experimental design代考|SPECIFIC HYPOTHESES

任何实验都应该旨在回答特定的问题。如果清楚地说明这些问题，则可以构建回答每个问题的治疗手段的单个线性函数。统计学家可能很难发现这些问题是什么，但这类问题超出了本书的范围。我们将介绍一些例子。
示例 6.2+1 药物比较示例
在第 1 节中提到的药物比较实验中，一个问题可能是，药物有效吗？而不是做两个单独的

测试（一种∨乙和一个∨C)、单次测试一种反对平均水平乙和C给出一个使用所有相关数据的明确答案。那就是使用
是的¯一种−(是的¯乙+是的¯C)/2有差异[1/r一种+(1/r乙+1/r乙)/4]σ2
确定药物有效果后，下一个问题可能是，两个半剂量比一个完整剂量好多少。这将通过治疗手段之间的差异来估计乙和 C. 对于推论，请记住σ2估计为s2, 这在 ANOVA 表中显示为它的自由度。

统计代写|实验设计作业代写experimental design代考|Exper imentwise Error Rate

以上是回答特定问题的推理示例。每个单独的推论都是正确的，但每个实验都有几个推论。如果所有四个建议的比较都在肥料实验中进行，那么犯至少一个 I 类错误的概率将远高于单个测试的显着性水平。如果传统5%使用水平，并且根本没有治疗效果，并且各个测试是独立的，实验中显着结果的数量将是一个二项式随机变量n=4和p=.05. 没有显着结果的概率为(1−0.05)4, 所以至少有一个的概率是1−(1−0.05)4=0.185。如果真的想让每个实验的错误率等于0.05每个单独的测试都必须使用显着性水平，p, 满足
1−(1−p)4=0.05 或者 p=0.013

不幸的是，基本假设是错误的，因为正如我们在第 1 节中所指出的，每个推论都不是独立的。检验统计量之间的相关性通常是正的，因为每个都依赖于相同的方差估计，因此所有四个不显着的概率将大于上面计算的概率，因此上面给出的 p 值将太低。如果每次实验的错误率很重要，则上述程序至少提供了一个下限。通常，尽管对产生许多重要结果的实验持怀疑态度是无足轻重的，特别是如果 var fance 估计1s基于相当少的自由度，并且比通常在类似实验中发现的要小。不一定要祝贺实验者获得了许多重要的结果。

在第 1 节中，提到了另一个依赖来源。这是由于在不同的比较中使用了相同的处理手段。如果被问的问题本身不是独立的，那么推论也不能是独立的。但是，可以设计一个处理结构，以便可以独立评估独立问题。这将是下一节的主题。

统计代写|实验设计作业代写experimental design代考请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。

有限元方法代写

有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

随机分析代写

随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

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，工具箱允许您学习和应用专业技术。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。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|实验设计作业代写experimental design代考|THE EXPERIMENTAL DESIGN MODEL

Posted on 2022年5月2日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|THE EXPERIMENTAL DESIGN MODEL

Back in Chapter 1, Section 1, it was explained that the aim of all the work so far is to fit models to a population using data from a sample. The model so fitted shows what values of $y$ are 1 kely to be associated with any given values of the $x$ ‘s. Just as any elementary statistics text will warn that a correlation does not imply causation, so a well fltting regression model does not imply that changes in the $x$ values will cause changes in the y variable in’ accordance the with model. If the model has been constructed by passive observation of sets of $y^{\prime} s$ and $x^{\prime} s$, any intervention to change the $x$ values to values which do not occur naturally will change the population to be something different from what the model describes, and so the model no longer applies.
In an experiment a population is not passively observed, but the $x$ values are the result of intervention by the experimenter. The aim then is to intervene to choose $x$ values in such a way as to give accurate estimates of the model parameters with a minimum of effort, and to ensure that the relationships described by the model really do describe the way changes in $y$ are caused by changes in $x$.

统计代写|实验设计作业代写experimental design代考|WHAT MAKES AN EXPERIMENT?

One of the 1 argest experiments ever conducted makes an interesting example, partly because it was almost a disaster. The experiment was designed to test the effectiveness of the Salk polio vacoine, and was conducted in the United States in 1954 . A good account of the experiment is in Freedman, Pisani, and Purves, 1978 . There were two difficulties with the experiment. First, polio is a relatively uncommon disease, The vacoine can only be tested if 1 t is tried on a group large enough to contain a reasonable number of polio victims. For the common cold a fer hundred people would be plent y, but for pol1o several hundred thousand were required. Second, polio is a disease which comes and goes from one season to the next. With the common cold, which most people catch most years, if the incidence drops in a test group after administering a vaccine, the drop can probably be attributed to the vacoine. But not so with polio = 1 t may well have been a year in which the disease would have waned anyway.
The original experimental plan for the polio vaccine was to vaccinate second year school children and compare their incidence of polio with that of first and third year children. The intention is clear. The children being compared should be as alike as possible, and this plan would ensure that the geographical area and the time period would be the same for both groups. Of course they would be of different ages, but since the ages of the untreated group brackets that of the treated group one might not expect this to matter too much. A large number of experts must have considered that these remaining differences would not matter because this experiment was put into effect. 221,998 children were vaceinated, 725, 173 here not, and the rate of polio following vaccination was about twice as great $1 n$ the unvaceinated group as in the vaccinated group, $(54$ per 100,000 instead of 25 ).

统计代写|实验设计作业代写experimental design代考|Experimental Unit

We will define an experimental unit as that object or group of objects to which a treatment has been randomly assigned. Some examples will make this definftion clear. An educationalist may be comparing teaching methods. Each child is given a test after being taught by the method assigned to $1 \mathrm{t}$, so there is one observation per child. However the child is only an experimental unit if each child were individually assigned to a teaching method. If the children were first divided into small groups, and groups were assigned randomly to teaching method, then the group would become an experimental unft and the observation on it would be the average of all the observations on the individual children. If the two classes were used, each randomly assigned to a teaching method, a class would be an experimental unit, and because there would be no replication, no assessment would be possible. In an experiment comparing weedicides, various combinations of weedicides are randomly assigned to $5 \mathrm{~m} \times 2 \mathrm{~m}$ areas. Within each of these areas $f$ ive $+25 \mathrm{~m} x+25 \mathrm{~m}$ quadrats,

positioned at random, are examined for percent weed cover. This is a very common type of biological experiment, and one where our definition of experimental units is important. The weedicides were assigned to the $5 \mathrm{~m} \times 2 \mathrm{~m}$ areas, and so these are the experimental units, not the $.25 \mathrm{~m} \times .25 \mathrm{~m}$ quadrats.
As a very general and 1 mportant principle, remember that any treatment comparison must be based on one number per experimental unit. This number might often be a mean of several observations, but one must beware of pretending that by increasing the number of subsamples one can increase the replication. It is experimental units which must be replicated.

实验设计代考

统计代写|实验设计作业代写experimental design代考|THE EXPERIMENTAL DESIGN MODEL

回到第 1 章第 1 节，已经解释过到目前为止所有工作的目的是使用来自样本的数据将模型拟合到总体。如此拟合的模型显示了是的是 1 主要与任何给定的值相关联X的。正如任何基本统计文本都会警告相关性并不意味着因果关系一样，一个良好的拟合回归模型并不意味着X值将根据 with 模型导致 y 变量发生变化。如果模型是通过被动观察是的′s和X′s, 任何改变X非自然发生的值将改变总体，使其与模型描述的不同，因此模型不再适用。
在实验中，群体不是被动观察的，而是X值是实验者干预的结果。然后的目的是干预以选择X以最小的努力给出模型参数的准确估计，并确保模型描述的关系确实描述了模型参数的变化方式是的是由变化引起的X.

统计代写|实验设计作业代写experimental design代考|WHAT MAKES AN EXPERIMENT?

有史以来最大的实验之一就是一个有趣的例子，部分原因是它几乎是一场灾难。该实验旨在测试 Salk polio vacoine 的有效性，并于 1954 年在美国进行。Freedman、Pisani 和 Purves，1978 年对该实验进行了很好的说明。实验有两个困难。首先，脊髓灰质炎是一种相对少见的疾病，只有在一个足以容纳合理数量的脊髓灰质炎受害者的群体上试用 1 t 才能测试 vacoine。对于普通感冒，一百人就足够了，但对于 pol1o，则需要数十万人。其次，脊髓灰质炎是一种从一个季节到下一个季节来来去去的疾病。对于大多数人大多数年都感染的普通感冒，如果在接种疫苗后测试组的发病率下降，下降可能归因于 vacoine。但小儿麻痹症并非如此 = 1 t 很可能是该疾病无论如何都会减弱的一年。
脊髓灰质炎疫苗最初的实验计划是为二年级的学童接种疫苗，并将他们的脊髓灰质炎发病率与一年级和三年级儿童的发病率进行比较。意图很明确。被比较的孩子应该尽可能相似，这个计划将确保两组的地理区域和时间段相同。当然，他们的年龄会不同，但由于未治疗组的年龄包含治疗组的年龄，因此人们可能不会认为这有太大影响。一定有很多专家认为，这些剩余的差异并不重要，因为这个实验已经生效了。221,998 名儿童接种了疫苗，725 名，173 名未接种疫苗，接种后小儿麻痹症的发病率大约是其两倍1n未接种组与接种组相同，(54每 100,000 人而不是 25 人）。

统计代写|实验设计作业代写experimental design代考|Experimental Unit

我们将实验单元定义为随机分配处理的对象或对象组。一些例子将使这个定义变得清晰。教育家可能会比较教学方法。在按照分配给每个孩子的方法进行教学后，每个孩子都会接受一次测试1吨，所以每个孩子有一个观察值。然而，如果每个孩子都被单独分配到一种教学方法，那么孩子只是一个实验单元。如果先把孩子分成小组，然后随机分配到教学方法的小组，那么小组将成为一个实验性的小组，对它的观察将是对单个孩子的所有观察的平均值。如果使用两个班级，每个班级随机分配一种教学方法，一个班级就是一个实验单元，因为没有复制，所以不可能进行评估。在一项比较除草剂的实验中，各种除草剂组合被随机分配到5 米×2 米领域。在这些区域中的每一个F我有+25 米X+25 米正方形，

