统计代写|linear regression代写线性回归代考|Samples and Populations

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在统计学中,线性回归是对标量响应和一个或多个解释变量(也称为因变量和自变量)之间的关系进行建模的一种线性方法。一个解释变量的情况被称为简单线性回归;对于一个以上的解释变量,这一过程被称为多元线性回归。这一术语不同于多元线性回归,在多元线性回归中,预测的是多个相关的因变量,而不是单个标量变量。

线性回归中,关系是用线性预测函数建模的,其未知的模型参数是根据数据估计的。 最常见的是,假设给定解释变量(或预测因子)值的响应的条件平均值是这些值的仿生函数;不太常见的是,使用条件中位数或其他一些量化指标。像所有形式的回归分析一样,线性回归关注的是给定预测因子值的响应的条件概率分布,而不是所有这些变量的联合概率分布,这是多元分析的领域。

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我们提供的linear regression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 高等概率论
  • 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|linear regression代写线性回归代考|Samples and Populations

统计代写|linear regression代写线性回归代考|Samples and Populations

We learned earlier that one way to classify statistics is to distinguish between descriptive and inferential methods. At the heart of inferential statistics is a question: how do we know that what we find using a sample reflects what occurs in a population? Can we infer what happens in a population with information from a sample? For instance, suppose we’re interested in determining who is likely to win the next presidential election in the U.S. Assume only two candidates from whom to choose: Warren and Haley. It would be enormously expensive to ask all people who are likely to vote in the next election their choice of president. But we may take a sample of likely voters and ask them for whom they plan to vote. Can we deduce anything about the population of voters based on this sample? The answer is that it depends on a number of factors. Did we collect a good sample? Were the people who responded honest? Do people change their minds as the election approaches? We don’t have space to get into the many issues involved in sampling, so we’ll just assume that our sample is a good representation of the population from which it is drawn.. ${ }^{13}$ Most important for our purposes is this: inferential statistics include a set of methods designed to help researchers answer questions about a population from a sample. Other forms of inferential statistics are not concerned in the same way with a hypothetical population, though. A growing movement is the use of Bayesian inference. We’ll refer to this later, but an adequate description is outside the scope of this book.

An aim of many statistical procedures is to infer something about the population from patterns found in samples. Yet, the cynical-but perhaps most honest-answer is that we never know if what we found says anything accurate about a population. Recall that the definition of statistics provided earlier mentioned uncertainty; statistics is occasionally called the science of uncertainty. The best we can do given a sample is to offer degrees of confidence that our results reflect characteristics of a population. But what do we mean by population? Populations may be divided into target populations and study populations. Target populations are the group about which we wish to learn something. This might include a group in the future (“I wish to know the average weights of future litters sired by my Siberian Husky”) or in the past. Regardless, we typically try to find a population that closely resembles the target population-this is the study population. Many types of populations exist. For instance, we might be interested in the population of seals living on Seal Island off the coast of South Africa; the population of labradoodles in New York City; or the population of voters in Oregon during the 2020 presidential election. Yet some people, when they hear the term population, think it signifies the U.S. population or some other large group. A sample is a set of items chosen from a population. The best known is the simple random sample. Its goal is to select members from the population so that each has an equal chance of being in the sample. Most of the theoretical work on inferential statistics is based on this type of sample. But researchers also use other types, such as clustered samples, stratified samples, and several others.

统计代写|linear regression代写线性回归代考|Sampling Error and Standard Errors

Statistical studies are often deemed valuable because they may be used to deduce something about a population from samples, but keep in mind that researchers usually take only a single sample even though they could conceivably draw many.. ${ }^{14}$ Any sample statistic we compute or test we run must thus consider the uncertainty involved in sampling-the sampling error or the “error” due to using only a portion of a population to estimate a parameter

from that population. ${ }^{15}$ The solution to the problem of uncertainty typically involves using standard errors for test statistics, including the mean, the standard deviation, correlations, medians, and, as we shall see, slope coefficients in LRMs. Briefly, a standard error is an estimate of the standard deviationthe variability-of the sampling distribution. The simplest way to understand this is with an example.

Recall that when we compute the variance or the standard deviation, we are concerned with the spread of the distribution of the variable. But imagine drawing many, many samples from a population and computing a mean for each sample. The result is a sample of means from the population $\left(\bar{x}{i} s\right)$ rather than a sample of observations $\left(x{i} s\right)$. We could then compute a mean of these means, or an overall mean, which should reflect pretty accurately-assuming we do a good job of drawing the samples-the actual mean of the population of observations $\left(\frac{\sum \bar{x}{n i}}{n{s}} \cong \mu\right)$. Let’s expand our examination of puppy litters to help us understand this better.
Litter 1: $[40,45,50,55,60,65,70]$
Litter 2: $[40,45,49,56,60,66,75]$
Litter 3: $[39,55,56,58,61,66,69]$
Litter 4: $[42,44,48,55,57,60,66]$
The means for the litters are $55,56,57$, and 53 . Their average-the mean of the means-is $(55+56+57+53) / 4=55.3$. Suppose the samples exhausted the population of puppies. The population mean is thus 55.4. This is close to the mean of the sample means, off by a skosh because of rounding error.

Imagine if we were to take many more samples of puppies. The means from the samples also have a distribution, which is called the sampling distribution of the means. We could plot these means to determine if they follow a normal distribution. In fact, an important theorem from mathematical statistics states that, as more and more samples are drawn, their means follow a normal distribution even if they come from a non-normally distributed variable in the population (see Chapter 4). This allows us to make important inferential claims about LRMs. We shall learn about these claims in later chapters.

统计代写|linear regression代写线性回归代考|Significance Tests

Standard errors are utilized in a couple of ways. First, recall from elementary statistics that when we use, say, a $t$-test, we compare the $t$-value to a table of $p$-values. All else being equal, a larger $t$-value equates to a smaller $p$-value. This approach is known as significance testing $g^{16}$ because we wish to determine

if our results are “significantly” different from some other possible result. ${ }^{17}$ Significance testing using standard errors is an inferential approach because it is designed to deduce something about a population based on a sample. But the term significant does not mean important. Rather, it originally meant that the results signified or showed something. ${ }^{18} \mathrm{~A} p$-value is only one piece of evidence that indicates, at best, that a finding is worthy of further consideration; we should not claim that a low $p$-value demonstrates we have found the answer or that it reveals the “truth” about some relationship in a population (recall the section on best statistical practices in Chapter 1). A worthwhile adage to remember is “statistical significance is not the same as practical significance.” We’ll discuss these issues in more detail later in the chapter.

Let’s consider an interpretation of a $p$-value and how it’s used in a significance test rather than derive its computation. Recall that many statistical exercises are designed to compare two hypotheses: the null and the alternative. The null hypothesis usually claims that the result of some observation or an association in the data is due to chance alone, such as sampling error only, whereas the alternative hypothesis is that the result or association is due to some nonrandom mechanism. Imagine, for instance, we measure weights from the litters of two distinct dog breeds: Siberian Husky and German Shepherd. We compute the two means and find that litter 1’s is 5 ounces more than litter 2’s. Assuming we treat the two litters as samples from target populations of Siberian Husky and German Shepherd puppies, we wish to determine whether or not the 5 -ounce difference suggests a difference in the population means. The null and alternative hypotheses are usually represented as:
Null: $\quad H_{0}^{0}:$ Mean weight, litter $1\left(\mu_{1}\right)=$ Mean weight, litter $2\left(\mu_{2}\right)$
Alternative: $H_{a}:$ Mean weight, litter $1\left(\mu_{1}\right) \neq$ Mean weight, litter $2\left(\mu_{2}\right)$
Another way of stating the null hypothesis is that the mean weight of Siberian Husky puppies is actually the same as the mean weight of German Shepherd puppies in the populations of these dog breeds. Because a hypothesis of zero difference is frequently used, though often implicit, some call it the nil hypothesis. Recall that the most common way to compare means from two independent groups is with a $t$-test. We’ll see a detailed example of this test later. For now, suppose the $t$-test provides a $p$-value of $0.04$. One way to interpret this value is with the following garrulous statement:
If the difference in population means is zero $\left(\mu_{1}-\mu_{2}=0\right)$ and we draw many, many samples from the two populations, we expect to find a Do you recognize how a $p$-value is a type of probability based on a frequentist inference approach? Researchers are prone to making statements such as “since the $p$-value is below the conventional threshold of $0.05$, the $t$-test provides evidence with which to reject the null hypothesis” or it “validates the alternative hypothesis. ${ }^{\prime 19}$ But, as outlined later, such statements should be avoided. The $p$-value provides only one piece of evidence-some argue only a sliver-with which to evaluate hypotheses.