随机放置，检查杂草覆盖率。这是一种非常常见的生物实验类型，我们对实验单位的定义很重要。除草剂被分配到5 米×2 米地区，所以这些是实验单位，而不是.25 米×.25 米样方。
作为一个非常普遍且重要的原则，请记住，任何治疗比较都必须基于每个实验单位的一个数字。这个数字通常可能是多个观察值的平均值，但必须注意不要假装通过增加子样本的数量可以增加复制。它是必须复制的实验单元。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|实验设计作业代写experimental design代考| AGGREGATION OF DATA

Posted on 2022年5月1日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|AGGREGATION OF DATA

The dummy variable approach of the previous section provides one method of combining together different sets of data. In other situations $1 \mathrm{t}$ may be appropriate to merely sum or average data sets, but it is wise to tread warily for the pattern followed by an individual data set may be quite different from that of the aggregate of the data sets. Aggregation sometimes gives rather disturbing and nonsensical results. Consider Figure $3.9 .1$ in which there is a slight overall downwards trend in the $y$ values as the $x$ values inorease. If there are, as shown, three identifiable subgroups in the data, they may, in fact, suggest a positive trend within each group. In this example, it would be spurious to aggregate the groups. One overall model could be used provided that dummy variables were included to distinguish the $y$-intercepts of each group.
For the lactation records of Appendix $C 3$, it would be useful to fit an overall model to the aggregated data of the five cows. One approach may be to fit a model to each cow’s yield and then to average the estimated coefficients. Problems remain, however, for the model with these averaged coefficients may not fit well any of the individual data sets. Another approach is to average the sets of values of the dependent variable. With different patterns of ylelds, one must ask whether this aggregation is a reasonable thing to do. For example, the maximum yield for cow no, 1 occurred in the sixth week, but for cow no. 5 it occurred in the ninth week. Perhaps the data for each cow should be lagged so that the maxima correspond, and then the appropriate milk yields added (that is $16.30$ of cow no. 1 added to $31.27$ of cow no. 2 etc.). This would ensure that the maxima correspond, but it does not take into account the different shapes of the graphs or that one cow may give milk for a longer time than another. (For convenience, the lactation records here were all truncated to 38 weeks even though some actually gave milk for a longer period).

统计代写|实验设计作业代写experimental design代考|PECULIARITIES OF OBSERVATIONS

In Chapter 3 we considered the relationship between variables $\mathbf{y}$ and $X=\left(x_{1}, x_{2}, \ldots, x_{k}\right)$, that $1 s$, the relationship between the column vectors. In this chapter, we turn our attention to the rows or individual data points
$$
\left(x_{11}, x_{2 i}, \ldots, x_{k i}, y_{1}\right)
$$
We have already seen that the variances of the predicted values and of the residuals depend on the particular values of the predictor variables, $x$. Peculiar values of the $x^{\prime} s$ could be termed sensitive, or high leverage, points as will be explained in Section 2. On the other hand, the observed value of $y$ may be unusual for a given set of $x$ values and y may then be termed an outlier as explained in Section $3 .$
Also, in Sections 6 through 8 , the emphasis is again on the variables in the model and perhaps these topios, more logically, should fall into Chapter 3. They have been added for completeness as they are topics often referred to in other texts.

统计代写|实验设计作业代写experimental design代考|OUTLIERS

Both the prediotor and dependent variables will have their parts to play $1 n$ deciding whether an observation $1 s$ unusual. The predictor variables determine whether a point has hfgh leverage. The value of the dependent variable, $y$, for a given set of $x$ values will determine whether the point is an outlier.

Finst, we consider the residuals, or preferably the studentized residuals. As explained in section 1.3, it is good practice to plot the residuals against the predioted values of $y$ and the predictor variables which are already in the model or which are being considered for inelusion $1 n$ the model. A studentized residual of large absolute value may suggest that an error of measurement or of coding or some such has occurred in the response variable. If the sample size is reasonably large, the observation could be deleted from the analys1s. It is always worthwhile, though, to consider such outliers

very carefully for they may suggest conditions under whioh the model is not valid.

It should be noted that the size of the residuals depends on the model which is fitted. If more, or different, predictor variables are included in the model then it is likely that different points will show up as being potential outliers. It is not possible, then, to completely divorce the detection of outliers from the search for the best model.

Outliers may also be obscured by the presence of points of high leverage for these tend to constrain the prediction curve to pass close to their associated y values. These interrelated effects should warn us to tread cautiously as there is no guaranteed failsafe approach to the problem. Many solutions have been suggested and the interested reader may consult Hoaglin and Welsch (1978). We shall not consider the tests in detail which are contained in this article. To decide whether the i-th observation is an outlier, a fruitful approach is to see the effect that would result from the omission of the 1 -th row of the data. In particular, how would this omission affect the residual at the point and how would it affect the slope of the prediction line?

实验设计代考

统计代写|实验设计作业代写experimental design代考|AGGREGATION OF DATA

上一节的虚拟变量方法提供了一种将不同数据集组合在一起的方法。在其他情况下1吨可能仅适用于汇总或平均数据集，但明智的做法是谨慎行事，因为单个数据集所遵循的模式可能与数据集聚合的模式完全不同。聚合有时会产生相当令人不安和荒谬的结果。考虑图3.9.1其中整体呈小幅下降趋势是的值作为X价值观。如图所示，如果数据中有三个可识别的子组，实际上它们可能表明每个组内都有积极的趋势。在此示例中，聚合组是虚假的。可以使用一个整体模型，前提是包含虚拟变量来区分是的- 每组的截距。
对于附录的泌乳记录C3，将整体模型拟合到五头奶牛的聚合数据中会很有用。一种方法可能是将模型拟合到每头奶牛的产量，然后对估计的系数进行平均。然而，问题仍然存在，因为具有这些平均系数的模型可能无法很好地拟合任何单个数据集。另一种方法是平均因变量的值集。对于不同的 yeld 模式，人们必须问这种聚合是否合理。例如，第 1 号奶牛的最大产量出现在第六周，但第 1 号奶牛的最大产量发生在第 6 周。5 它发生在第九周。也许每头奶牛的数据应该滞后以便最大值对应，然后添加适当的牛奶产量（即16.30牛号 1 添加到31.27牛号 2等）。这将确保最大值对应，但它没有考虑图表的不同形状，或者一头奶牛可能比另一头奶牛产奶的时间更长。（为方便起见，这里的哺乳记录都被截断为 38 周，尽管有些人实际上喂奶的时间更长）。

统计代写|实验设计作业代写experimental design代考|PECULIARITIES OF OBSERVATIONS

在第 3 章中，我们考虑了变量之间的关系是的和X=(X1,X2,…,Xķ)，那1s，列向量之间的关系。在本章中，我们将注意力转向行或单个数据点
(X11,X2一世,…,Xķ一世,是的1)
我们已经看到，预测值和残差的方差取决于预测变量的特定值，X. 独特的价值观X′s可以称为敏感点或高杠杆点，这将在第 2 节中解释。另一方面，观察到的值是的对于给定的一组可能是不寻常的X值和 y 可以称为异常值，如第 1 节所述3.
此外，在第 6 节到第 8 节中，重点再次放在模型中的变量上，从逻辑上讲，这些主题应该属于第 3 章。为了完整起见，添加了它们，因为它们是其他文本中经常提到的主题。

统计代写|实验设计作业代写experimental design代考|OUTLIERS

prediotor 和因变量都将发挥作用1n决定是否观察1s异常。预测变量确定一个点是否具有 hfgh 杠杆。因变量的值，是的, 对于给定的一组X值将确定该点是否为异常值。

Finst，我们考虑残差，或者最好是学生化的残差。如第 1.3 节所述，将残差与是的以及已经在模型中或正在考虑排除的预测变量1n该模型。绝对值较大的学生化残差可能表明响应变量中出现了测量或编码错误等。如果样本量相当大，则可以从分析中删除观察值。不过，考虑这些异常值总是值得的

非常小心，因为他们可能会建议模型无效的条件。

应该注意的是，残差的大小取决于拟合的模型。如果模型中包含更多或不同的预测变量，那么不同的点很可能会显示为潜在的异常值。因此，将异常值的检测与寻找最佳模型完全分开是不可能的。

异常值也可能被高杠杆点的存在所掩盖，因为这些点往往会限制预测曲线接近其相关的 y 值。这些相互关联的影响应该警告我们要谨慎行事，因为没有保证可以解决问题的故障安全方法。已经提出了许多解决方案，感兴趣的读者可以参考 Hoaglin 和 Welsch (1978)。我们将不详细考虑本文中包含的测试。要确定第 i 个观察值是否为异常值，一个富有成效的方法是查看遗漏第 1 行数据所产生的影响。特别是，这种遗漏将如何影响该点的残差以及它将如何影响预测线的斜率？

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|实验设计作业代写experimental design代考| Forward Selection

Posted on 2022年5月1日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|Forward Selection

We shall use the heart data of the last two sections to illustrate this. In section 3.5, this data is written in correlation form. If the model is to include only one predictor variable, then $B$ would be chosen as it gives the highest SSR which is also the correlation coefficient with $y$. Before B is placed in the model, we test that it has a significant effect on $y$ by using an $F$-test, or equivalently, a t-test.
We test $\mathrm{H}: B_{2}=0$ in the model $y=B_{0}+B_{2} x_{2}+\varepsilon$
$$
F=(S S R / 1) /(\mathrm{SSE} / 44)=0.657 /(0.342 / 44)=84.7
$$
Clearly, we reject $H$ and include $x_{2}$ in the model. We now try to add

another predictor variable to the model. We look for the variable which, with B, gives the nighest value of SSR. From Table 3.6.1, we see that SSR for $B$ and $C=0.715$ which $1 s$ greater than for $A B=$ $0.667, \mathrm{BD}=0.686, \mathrm{FB}=0.676$, and $\mathrm{BE}=0.659$. Does $\mathrm{C}$ add significantly to SSR over and above B itself? We use the method of reduced models to determine this.
Full model: $y=\beta_{0}+\beta_{2} x_{2}+B_{3} x_{3}+\varepsilon ; \quad$ SSE $=0.285$
Reduced model: $y=\beta_{0}+\beta_{2} x_{2}+\varepsilon ; \quad$ SSE $=0.342$
Difference $=0.05 ?$
$F=0.057 /(0.285 / 43)=8.6$
The tabulated $F$ at $5 \%$ level with 1,43 degrees of freedom = $4.190$ that we reject the reduced model in favor of the full model. We then attempt to add a third variable to the model. The vari= able which adds most to SSR in association with $B$ and $C$ is D as BCD gives an $\mathrm{SSR}=0.718 .$ An $\mathrm{F}$ statistic is evaluated to determine whether $D$ adds significantly to SSR over and above $B$ and $C$.