统计代写|linear regression代写线性回归代考|Samples and Populations

linear regression代写

统计代写|linear regression代写线性回归代考|Samples and Populations

我们之前了解到,对统计数据进行分类的一种方法是区分描述性方法和推理性方法。推论统计的核心是一个问题:我们如何知道我们使用样本发现的内容反映了人口中发生的事情?我们能否通过样本信息推断人口中发生了什么?例如,假设我们有兴趣确定谁有可能赢得美国下一届总统选举 假设只有两个候选人可供选择:沃伦和黑利。向所有可能在下次选举中投票的人询问他们选择的总统将是非常昂贵的。但我们可能会抽取可能选民的样本,并询问他们计划投票给谁。我们能根据这个样本推断出选民人数吗?答案是它取决于许多因素。我们是否收集到了好的样本?回答的人诚实吗?随着选举的临近,人们会改变主意吗?我们没有篇幅来讨论抽样中涉及的许多问题,所以我们只是假设我们的样本很好地代表了从中抽取它的总体。13对我们来说最重要的是:推论统计包括一组旨在帮助研究人员从样本中回答有关人口问题的方法。不过,其他形式的推论统计与假设的人口不同。越来越多的运动是使用贝叶斯推理。我们稍后会提到这一点,但适当的描述超出了本书的范围。

许多统计程序的目的是从样本中发现的模式推断出有关人口的一些信息。然而,愤世嫉俗但也许是最诚实的答案是,我们永远不知道我们的发现是否能准确地说明人口。回想前面提到的不确定性提供的统计定义;统计学有时被称为不确定性科学。给定样本,我们能做的最好的事情就是提供我们的结果反映总体特征的置信度。但是我们所说的人口是什么意思?人群可分为目标人群和研究人群。目标人群是我们希望了解的群体。这可能包括未来的一组(“我想知道我的西伯利亚哈士奇未来产仔的平均重量”)或过去。不管,我们通常会尝试找到一个与目标人群非常相似的人群——这就是研究人群。存在许多类型的人口。例如,我们可能对生活在南非海岸海豹岛上的海豹数量感兴趣;纽约市的拉布拉多犬数量;或 2020 年总统选举期间俄勒冈州的选民人数。然而有些人,当他们听到人口这个词时,认为它表示美国人口或其他一些大群体。样本是从总体中选择的一组项目。最著名的是简单随机样本。它的目标是从总体中选择成员,以便每个人都有平等的机会进入样本。大多数关于推论统计的理论工作都是基于这种类型的样本。但研究人员也使用其他类型,

统计代写|linear regression代写线性回归代考|Sampling Error and Standard Errors

统计研究通常被认为是有价值的,因为它们可以用来从样本中推断出一些关于人口的信息,但请记住,研究人员通常只采集一个样本,即使他们可以想象得到很多样本。14因此,我们计算或运行的任何样本统计量都必须考虑抽样中涉及的不确定性——抽样误差或由于仅使用总体的一部分来估计参数而产生的“误差”

从那个人口。15不确定性问题的解决方案通常涉及使用测试统计的标准误差,包括平均值、标准差、相关性、中位数,以及我们将看到的 LRM 中的斜率系数。简而言之,标准误差是对抽样分布的变异性的标准偏差的估计。理解这一点的最简单方法是举个例子。