Ful1 mode1: $y=\beta_{0}+\beta_{2} x_{2}+B_{3} x_{3}+B_{4} x_{4}+\varepsilon ; S S E=0.282$
Reduced model: $y=\beta_{0}+\beta_{2} x_{2}+\beta_{3} x_{3}+E ; \quad$ SSE $=0,285$
Difference $=0.003$
$$
F=0.003 /(0.282 / 42)=0.4
$$
Clearly this is too small to reject the reduced model and we select as the optimal model that with B and $C$ as predictor variables.

统计代写|实验设计作业代写experimental design代考|Backward Elimination

Another approach is to commence with the full model of six prediotor variables and to attempt to remove variables sequentially. In Table 3.6.1, the five predictor model with the greatest SSR Is BCDEF $0.749$ or SSE $=0.251$. To declde if A should be removed, we conpare this SSE with that of the full model using the F statistio.
$$
F=(0.251-0.247) /(0.247 / 39)=0.004 /(0.247 / 39)=0.6
$$

Clearly, the effect of $A$ is not significant and can be removed. We look to remove one of these remaining five variables by considering the SSR for each of the four predictor models. These are:
$\mathrm{BCDE}=0.719, \quad \mathrm{CDEF}=0.703, \quad \mathrm{BDEF}=0.712, \quad \mathrm{FBCD}=0.721$
and $\mathrm{BEFC}=0.741$
We choose this last one with $D$ omitted and test whether this causes a significant reduction in SSR. The full model is now BCDEF and the reduced model is BCEF.
$$
F=0.008 /(0.251 / 40)=1.3
$$
This value is low compared with the $5 \%$ tabulated value for 1 and 40 degrees of freedom which equals $4.08$ so that we proceed to eliminate a further variable. The three variable sums of squares are
$$
C E F=0.684, \quad F B C=0.717, \quad B E F=0.704, \quad E B C=0.717
$$
For either of the models with SSR $=0.717$,
$$
E=0.024 /(0.259 / 41)=3.8
$$
This is slightly below the oritical value of $4.08$ so that we proceed and compare these two models, FBC and $\mathrm{EBC}$, with $\mathrm{BC}$ the last subset of these with two variables.
$$
F=0.002 /(0.283 / 42)=0.3
$$
We are then reduced to the model BC as in the forwand selection process.
There are a number of points to notice about these sequential methods.

统计代写|实验设计作业代写experimental design代考|QUALITATIVE (DUMMY) VARIABLES

It is of ten useful to introduce variables into a model to enable certain specifio effects to be revealed and tested. Usually these take the form of qualitative variables which show up the differences

between subgroups in the data. We shall use an example to explore these ideas.

In Example 1.5.1, we listed the value of an Australian stamp (1963 twopenny sepia coloured in the years 1972-1980). We could compare this with the listed value of another stamp, and for few obvious reasons, we have chosen the 1867 New Zealand fourpenny rose colored full face queen. We shall use the same transformation as before, namely
$$
y_{1}=\ln v_{t}, y_{2}=\ln v_{t}
$$
for the Australian and New zealand stamp respectively. The data is given in Table 3.8.1. We could $f$ it a separate model to each stamp, that is, for the Australian stamp
$$
y_{1}=a_{1} 1+\alpha_{2} t_{1}+\varepsilon_{1}
$$
and the New Zealand stamp
$$
\boldsymbol{y}{2}=B{1} \mathbf{1}+B_{2} \mathrm{t}{2}+\varepsilon{2}
$$
If the distributions of the deviations can be assumed to be the same, it will be adrisable to join these models into a single model.

实验设计代考

统计代写|实验设计作业代写experimental design代考|Forward Selection

我们将使用最后两节的心脏数据来说明这一点。在 3.5 节中，该数据以相关形式编写。如果模型只包含一个预测变量，那么乙将被选择，因为它给出了最高的 SSR，这也是与是的. 在将 B 放入模型之前，我们测试它对是的通过使用F-test 或等效的 t 检验。
我们测试H:乙2=0在模型中是的=乙0+乙2X2+e
F=(小号小号R/1)/(小号小号和/44)=0.657/(0.342/44)=84.7
很明显，我们拒绝H并包括X2在模型中。我们现在尝试添加

模型的另一个预测变量。我们寻找与 B 一起给出 SSR 最接近值的变量。从表 3.6.1 中，我们看到 SSR 为乙和C=0.715哪一个1s大于一种乙= 0.667,乙D=0.686,F乙=0.676，和乙和=0.659. 做C除了 B 本身之外，还显着增加了 SSR？我们使用简化模型的方法来确定这一点。
完整型号：是的=b0+b2X2+乙3X3+e;上证所=0.285
缩小型号：是的=b0+b2X2+e;上证所=0.342
不同之处=0.05?
F=0.057/(0.285/43)=8.6
列表中的F在5%自由度为 1,43 的水平 =4.190我们拒绝简化模型而支持完整模型。然后我们尝试将第三个变量添加到模型中。对 SSR 增加最多的变量乙和C是 D，因为 BCD 给出了小号小号R=0.718.一个F统计数据被评估以确定是否D大大增加了 SSR乙和C.

全模式1：是的=b0+b2X2+乙3X3+乙4X4+e;小号小号和=0.282
缩小型号：是的=b0+b2X2+b3X3+和;上证所=0,285
不同之处=0.003
F=0.003/(0.282/42)=0.4
显然，这太小而无法拒绝简化模型，我们选择 B 和C作为预测变量。

统计代写|实验设计作业代写experimental design代考|Backward Elimination

另一种方法是从六个前因子变量的完整模型开始，并尝试依次删除变量。在表 3.6.1 中，SSR 最大的五个预测模型是 BCDEF0.749或上证所=0.251. 为了确定是否应该删除 A，我们使用 F 统计量将此 SSE 与完整模型的 SSE 进行比较。
F=(0.251−0.247)/(0.247/39)=0.004/(0.247/39)=0.6

很明显，效果一种不重要，可以删除。我们希望通过考虑四个预测模型中的每一个的 SSR 来删除剩余的五个变量之一。这些都是：
乙CD和=0.719,CD和F=0.703,乙D和F=0.712,F乙CD=0.721
和乙和FC=0.741
我们选择最后一个D省略并测试这是否会导致 SSR 显着降低。完整模型现在是 BCDEF，简化模型是 BCEF。
F=0.008/(0.251/40)=1.3
这个值是比较低的5%1 和 40 自由度的列表值，等于4.08以便我们继续消除另一个变量。三个变量平方和是
C和F=0.684,F乙C=0.717,乙和F=0.704,和乙C=0.717
对于带有 SSR 的任一型号=0.717,
和=0.024/(0.259/41)=3.8
略低于原值4.08以便我们继续比较这两个模型，FBC 和和乙C，和乙C这些的最后一个子集有两个变量。
F=0.002/(0.283/42)=0.3
然后我们被简化为模型 BC，就像在前锋选择过程中一样。
关于这些顺序方法，有许多需要注意的地方。

统计代写|实验设计作业代写experimental design代考|QUALITATIVE (DUMMY) VARIABLES

将变量引入模型以显示和测试某些特定效果是非常有用的。通常这些采用显示差异的定性变量的形式

数据中的子组之间。我们将用一个例子来探索这些想法。

在示例 1.5.1 中，我们列出了澳大利亚邮票的价值（1963 年两便士棕褐色，1972-1980 年）。我们可以将其与另一张邮票的上市价值进行比较，出于几个明显的原因，我们选择了 1867 年新西兰四便士玫瑰色全脸女王。我们将使用与之前相同的变换，即
是的1=ln⁡在吨,是的2=ln⁡在吨
分别为澳大利亚和新西兰邮票。数据见表 3.8.1。我们可以F每个邮票都有一个单独的模型，即澳大利亚邮票
是的1=一种11+一种2吨1+e1
和新西兰邮票
是的2=乙11+乙2吨2+e2
如果可以假设偏差的分布是相同的，那么将这些模型合并为一个模型将是可取的。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|实验设计作业代写experimental design代考|CORRELATION FORM

Posted on 2022年4月30日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|CORRELATION FORM

When the main concern is to decide which variables to include in the model, a very useful transformation of the data is to scale each variable, predictors and dependent variables alike, so that the normal equations can be written in correlation form. This enables us to identify important variables which should be included in the model and it also reveals some of the dependenoles between the predictor variables.

As usual, we consider the variables to be in deviation form. The correlation coefficient between $x_{1}$ and $x_{2}$ is
$$
\left.\left.r_{12}=s_{12} / \sqrt{\left(s_{11}\right.} s_{22}\right)=\sum x_{1} x_{2} / \sqrt{\left(s_{11}\right.} s_{22}\right)
$$
If we divide each variable $x_{1}$ by $\sqrt{S}{11}$ and denote the result as $$ x{1}^{}=x_{1} / \sqrt{s}{1 i} $$ then $x{i}^{}$ is said to be in correlation form. Notice that
$$
\Sigma x_{i}^{}=0 $$ $$ \Sigma\left(x_{i}^{}\right)^{2}=1
$$
$$
\Sigma x_{i}^{} x_{j}^{}=r_{1 j}
$$
We have transformed the model from

$$
y=B_{1} x_{1}+B_{2} x_{2}+\varepsilon \text { to } y^{}=\alpha_{1} x_{1}^{}+\alpha_{2} x_{2}^{*}+\varepsilon
$$
and the normal equations simplify from
$$
\begin{aligned}
&s_{11} b_{1}+s_{12} b_{2}=s_{y 1} \
&s_{12} b_{1}+s_{22} b_{2}=s_{y 2}
\end{aligned} \text { to } \quad r_{12} a_{1}+r_{12}+a_{2}=r_{y 1}=r_{y 2} \quad \text { (3.5.3) }
$$

统计代写|实验设计作业代写experimental design代考|VARIABLE SELECTION – ALL POSSIBLE REGRESSIONS

In many situations, researchers know which variables may be included in the predictor model. There is some advantage in reducing the number of predictor variables to form a more parsimonious model. One way to achieve this is to run all possible regressions and to consider such statistics as the coefficient of determination, $R^{2}=$ SSR/SST.
We will use the heart data of Section 3.5, again relabelling the variables as A through $F$. With the variables in correlation form, $R^{2}=S S R$, the sum of squares for regression, and this is given for each possible combination of predictor variables in Table $3.6 .1$.

To assist the choice of the best subset, C.L. Mallows suggested fitting all possible models and evaluating the statistic
$$
C_{p}=S S E_{p} / s^{2}-(n-2 p)
$$
Here, $n$ is the number of observations and $p$ is the number of predictor variables in the subset, including a constant term. For each subset, the value of Mallows’ statistio can be evaluated from the correponding value of SSR. The complete set of these statistics are listed in Table 3.6.2. For each subset we use the mean squared error, MSE, of the full model as an estimate of the variance.

Suppose that the true model has q predictor variables.

统计代写|实验设计作业代写experimental design代考|VARIABLE SELECTION – SEQUENTIAL METHODS

When the number of possible variables in a model is large, it may be inappropriate to run every possible regression and evaluate Mallows’ statistic for each one, even though short cuts can be taken to evaluate such statistios by adding or subtracting terms rather than by evaluating each one from scratch.

Another approach is to add, or remove, variables, sequentially. We have seen that adding a variable will increase SSR, the sum of squares for regression. From Section $3.4$ we could perform an F-test to decide if the increase in SSR is si gnificant. The first method we consider is that of forward selection.

实验设计代考

统计代写|实验设计作业代写experimental design代考|CORRELATION FORM

当主要关心的是决定模型中包含哪些变量时，一个非常有用的数据转换是缩放每个变量、预测变量和因变量等，以便可以以相关形式编写正规方程。这使我们能够识别应该包含在模型中的重要变量，它还揭示了预测变量之间的一些依赖关系。

像往常一样，我们认为变量是偏差形式。之间的相关系数X1和X2是
r12=s12/(s11s22)=∑X1X2/(s11s22)
如果我们划分每个变量X1经过小号11并将结果表示为X1=X1/s1一世然后X一世据说是相关形式。请注意
ΣX一世=0Σ(X一世)2=1
ΣX一世Xj=r1j
我们已经将模型从

$$
y=B_{1} x_{1}+B_{2} x_{2}+\varepsilon \text { to } y^{ }=\alpha_{1} x_{1}^{ }+\alpha_{ 2} x_{2}^{*}+\varepsilon
一种nd吨H和n这r米一种l和q在一种吨一世这nss一世米pl一世F是的Fr这米
s11b1+s12b2=s是的1 s12b1+s22b2=s是的2\text { to } \quad r_{12} a_{1}+r_{12}+a_{2}=r_{y 1}=r_{y 2} \quad \text { (3.5.3) }
$$

统计代写|实验设计作业代写experimental design代考|VARIABLE SELECTION – ALL POSSIBLE REGRESSIONS

在许多情况下，研究人员知道哪些变量可能包含在预测模型中。减少预测变量的数量以形成更简洁的模型有一些优势。实现这一目标的一种方法是运行所有可能的回归并将这些统计数据视为决定系数，R2=SSR/SST。
我们将使用第 3.5 节的心脏数据，再次将变量重新标记为 A 到F. 以相关形式的变量，R2=小号小号R, 回归的平方和，这是针对表中预测变量的每个可能组合给出的3.6.1.

为了帮助选择最佳子集，CL Mallows 建议拟合所有可能的模型并评估统计量
Cp=小号小号和p/s2−(n−2p)
这里，n是观察次数和p是子集中预测变量的数量，包括一个常数项。对于每个子集，可以根据 SSR 的相应值来评估 Mallows statistio 的值。表 3.6.2 列出了这些统计数据的完整集合。对于每个子集，我们使用完整模型的均方误差 MSE 作为方差的估计。

假设真实模型有 q 个预测变量。

统计代写|实验设计作业代写experimental design代考|VARIABLE SELECTION – SEQUENTIAL METHODS

当模型中可能变量的数量很大时，运行每个可能的回归并评估每个可能的 Mallows 统计量可能是不合适的，即使可以通过添加或减去项而不是通过评估来评估这些统计量的捷径每一个从头开始。

另一种方法是按顺序添加或删除变量。我们已经看到，添加一个变量会增加 SSR，即回归的平方和。从部分3.4我们可以进行 F 检验来确定 SSR 的增加是否显着。我们考虑的第一种方法是前向选择。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|实验设计作业代写experimental design代考|WHICH VARIABLES SHOULD BE INCLUDED IN THE MODEL

Posted on 2022年4月30日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|WHICH VARIABLES SHOULD BE INCLUDED IN THE MODEL

统计代写|实验设计作业代写experimental design代考|INTRODUCTION

When a model can be formed by including some, or all, of the predictor variables, there is a problem in deciding how many variables to include. The decision we arrive at will depend to some extent on the purpose we have in mind. If we merely wish to explain the variation of the dependent variable in the sample, then $1 \mathrm{t}$ would seem obvious that as many predictor variables as possible should be included. This can be seen with the lactation curve of Example $2.11$. If enough powers of $w$ were added to the model the curve would pass through every observed value, but it would be so jagged and complicated it would be difficult to understand what was happening. On the other hand, a small model has the advantage that it is easy to understand the relationships between the variables. Further more, a small model will usually yield estimators which are less influenced by peculiarites of the sample and so are more stable. Another important decision which must be made is whether to use the original predictor variables or to transform them in some way, often by taking a linear combination. For example, the cost of a particular kind of fencing for a rectangular field may largely depend on the length and breadth of the field. If all the fields in the

sample are in the same proportions then only one variable (length or breadth) would be needed. Even if they are not in the same proportions, one variable may be sufficient, namely the sum of the length and the breadth or, indeed, the perimeter. This is our ideal solution, reducing the number of predictor variables from two to one and at the same time obtaining a predictor variable which has physi= cal meaning, With a particular data set, the predicted value of the cost may be $y=1.11+0.9$ b so that the best single variable would be the $r$ ight hand side with $1=l$ ength and $b=b r e a d t h$, but this particular linear combination would have no physical meaning. We need to keep both aspects in mind, balancing statistioal optimum against physical meaning.
In the first section we shall 11 mit our discussion to orthogonal predictor variables, Although this may seem an unnecessarily strong restriction to place on the model, orthogonal variables of ten exist in experimental design situations. Indeed the values of the variables in the sample are often deliberately chosen to be orthogonal. We explain the advantages of this in section $3.2$, while in section $3.4$ we show that 1 t is possible to transform variables, for any data set, so that they are orthogonal.

统计代写|实验设计作业代写experimental design代考|ORTHOGONAL PREDICTOR VARIABLES

If the variables in a model are expressed as deviations from their means and if there are $k$ predictor variables, the sum of squares for regression is given by
$$
\begin{aligned}
\mathrm{SSR} &=b_{1} s_{y 1}+b_{2} s_{y 2}+\cdots+b_{k} s_{y k} \
&=s_{y 1}^{2} / s_{11}+s_{y 2}^{2} / s_{22}+\cdots+s_{y k}^{2} / s_{k k}
\end{aligned}
$$
The total sum of squares is
$$
\text { SST }-s_{y y}=\sum y_{i}^{2}
$$
By subtraction, we find the sum of squares for error (residual) is

$$
\mathrm{SSE}=S S T-S S R
$$
In this seotion, we assume that the predicton variables are orthog= onal and explore the implications of the number of variables included in the model.

We consider now the effect of adding another variable, $x_{k+1}$, to the model and assume that this variable $1 s$ also orthogonal to the other predfotor variables. The SST will not be affected by adding $x_{k+1}$ to the model. We introduce the notation that SSR(k) is the sum of squares for negression when the variables $x_{1}, x_{2}, \cdots x_{k}$ are in the model. It is clear that
(i) $\operatorname{SSR}(k+1) \geq \operatorname{SSR}(k)$
This follows from $(3.2 .1)$ as each term in the sum cannot be negative so that adding a further variable cannot decrease the sum of squares for regression.
(ii) $\operatorname{SSE}(k+1) \leq \operatorname{SSE}(k)$
This is the other side of the coin and follows from $(3.2 .2)$.
(111)
$$
R(k+1)^{2}=\operatorname{SSR}(k+1) / \operatorname{SST} \geq \mathrm{R}(k)^{2}=\operatorname{SSR}(k) / \mathrm{SST}
$$
SSR $(k+1)$ can be thought of as the amount of variation in $y$ explained by the $(k+1)$ predictor variables, and $R(k+1)^{2}$ is the proportion of the variation in y explained by these variables. These monotone properties are illustrated by the diagrams in figure $3.2 .1$.

统计代写|实验设计作业代写experimental design代考|ADDING NONORTHOGONAL VARIABLES SEQUENTIALLY

Although orthogonal predictor variables are the ideal, they will rarely occur in practice with observational data. If some of the predictor variables are highly correlated, the matrix $X \mathrm{~T} X$ will be nearly singular. This could raise statistical and numerical problems, particularly if there is interest in estimating the coefficients of the model. We nave more to say on this in the next section and in a later section on Ridge Estimators.

Moderate correlations between predictor variables will cause few problems. While it is not essential to convert predictor variables to others which are orthogonal, it is instruotive to do so as it gives insight into the meaning of the coefficients and the tests of significance based on them.

In Problem 1.5, we considered predicting the outcome of a student in the mathematics paper 303 (which we denoted by y) by marks

recelved in the papers 201 and 203 (denoted by $x_{1}$ and $x_{2}$, respectively). The actual numbers of these papers are not relevant, but, for interest sake, the paper 201 was a calculus paper and 203 an al gebra paper, both at second year university level and 303 was a third year paper in algebra. The sum of squares for regression when $y$ is regressed singly and together on the $x$ variables (and the $F^{2}$ values) are:
$\begin{array}{lll}\text { SSR on } 201 \text { alone : } & 1433.6 & (.405) \ \text { SSR on } 203 \text { alone : } & 2129.2 & (.602) \ \text { SSR on } 201 \text { and } 203: & 2265.6 & (.641)\end{array}$
Clearly, the two $x$ variables are not orthogonal (and, in fact, the correlation coefficient between them is 0.622) as the individual sums of squares for regression do not add to that given by the model with both variables included. Once we have regressed the 303 marks on the 201 marks, the additional sum of squares due to $2031 \mathrm{~s}$ (2265.6 $1433.6)=832$. In this section we show how to adjust one variable for another so that they are orthogonal, and, as a consequence, their sums of squares for regression add to that given by the model with both variables included.
$\begin{array}{ll}\text { SSR for } 201 & =1433.6=\text { SSR for } x_{1} \ \text { SSR for } 203 \text { adjusted for } 201=832.0=\text { SSR for } z_{2} \ \text { SSR for } 201 \text { and } 203 & =2265.6\end{array}$

实验设计代考

统计代写|实验设计作业代写experimental design代考|INTRODUCTION

当可以通过包含一些或全部预测变量来形成模型时，在决定要包含多少变量时会出现问题。我们做出的决定在某种程度上取决于我们心中的目的。如果我们只是想解释样本中因变量的变化，那么1吨显然应该包括尽可能多的预测变量。这可以通过实施例的泌乳曲线看出2.11. 如果有足够的权力在被添加到模型中，曲线将通过每个观察值，但它会如此参差不齐和复杂，很难理解发生了什么。另一方面，小模型的优点是易于理解变量之间的关系。此外，小模型通常会产生受样本特性影响较小的估计量，因此更稳定。另一个必须做出的重要决定是是使用原始预测变量还是以某种方式转换它们，通常是通过线性组合。例如，矩形场地的特定类型围栏的成本可能在很大程度上取决于场地的长度和宽度。如果所有字段在

样本的比例相同，则只需要一个变量（长度或宽度）。即使它们的比例不同，一个变量可能就足够了，即长度和宽度的总和，或者实际上是周长。这是我们理想的解决方案，将预测变量的数量从两个减少到一个，同时得到一个具有物理意义的预测变量，对于特定的数据集，成本的预测值可能是是的=1.11+0.9b 这样最好的单一变量将是r右手边1=l长度和b=br和一种d吨H，但这种特殊的线性组合没有物理意义。我们需要牢记这两个方面，平衡统计优化与物理意义。
在第一节中，我们将讨论 11 到正交预测变量，尽管这似乎对模型施加了不必要的强限制，但在实验设计情况下存在 10 个正交变量。实际上，样本中变量的值通常被故意选择为正交的。我们在章节中解释了它的优点3.2, 而在截面3.4我们表明，对于任何数据集，1 t 都可以转换变量，使它们是正交的。

统计代写|实验设计作业代写experimental design代考|ORTHOGONAL PREDICTOR VARIABLES

如果模型中的变量表示为与其均值的偏差，并且如果存在ķ预测变量，回归的平方和由下式给出
小号小号R=b1s是的1+b2s是的2+⋯+bķs是的ķ =s是的12/s11+s是的22/s22+⋯+s是的ķ2/sķķ
总平方和为
SST −s是的是的=∑是的一世2
通过减法，我们发现误差（残差）的平方和为小号小号和=小号小号吨−小号小号R
在本节中，我们假设预测变量是正交的，并探讨模型中包含的变量数量的含义。

我们现在考虑添加另一个变量的效果，Xķ+1, 到模型并假设这个变量1s也与其他预测变量正交。SST 不会受到添加的影响Xķ+1到模型。我们引入符号 SSR(k) 是当变量X1,X2,⋯Xķ在模型中。很明显
（一）固态硬盘⁡(ķ+1)≥固态硬盘⁡(ķ)
这是从(3.2.1)因为总和中的每一项不能为负数，因此添加更多变量不能减少回归的平方和。
(二)上证所⁡(ķ+1)≤上证所⁡(ķ)
这是硬币的另一面，从(3.2.2).
(111)
R(ķ+1)2=固态硬盘⁡(ķ+1)/SST≥R(ķ)2=固态硬盘⁡(ķ)/小号小号吨
固态硬盘(ķ+1)可以认为是变化量是的由解释(ķ+1)预测变量，和R(ķ+1)2是这些变量解释的 y 变化的比例。这些单调特性由图中的图表说明3.2.1.

统计代写|实验设计作业代写experimental design代考|ADDING NONORTHOGONAL VARIABLES SEQUENTIALLY

尽管正交预测变量是理想的，但它们在实际观测数据中很少出现。如果某些预测变量高度相关，则矩阵X 吨X几乎是单数。这可能会引发统计和数值问题，特别是如果有兴趣估计模型的系数。我们将在下一节和后面关于岭估计器的部分中对此进行更多说明。

预测变量之间的中等相关性将导致很少的问题。虽然将预测变量转换为其他正交变量并不是必需的，但这样做具有指导意义，因为它可以深入了解系数的含义以及基于它们的显着性检验。

在问题 1.5 中，我们考虑用分数来预测学生在数学试卷 303（我们用 y 表示）中的结果

在 201 和 203 号论文中得到认可（记为X1和X2，分别）。这些论文的实际数量无关紧要，但出于兴趣，论文 201 是微积分论文，203 是代数论文，都是大学二年级的论文，303 是代数三年级的论文。回归时的平方和是的在X变量（和F2值）是：
SSR 开启 201 独自的： 1433.6(.405) SSR 开启 203 独自的： 2129.2(.602) SSR 开启 201 和 203:2265.6(.641)
很明显，两人X变量不是正交的（实际上，它们之间的相关系数为 0.622），因为回归的各个平方和不会添加到包含两个变量的模型给出的平方和。一旦我们在 201 分上回归了 303 分，额外的平方和由于2031 s (2265.6 1433.6)=832. 在本节中，我们将展示如何将一个变量调整为另一个变量，以使它们正交，因此，它们的回归平方和与包含两个变量的模型给出的平方和相加。
SSR 为 201=1433.6= SSR 为 X1 SSR 为 203 调整为 201=832.0= SSR 为和2 SSR 为 201 和 203=2265.6

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|实验设计作业代写experimental design代考|Adjustment for Degrees of Freedom

Posted on 2022年4月29日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|Adjustment for Degrees of Freedom

The coefficient $R^{2}$ measures the proportion of the variation in $y$ which is explained by the predictor variables. Actually, it overestimates this proportion and the adjustment suggested here aims to correct this.

If the $y$ values were entirely random in the space of $n d 1 m e n-$ sions (the deviations from their mean would then be in an $n-1$ dimensioned sub-space) the $k$ predictor variables would still explain some variation in $y$, on average $k /(n-1) . R^{2}$ is corrected for this random effect by subtracting $k /(n-1)$. This is then scaled to give a value of 1 (perfect explanation of $y$ ) when $R^{2}=1$. Finally
$\operatorname{adj} R^{2}=\left[R^{2}-k /(n-1)\right][n-1] /[n-k-1]$
This adjusted value could even be negative if $\mathrm{R}^{2}$ is small, which highlights the only problem with it. What would a negative value mean? On the other hand the unadjusted value has a clear interpretation as the proportion of the variance of $y$ explained by the predictor variable.

统计代写|实验设计作业代写experimental design代考|The Univariate Case

Consider again the simple model
$$
y=\alpha 1+\beta x+E
$$
with $x$ in deviation form and $\varepsilon=N\left(0, \sigma^{2} I\right)$. Notice that 1 is orthogonal to $x$ so that the least squares estimates of $\alpha$ and $\beta$ are the same as would be obtained by regressing $y$ separately on 1 and $x$.

$$
a=\Sigma y_{1} / n, b=\Sigma x_{1} y_{1} / \Sigma x_{1}^{2}
$$
For a given value of $x=x_{0}$, the predicted value of $y$ is
$$
\hat{y}{0}=a+b x{0}
$$
A number of points should be kept in mind relating to this expression.
(i) The $x_{0}$ need not be one of the $x$ in the sample, but there are obvious dangers in predicting outside of the range of the sample. For one thing, the relationships between $x$ and $y$ may be linear for the $x$ values of the sample but the relationship may change outside of these values, as in Figure $2.7 .1$. One example of this could be the cancer causing effects of low doses of radiation. The incidence of cancer in this situation would be so low that it would be difficult to measure, requiring a very large sample size. To facilitate the research one could work at higher dosage rates $(x)$ and hope that one could extrapolate down to lower dosage rates, but this procedure is fraught with danger.
(ii) The predicted value of $y$ depends on all the $y$ values in the sample. We shall comment further on this in Chapter 4 where we shall discuss sensitive or high leverage values of $x$, by which we mean those $x^{\prime} s$ which have a very large effect on the predicted values of $\mathrm{y}$.
(iii) $\hat{y}$ estimates the mean value of $y$ when $x=x_{0}$.
(iv) $y$ is a linear combination of the $y$ values in the sample.

统计代写|实验设计作业代写experimental design代考|RESIDUALS

If the fltted model is the correct one (or close to the correct one), we would expect the residuals to refzect the properties of the deviations. In this chapter, we are mainly concerned with checking the residuals to be assured that the model with its assumptions is reasonable for the data, Is the distribution of the residuals consonant with the assumed distribution of the deviations? Does it appear that the variance about the line is constant? Does it appear that the deviations are independent?

If we recall that the prediction equation is $\mathbf{y}=\hat{y}+e$ then, in a sense, the residual and the predicted y value are opposite faces of the same coin for when one is large, the other is small. We shall not have much to say at this point on the sizes of individual residuals. Large values may indicate that the points are outliers but we shall say more on this in Chapter $4 .$

实验设计代考

统计代写|实验设计作业代写experimental design代考|Adjustment for Degrees of Freedom

系数R2测量变化的比例是的这是由预测变量解释的。实际上，它高估了这个比例，这里建议的调整旨在纠正这一点。

如果是的值在空间中是完全随机的nd1米和n−sions（与它们的平均值的偏差将在一个n−1维度子空间）的ķ预测变量仍然可以解释一些变化是的，一般ķ/(n−1).R2通过减去这个随机效应来校正ķ/(n−1). 然后将其缩放以给出 1 的值（完美解释是的）什么时候R2=1. 最后
形容词⁡R2=[R2−ķ/(n−1)][n−1]/[n−ķ−1]
这个调整后的值甚至可能是负数，如果R2很小，这突出了它的唯一问题。负值意味着什么？另一方面，未经调整的值有一个明确的解释，即方差的比例是的由预测变量解释。

统计代写|实验设计作业代写experimental design代考|The Univariate Case

再次考虑简单模型
是的=一种1+bX+和
和X以偏差形式和e=ñ(0,σ2一世). 请注意，1 与X使得最小二乘估计一种和b与通过回归得到的相同是的分别在 1 和X.一种=Σ是的1/n,b=ΣX1是的1/ΣX12
对于给定的值X=X0, 的预测值是的是
是的^0=一种+bX0
与此表达式有关的一些要点应牢记在心。
(一)X0不必是其中之一X在样本中，但在样本范围之外进行预测存在明显的危险。一方面，之间的关系X和是的可能是线性的X样本的值，但关系可能会在这些值之外发生变化，如图2.7.1. 这方面的一个例子可能是低剂量辐射的致癌作用。在这种情况下，癌症的发病率将非常低，以至于难以测量，需要非常大的样本量。为了促进研究，可以在更高的剂量率下工作(X)并希望人们可以推断出更低的剂量率，但这个过程充满了危险。
(ii) 的预测值是的取决于所有是的样本中的值。我们将在第 4 章进一步评论这一点，我们将讨论敏感或高杠杆值X, 我们的意思是那些X′s对预测值有很大影响是的.
㈢是的^估计平均值是的什么时候X=X0.
(四)是的是一个线性组合是的样本中的值。

统计代写|实验设计作业代写experimental design代考|RESIDUALS

如果 fltted 模型是正确的模型（或接近正确的模型），我们预计残差会反映偏差的属性。在本章中，我们主要关注检查残差以确保模型及其假设对数据是合理的，残差的分布是否与假设的偏差分布一致？看起来这条线的方差是恒定的吗？看起来这些偏差是独立的吗？

如果我们回想一下预测方程是是的=是的^+和那么，从某种意义上说，残差和预测的 y 值是同一枚硬币的相反面，因为一个大，另一个小。在这一点上，我们不会对单个残差的大小说太多。较大的值可能表明这些点是异常值，但我们将在本章中详细说明4.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|实验设计作业代写experimental design代考|GOODNESS OF FIT OF THE MODEL

Posted on 2022年4月29日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|GOODNESS OF FIT OF THE MODEL

统计代写|实验设计作业代写experimental design代考|AN EXAMPLE – VALUE OF A POSTAGE STAMP OVER TIME

The value of an Australian stamp ( $1963 \& 2$ sepia colored) given, in $\boldsymbol{L}$ sterling, by the Stanley Gibbons Catalogues is shown in Table $1.7 .1$ for the years 1972-1980. The aim is to $f$ it a model to the value of the stamp over time.

Let the time be $x=0$ for $1972, x=1$ for 1973 , etc. In this example, interest probably centres on the relative value of the stamp from one year to the next. Alternatively, if there is interest in the investment value of the stamp over the period 1972-1980, it may be useful to express the value as $y$, the value relative to that of 1972. The values of $y$ and $x$ are also shown above and are graphed in Figure 1.7.1. The relationship between $y$ and $x$ is not a 1 inear one. When $y$ is transformed by taking natural logarithms, a strong linear trend is apparent as shown by Figure 1.7.2. The predicted values of in $y$ and the residuals are shown in Table 1.7.2. The prediction equation is

Of course, the constant term could be omitted and the graph forced to pass through the orlgin.
The residuals fall into a reasonable horizontal band so that there is 1 ttle evidence to contradict the assumptions that the deviations are distributed with mean zero and constant variance.
However, there is a marked pattern in the residuals for their signs are:
Clearly, the residuals are positively correlated (as a positive residual is often followed by a positive residual, and a negative residual followed by a negative). With the small number of observations in the sample, we should hesitate to make dogmatio statements about the model but the pattern in the residuals may suggest that
(i) The population mean is not correct.
The residuals could indicate that a cubed term would remove.

统计代写|实验设计作业代写experimental design代考|INTRODUCTION

In Chapter 1, we considered fitting models to data. To answer the question of how well a model fits the data, we need to develop statistical tests and, to do so, we lean heavily on the assumption that the deviations have independent normal distributions. For our purposes, the main benefit of the normality assumption is that we can find the distribution of estimates and perform test of significance. The theorems listed in Appendix B will be of assistance in this. For the general linear model
$$
y=1 \alpha+X_{\beta}+\varepsilon
$$
where $\alpha$ is a constant term, $X$ is an $n \times k$ matri $x$ of known constants, deviations from their mean, and $\varepsilon$ are the deviations, assumed to be independent and normally distributed with mean zero and constant variance of $\sigma^{2}$, that is $\varepsilon-N\left(0, \sigma^{2} I\right)$. I is an $n \times n$ identity matrix with all diagonal elements equal to 1 and off diagonal elements equal to zero. Thus, the covariances are zero and the variances are all equal.

With these assumptions, we have, in effect, made assumptions about $y$. The mean, or expected value, of $y$ is $X$ a as $E(\varepsilon)$ is 0 . The variance of $y$ is the variance of $\varepsilon_{,} \delta^{2} I$.
2.2 COEEFICIENT ESTIMATES FOR UNIVARIATE REGRESSION
Consider the simple univariate regression with a constant term included, that is
$y=a 1+B x+\varepsilon$ With $\varepsilon \sim N\left(0, \sigma^{2} I\right)$
or $\boldsymbol{y} \sim \mathrm{N}\left(\alpha 1+\beta x, \theta^{2} I\right)$
The least squares estimate of $B$ is
$$
b=\left(x^{T} x\right)^{-1} x^{T} y
$$
Note that since the $x^{\prime} s$ are deviations from thefr means
$$
\begin{aligned}
b &=S_{x y} / S_{x x} \quad(\text { from } 1+6.2) \
\text { and } S_{x y} &=\sum x_{1}\left(y_{1}-y\right)=\sum x_{i} y_{1}=x^{T} y
\end{aligned}
$$
As $b 1 s$ a linear combination of the observed $y$ values, then Appendix B 1 can be invoked to give
$d^{2}$ can be estimated by the sample variance of the residuals, namely
$$
s^{2}=\sum e_{1}^{2} /(n-2)
$$
This has $n-2$ degrees of freedom as there are $n$ observations, but two parameters, $\alpha$ and $\beta$, to be estimated.

统计代写|实验设计作业代写experimental design代考|ANOVA TABLES

The analysis of variance table, ANOVA, represents the components of the variation of the dependent variable, $y$. In section $1.5$, we

showed that, for any number of predictor variables, we can divide the vector of observations, $y$, into two orthogonal parts consisting of the predicted values and the residuals, which we can represent by Eigure 1.5.1.
As the vectors e and $\boldsymbol{y}$ are orthogonal, e $\boldsymbol{9}$, then from Pythagoras’ Theorem we know that
$(\operatorname{length} y)^{2}=(\text { ength } \mathbf{y})^{2}+(1 \text { ength e })^{2}\left(r^{2}\right.$
$$
y^{T} y=\boldsymbol{y}^{T} \boldsymbol{y}=e^{T} e
$$
If there are k predictor terms in the model, but no constant (intercept) term, then the sums of squares and degrees of freedom, d.f., can be displayed as in Table $2.4 .1 .$
Almost invariably it is deviations from the mean which the model is required to explain, so a constant term is included in the model. We have seen from section $1.6 .2$, this has the effect of adjusting each var iable for its mean, and the sum of squares for the mean is given by
$$
S S(M e a n)=y^{T} 1\left(1_{1}^{T}\right)^{-1} 1^{T} y=\left(\Sigma y_{j}\right)^{2} / n=n y^{2}
$$

实验设计代考

统计代写|实验设计作业代写experimental design代考|AN EXAMPLE – VALUE OF A POSTAGE STAMP OVER TIME

澳大利亚邮票的价值（1963&2棕褐色）给定，在大号英镑，由 Stanley Gibbons 编目显示在表中1.7.11972-1980 年。目的是F它是随时间变化的邮票价值的模型。

让时间成为X=0为了1972,X=1对于 1973 等。在这个例子中，兴趣可能集中在邮票从一年到下一年的相对价值上。或者，如果对 1972-1980 年期间邮票的投资价值感兴趣，将价值表示为是的，相对于 1972 年的值。是的和X也显示在上面，并在图 1.7.1 中绘制。之间的关系是的和X不是 1 线性的。什么时候是的用自然对数变换，如图 1.7.2 所示，呈现出明显的强线性趋势。的预测值是的残差如表 1.7.2 所示。预测方程为

当然，常数项可以省略，图形被迫通过 orlgin。
残差落在一个合理的水平范围内，因此有 1 个证据与偏差以均值零和恒定方差分布的假设相矛盾。
然而，残差中有一个明显的模式，因为它们的符号是：
显然，残差是正相关的（因为正残差后面通常是正残差，负残差后面跟着负数）。由于样本中的观察数量很少，我们应该犹豫对模型做出教条式的陈述，但残差中的模式可能表明
（i）总体均值不正确。
残差可能表明立方项将被删除。

统计代写|实验设计作业代写experimental design代考|INTRODUCTION

在第 1 章中，我们考虑了将模型拟合到数据。为了回答模型与数据的拟合程度的问题，我们需要开发统计测试，为此，我们严重依赖于偏差具有独立正态分布的假设。就我们的目的而言，正态性假设的主要好处是我们可以找到估计的分布并进行显着性检验。附录 B 中列出的定理将对此有所帮助。对于一般线性模型
是的=1一种+Xb+e
在哪里一种是一个常数项，X是一个n×ķ母亲X已知常数、与平均值的偏差，以及e是偏差，假设为独立且正态分布，均值为 0，方差为常数σ2，那是e−ñ(0,σ2一世). 我是一个n×n所有对角线元素都等于 1 且非对角线元素等于 0 的单位矩阵。因此，协方差为零并且方差都相等。

有了这些假设，我们实际上已经做出了关于是的. 的平均值或期望值是的是X一个作为和(e)是 0 。的方差是的是方差e,d2一世.
2.2 单变量回归的系数估计
考虑包含常数项的简单单变量回归，即
是的=一种1+乙X+e和e∼ñ(0,σ2一世)
或者是的∼ñ(一种1+bX,θ2一世)
最小二乘估计乙是
b=(X吨X)−1X吨是的
请注意，由于X′s是偏离均值
b=小号X是的/小号XX( 从 1+6.2) 和小号X是的=∑X1(是的1−是的)=∑X一世是的1=X吨是的
作为b1s观察到的线性组合是的值，则可以调用附录 B 1 给出
d2可以通过残差的样本方差来估计，即
s2=∑和12/(n−2)
这有n−2自由度n观察，但有两个参数，一种和b, 待估计。

统计代写|实验设计作业代写experimental design代考|ANOVA TABLES

方差分析表 ANOVA 表示因变量的变化分量，是的. 在部分1.5，我们

表明，对于任意数量的预测变量，我们可以划分观察向量，是的，分成两个正交部分，由预测值和残差组成，我们可以用 Eigure 1.5.1 表示。
作为向量 e 和是的是正交的，e9, 那么从毕达哥拉斯定理我们知道
(长度⁡是的)2=( 长度是的)2+(1 英语 )2(r2
是的吨是的=是的吨是的=和吨和
如果模型中有 k 个预测项，但没有常数（截距）项，则平方和和自由度 df 可以显示为表2.4.1.
几乎总是偏离模型需要解释的平均值，因此模型中包含一个常数项。我们从部分看到1.6.2，这具有调整每个变量的均值的效果，均值的平方和由下式给出
小号小号(米和一种n)=是的吨1(11吨)−11吨是的=(Σ是的j)2/n=n是的2

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|实验设计作业代写experimental design代考|TRANSFORMATIONS TO OBTAIN LINEARITY

Posted on 2022年4月29日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|TRANSFORMATIONS TO OBTAIN LINEARITY

Two variables, $x$ and $y$, may be closely related but the relationship may not be linear. Ideally, theoretical clues would be present wh1ch point to a particular relationship such as an exponential growth model which is common in blology. Without such clues, we could firstly examine a scatter plot of $y$ against $x$.
Sometimes we may recognize a mathematical model which $f$ its the data well. Otherwise, we try to choose a simple transformation such

as ralsing the variable to a power p as in Table 1.4.1. A power of 1 leaves the variable unchanged, that is as raw data. As we proceed up or down the table from 1 , the strength of the transformation increases; as we move up the table the transformation stretohes larger values relatively more than smaller ones. Although the exponential does not flt in very well, we nave included $1 t$ as $1 t 1 s$ the inverse of the logarithmic transformation. other fractional powers oould be used but they may be difficult to interpret.
It would be feasible to transform either $y$ or $x$, and, indeed, a transformation of $y$ would be equivalent to the inverse transformation of $x$. For example, squaring $y$ would be equivalent to taking the square root of $x$. If there are two or more predictor variables, it is often advisable to transform these in different ways nather than $y$, for if y is transformed to be linearly related to one predictor variable it may then not be 1 inear ly related to another.
In Eigure 1.4.1, it is clear that we should stretoh out the graph by increasing large $x$ values, or, alternatively; reduce large $y$ values. Thus, we could try changing $x$ to $x$-squared, or $y$ to the square root of $y_{*}$ One point to be kept in mind here is that for p>0, $y=0$ when $x=0$ so that it may be advisable before invoking the power transformation to change the origin; in partfoular, we could onange y to $(y-a)$, and a good guess may be a $=30$. In Figure $1.4 .2$, it seems that large $x$ values and large $y$ values should be reduced suggesting that a reciprooal transformation may be appropriate. This would require the $x$ and $y$ axes to be asymptotes which, in particular, would

mean that a constant, perhaps 14 , should be subtracted from $y$. We could try changing
$$
\begin{aligned}
&y \text { to }(y-14)^{-1} \
&\text { or } y \text { to }(y=14)^{-0.5} \
&\text { or } x \text { to } x{ }^{-1} \
&\text { or } x \text { to } x=0.5
\end{aligned}
$$

统计代写|实验设计作业代写experimental design代考|FITTING A MODEL USING VECTORS AND MATRICES

Appendix A contains a review of vectors, vector spaces and matrices and some readers may wish to refer to that section while reading the following.

In regression, we consider the relationship between a string of values of the dependent variable, $y$, and one or more strings of corresponding values of the predictor variables, the $x$ ‘s. It is useful to think of each string as a vector for it turns out that the relationships of interest between the variables are encapsulated in the lengths of the vectors and the angles between them. For the simple Example $1.3 .1$, the $x$ and $y$ readings can be written as column vectors:

The simplest model for this example would be a line through the origin
$$
\mathrm{y}{\mathrm{i}}=B \mathrm{X}{\mathrm{i}}+\mathrm{E}{i} $$ or $\mathbf{y}=\beta \mathbf{x}+\boldsymbol{\varepsilon}$ in vector terms The normal equation $1 \mathrm{~s}$ $b \sum x{1}^{2}=\sum x_{1}^{y_{1}}$
or $\left(x^{T} x\right) b=x^{T} y$
giving $b=\left(x^{T} \mathbf{y}\right) /\left(x^{T} \mathbf{x}\right)=0.973$
$(1.5 .2)$
For each value of $x$ we can calculate the predicted value of $y$ as
$$
\mathbf{y}=b x \text { or } x b=\left|\begin{array}{l}
0.5 \
1.0 \
1.5 \
2.0 \
2.5
\end{array}\right| 0.973=\left|\begin{array}{l}
0.486 \
0.973 \
1.459 \
1.945 \
2.432
\end{array}\right|
$$
The predicted value can also be written as
$$
y=x b=x\left(x^{T} x\right)^{-1} x^{T} y=P y
$$
The matrix $P=x\left(x^{T} \mathbf{x}\right)^{-1} x^{T}$ is termed the projection matrix. More is said about this in section 1.7. Notice that for this case with $n=5$, $P$ is a $5 \times 5$ matrix, namely.

统计代写|实验设计作业代写experimental design代考|DEVIATIONS FROM MEANS

It is common practice when fitting a model to use the original (also called raw) data and to include $1 n$ the model a $y=i n t e r c e p t ~ t e r m ~(a l s o ~$ called a constant, or general mean). Most computer programs would convert the raw data to deviations from the mean, as these are used in such statistics as the correlation coefficient. Converting to deviations has the advantage of removing a parameter from the model, making 1 t easier to man1 pulate. Sometimes an examination of the deviations shows up trends which are not as clearly noticeable in the raw data. Problem $2.1$ is an example where deviations from the mean prove useful. It turns out that the estimated coefficients will be the same for the raw data with constant term as with the data 1 n deviation form.

For this section we change our notation slightly to make 1 t clear whether we are referring to the raw data (which we indicate by capital letters, $X, Y$, etc) or deviations from means (lower case $x$, $y$, etc).
$1.6 .1$ Estimates
Ignoring subsor ipts for simplicity, we can write for the case of one predictor variable,
$$
x=X=\bar{X} \text { and } y=Y-\bar{Y}
$$
where $\vec{X}$ and $\vec{Y}$ are the sample means. For the model
$$
\mathrm{y}=8 x+\varepsilon
$$
we saw in $(1.2 .7)$ the least squares estimates are given by
$\begin{aligned} b &=\sum_{1}^{y_{1} / 2 x_{1}^{2}} \quad(\text { from } 1.2 .7) \ &=\mathrm{S}{x y} / \mathrm{S}{x x} \end{aligned} \quad$ (def ined by 1.2.13)
$(1.6 .2)$
Notice that the predicted value of $y$ in this case is $\hat{y}=b x$

实验设计代考

统计代写|实验设计作业代写experimental design代考|TRANSFORMATIONS TO OBTAIN LINEARITY

两个变量，X和是的, 可能密切相关，但关系可能不是线性的。理想情况下，理论线索将指向特定关系，例如在 bloology 中常见的指数增长模型。如果没有这些线索，我们可以先检查一个散点图是的反对X.
有时我们可能会认识到一个数学模型F它的数据很好。否则，我们尝试选择一个简单的转换，例如

如表 1.4.1 所示，将变量转换为幂 p。1 的幂保持变量不变，即作为原始数据。当我们从 1 开始向上或向下移动时，转换的强度会增加；当我们在表格中向上移动时，转换比较小的值相对更多地延伸较大的值。虽然指数并没有很好地适应，但我们没有包括1吨作为1吨1s对数变换的倒数。可以使用其他分数幂，但它们可能难以解释。
改造任何一个都是可行的是的或者X，而且，事实上，一个转变是的将相当于的逆变换X. 例如，平方是的相当于取平方根X. 如果有两个或多个预测变量，通常建议以不同的方式转换它们，而不是是的，因为如果 y 被转换为与一个预测变量线性相关，则它可能与另一个变量不是 1 密切相关。
在 Eigure 1.4.1 中，很明显我们应该通过增加X价值观，或者，或者，减少大是的价值观。因此，我们可以尝试改变X到X-平方，或是的的平方根是的∗这里要记住的一点是，对于 p>0，是的=0什么时候X=0以便在调用功率转换以更改原点之前可能是可取的；在partfoular，我们可以onange y to(是的−一种), 一个好的猜测可能是=30. 如图1.4.2, 好像很大X值和大是的值应该减少，这表明互惠变换可能是合适的。这将需要X和是的轴是渐近线，尤其是

意味着应该减去一个常数，也许是 14是的. 我们可以尝试改变
是的到 (是的−14)−1 或者是的到 (是的=14)−0.5 或者 X 到 X−1 或者 X 到 X=0.5

统计代写|实验设计作业代写experimental design代考|FITTING A MODEL USING VECTORS AND MATRICES

附录 A 包含对向量、向量空间和矩阵的回顾，一些读者可能希望在阅读以下内容时参考该部分。

在回归中，我们考虑因变量的一串值之间的关系，是的，以及一串或多串对应的预测变量值，X的。将每个字符串视为一个向量是很有用的，因为事实证明，变量之间感兴趣的关系被封装在向量的长度和它们之间的角度中。对于简单的示例1.3.1，这X和是的读数可以写成列向量：

这个例子最简单的模型是一条穿过原点的线
是的一世=乙X一世+和一世或者是的=bX+e用向量表示正规方程1 s b∑X12=∑X1是的1
或者(X吨X)b=X吨是的
给予b=(X吨是的)/(X吨X)=0.973
(1.5.2)
对于每个值X我们可以计算出预测值是的作为
是的=bX 或者 Xb=|0.5 1.0 1.5 2.0 2.5|0.973=|0.486 0.973 1.459 1.945 2.432|
预测值也可以写成
是的=Xb=X(X吨X)−1X吨是的=磷是的
矩阵磷=X(X吨X)−1X吨称为投影矩阵。1.7 节对此进行了更多说明。请注意，对于这种情况n=5, 磷是一个5×5矩阵，即。

统计代写|实验设计作业代写experimental design代考|DEVIATIONS FROM MEANS

拟合模型以使用原始（也称为原始）数据并包含1n模型是的=一世n吨和rC和p吨吨和r米 (一种ls这称为常数或一般平均值）。大多数计算机程序会将原始数据转换为与平均值的偏差，因为这些数据用于相关系数等统计数据中。转换为偏差具有从模型中删除参数的优点，使 1 t 更容易计算。有时，对偏差的检查会发现在原始数据中不那么明显的趋势。问题2.1是一个证明偏离均值有用的例子。事实证明，具有常数项的原始数据的估计系数与数据 1 n 偏差形式的估计系数相同。

对于本节，我们稍微改变我们的符号，以明确我们是否指的是原始数据（我们用大写字母表示，X,是的等）或偏离均值（小写X, 是的， ETC）。
1.6.1估计
为简单起见忽略 subsor ipts，我们可以写一个预测变量的情况，
X=X=X¯ 和是的=是的−是的¯
在哪里X→和是的→是样本均值。对于模型
是的=8X+e
我们在(1.2.7)最小二乘估计由下式给出
b=∑1是的1/2X12( 从 1.2.7) =小号X是的/小号XX（由 1.2.13 定义）
(1.6.2)
注意预测值是的在这种情况下是是的^=bX

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|实验设计作业代写experimental design代考|FITTING A MODEL TO DATA

Posted on 2022年4月29日2022年4月29日 by statistics-lab

如果你也在怎样代写实验设计experimental design这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

实验设计是一个概念，用于有效地组织、进行和解释实验结果，确保通过进行少量的试验获得尽可能多的有用信息。

我们提供的实验设计experimental design及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等楖率论
Advanced Mathematical Statistics 高等数理统计学
(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|实验设计作业代写experimental design代考|FITTING A MODEL TO DATA

The title of this chapter could well be the title of this book. In the first four chapters, we consider problems associated with fitting a regression model and in the last four we consider experimental designs. Mathematically, the two topics use the same model. The term regression is used when the model is fltted to observational data, and experimental design is used when the data is carefully organized to give the model special properties. For some data, the distinction may not be at all clear or, indeed, relevant, he shall consider sets of data consisting of observations of a variable of Interest which we shall call $y$, and we shall assume that these observations are a random sample from a population, usually infinite, of possible values. It is this population which is of primary interest, and not the sample, for in trying to fit models to the data we are really trying to flt models to the population from which the sample is drawn. For each observation, $y$, the model will be of the fork
observed $y=$ population mean + deviation
$(1.1 .1)$
The population mean may depend on the corresponding values of a prem dictor variable which we often label as $x$. For this reason, y is

called the dependent variable. The deviation term indicates the individual peculiarity of the observation, $y$, which makes it differ from the population mean.

As an example, $\$ y$ could be the price paid for a house in a certain oity. The population mean could be thought of as the mean price paid for houses in that city, presumably in a given time period. In this case the deviation term could be very large as house prices would vary greatly depending on a number of factors such as the size and condition of the house as well as its position in the oity. In New Zealand, each house is given a government valuation, GV, which is reconsidered on a five year cycle. The price paid for a house will depend to some extent on its GV. The regression model could then be written in terms of $\$ x$, the $\mathrm{GV}$, as:

统计代写|实验设计作业代写experimental design代考|HON TO FIT A LINE

As the deviation term involves the unexplained variation in $y$, we try to minimise this in some way. Suppose we postulate that the mean value of $y$ is a function of $x$. That is
$$
E(y)=f(x)
$$
Then for a sample of $n$ pairs of $y^{\prime} s$ with their corresponding $x^{\prime} s$ we have

The above notation assumes that the $x^{\prime} s$ are not random variables but are fixed in advance. If the $x^{\prime} s$ were in fact random variables we should write

$$
f\left(x_{1}\right)=E\left(y_{1} \mid x_{1}=x_{1}\right)
$$
= mean of $Y_{i}$ given that $X_{i}=x_{i}$
which gives the same results. We wil1 therefore assume in future that the $x^{\prime} s$ are $f$ ixed.
The simplest example of a function $f$ would arise if $y$ was proportional to $x$. We could imagine a situation where an inspector of weights and measures set out to test the scales used by shopkeepers. In this case, the $x^{\prime} s$ would be the welghts of standand measures while $y^{\prime} s$ would be the corresponding weights indicated by the shopkeeper’s scales. The model would be
The mean value of $y$ when $x=x_{i}$ is given by
$$
E\left(y_{i}\right)=B x_{i}=f\left(x_{i}\right)
$$
This is called a regression curve. In this simple example we would expect the parameter $B$ to be 1 , or at least close to 1 . We think of the parameters as being fixed numbers which describe some attributes of the population.

统计代写|实验设计作业代写experimental design代考|Other Ways of Fitting a Curve

The main mroblem with the approach of least squares is that a large deviation will have an even larger square and this deviation may have an unduly large influence on the $f$ itted curve. To guard against such distortions we could try to isolate large deviations. We consider this in more detail in Chapter 4 under outliers and sensitive points. Alternatively, we could seek estimates which minimize a different function of the deviations.

If the model is expressed in terms of the population median of $y$, rather than its mean, another method of fitting a curve would be by minimizing $T$, the sum of the absolute values of deviations, that is
$$
T=\sum_{i=1}^{n}\left|\varepsilon_{1}\right|
$$
Although this is a sensible approach which works well, the actual mathematics is difficult when the distributions of estimates are sought. Hogg (1974) suggests minimizing
$T=\sum\left|\varepsilon_{i}\right|^{p} \quad$ with $\quad 1<p<2$
and $p=1.5$, in particular, may be a reasonable compromise. Again it is difficult to determine the exact distributions of the resulting estimates. If we are not so much interested in testing hypothesis as

estimating coefficients then this method provides estimates which are robust in the sense that they are not unduly affected by large dev1ations.

Notice that the deviations are the vertical distances from the regression line. It might, perhaps, seem more logical, or at least more symmetrical, to consider the perpendicular (orthogonal) distances from the regression line. However when our major concern is predicting $y$ from $x$ the vertical distances are more relevant because they represent the prediction error.

实验设计代考

统计代写|实验设计作业代写experimental design代考|FITTING A MODEL TO DATA

本章的标题很可能就是本书的标题。在前四章中，我们考虑了与拟合回归模型相关的问题，在后四章中，我们考虑了实验设计。在数学上，这两个主题使用相同的模型。当模型被用于观测数据时使用术语回归，当数据被仔细组织以赋予模型特殊属性时使用实验设计。对于某些数据，区别可能根本不明确，或者实际上不相关，他将考虑由我们称之为感兴趣变量的观察组成的数据集是的，并且我们将假设这些观察结果是来自总体的随机样本，通常是无限的可能值。主要关注的是这个总体，而不是样本，因为在尝试将模型拟合到数据时，我们实际上是在尝试将模型与从中抽取样本的总体进行匹配。对于每个观察，是的，模型将是
观察到的叉子是的=总体均值 + 偏差
(1.1.1)
总体均值可能取决于我们通常标记为的预测变量的相应值X. 因此，y 是

称为因变量。偏差项表示观察的个体特性，是的，这使得它不同于总体均值。

举个例子，$是的可能是为某个地区的房子支付的价格。人口平均值可以被认为是该城市的房屋支付的平均价格，大概是在给定的时间段内。在这种情况下，偏差项可能非常大，因为房价会因许多因素而有很大差异，例如房屋的大小和状况以及其在该地区的位置。在新西兰，每栋房屋都有政府估价 GV，每五年重新考虑一次。购买房屋的价格将在一定程度上取决于其 GV。回归模型可以写成$X，这G在，作为：

统计代写|实验设计作业代写experimental design代考|HON TO FIT A LINE

由于偏差项涉及无法解释的变化是的，我们试图以某种方式最小化这种情况。假设我们假设是的是一个函数X. 那是
和(是的)=F(X)
然后对于一个样本n对是的′s与他们对应的X′s我们有

上述符号假设X′s不是随机变量，而是预先固定的。如果X′s实际上是我们应该写的随机变量F(X1)=和(是的1∣X1=X1)
= 的平均值是的一世鉴于X一世=X一世
这给出了相同的结果。因此，我们将假设未来X′s是F固定。
最简单的函数示例F如果会出现是的正比于X. 我们可以想象这样一种情况，计量检查员开始测试店主使用的秤。在这种情况下，X′s将是标准措施的重要性，而是的′s将是店主秤所指示的相应重量。该模型将
是是的什么时候X=X一世是（谁）给的
和(是的一世)=乙X一世=F(X一世)
这称为回归曲线。在这个简单的例子中，我们期望参数乙为 1 ，或至少接近 1 。我们将参数视为描述总体某些属性的固定数字。

统计代写|实验设计作业代写experimental design代考|Other Ways of Fitting a Curve

使用最小二乘法的主要问题是，较大的偏差会产生更大的平方，而这种偏差可能会对Fitted 曲线。为了防止这种扭曲，我们可以尝试隔离较大的偏差。我们将在第 4 章的异常值和敏感点下更详细地考虑这一点。或者，我们可以寻求使偏差的不同函数最小化的估计值。

如果模型用人口中位数表示是的，而不是它的平均值，另一种拟合曲线的方法是通过最小化吨，偏差的绝对值之和，即
吨=∑一世=1n|e1|
尽管这是一种行之有效的明智方法，但在寻求估计分布时，实际数学是困难的。Hogg (1974) 建议最小化
吨=∑|e一世|p和1<p<2
和p=1.5，特别是，可能是一个合理的妥协。同样，很难确定结果估计值的准确分布。如果我们对检验假设不那么感兴趣

估计系数然后这种方法提供的估计是稳健的，因为它们不会受到大偏差的过度影响。

请注意，偏差是与回归线的垂直距离。考虑到回归线的垂直（正交）距离，可能看起来更合乎逻辑，或者至少更对称。然而，当我们主要关心的是预测是的从X垂直距离更相关，因为它们代表了预测误差。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写