回想一下,当我们计算方差或标准差时,我们关心的是变量分布的分布。但是想象一下,从一个总体中抽取很多很多样本并计算每个样本的平均值。结果是来自总体 $\left(\bar{x} {i} s\right)的平均值样本r一种吨H和r吨H一种n一种s一种米pl和这F这bs和r在一种吨一世这ns\left(x {i} s\right).在和C这在ld吨H和nC这米p在吨和一种米和一种n这F吨H和s和米和一种ns,这r一种n这在和r一种ll米和一种n,在H一世CHsH这在ldr和Fl和C吨pr和吨吨是一种CC在r一种吨和l是−一种ss在米一世nG在和d这一种G这这dj这b这Fdr一种在一世nG吨H和s一种米pl和s−吨H和一种C吨在一种l米和一种n这F吨H和p这p在l一种吨一世这n这F这bs和r在一种吨一世这ns\left(\frac{\sum \bar{x} {ni}}{n {s}} \cong \mu\right).大号和吨′s和Xp一种nd这在r和X一种米一世n一种吨一世这n这Fp在pp是l一世吨吨和rs吨这H和lp在s在nd和rs吨一种nd吨H一世sb和吨吨和r.大号一世吨吨和r1:[40,45,50,55,60,65,70]大号一世吨吨和r2:[40,45,49,56,60,66,75]大号一世吨吨和r3:[39,55,56,58,61,66,69]大号一世吨吨和r4:[42,44,48,55,57,60,66]吨H和米和一种nsF这r吨H和l一世吨吨和rs一种r和55,56,57,一种nd53.吨H和一世r一种在和r一种G和−吨H和米和一种n这F吨H和米和一种ns−一世s(55+56+57+53) / 4=55.3 美元。假设样本耗尽了小狗的数量。因此,总体平均值为 55.4。这接近样本均值的平均值,但由于舍入误差而偏离了 skosh。

想象一下,如果我们要采集更多的小狗样本。来自样本的均值也有一个分布,称为均值的抽样分布。我们可以绘制这些均值以确定它们是否服从正态分布。事实上,数理统计的一个重要定理指出,随着越来越多的样本被抽取,它们的均值遵循正态分布,即使它们来自总体中的非正态分布变量(参见第 4 章)。这使我们能够对 LRM 做出重要的推论。我们将在后面的章节中了解这些主张。

统计代写|linear regression代写线性回归代考|Significance Tests

标准误差有多种使用方式。首先,从基本统计中回想一下,当我们使用,比如说,吨-test,我们比较吨-值到表p-价值观。在其他条件相同的情况下,更大吨-值等于更小的p-价值。这种方法称为显着性检验G16因为我们想确定

如果我们的结果与其他一些可能的结果“显着”不同。17使用标准误差的显着性检验是一种推理方法,因为它旨在根据样本推断出有关总体的某些信息。但重要一词并不意味着重要。相反,它最初意味着结果表明或显示了某些东西。18 一种p-价值只是一个证据,充其量表明一项发现值得进一步考虑;我们不应该声称低p-value 表明我们已经找到了答案,或者它揭示了群体中某种关系的“真相”(回想第 1 章中关于最佳统计实践的部分)。值得记住的一句格言是“统计意义不等于实际意义”。我们将在本章后面更详细地讨论这些问题。

让我们考虑一个解释p-value 以及如何在显着性测试中使用它而不是推导其计算。回想一下,许多统计练习旨在比较两个假设:零假设和替代假设。原假设通常声称数据中某些观察或关联的结果仅是由于偶然性,例如仅是抽样误差,而替代假设是结果或关联是由于某些非随机机制造成的。例如,想象一下,我们测量两种不同犬种的幼崽的重量:西伯利亚哈士奇犬和德国牧羊犬。我们计算这两个平均值,发现垃圾 1 比垃圾 2 多 5 盎司。假设我们将这两窝作为西伯利亚雪橇犬和德国牧羊犬目标种群的样本,我们希望确定 5 盎司的差异是否表明总体均值存在差异。原假设和备择假设通常表示为:
空值:H00:平均重量,垃圾1(μ1)=平均重量,垃圾2(μ2)
选择:H一种:平均重量,垃圾1(μ1)≠平均重量,垃圾2(μ2)
陈述零假设的另一种方式是,西伯利亚哈士奇幼犬的平均体重实际上与这些犬种种群中德国牧羊犬幼犬的平均体重相同。因为经常使用零差异假设,尽管通常是隐含的,所以有些人称之为零假设。回想一下,比较两个独立组的平均值的最常见方法是使用吨-测试。稍后我们将看到此测试的详细示例。现在,假设吨-test 提供了一个p-的价值0.04. 解释该值的一种方法是使用以下含糊不清的陈述:
如果总体均值的差异为零(μ1−μ2=0)我们从这两个群体中抽取了很多很多样本,我们希望找到一个p-value 是一种基于频率论推理方法的概率吗?研究人员倾向于发表诸如“自从p-值低于常规阈值0.05, 这吨-test 提供了拒绝零假设的证据”或“验证备择假设”。′19但是,正如后面概述的那样,应该避免这样的陈述。这p-价值只提供了一个证据——有些人认为只提供了一个证据——用来评估假设。

统计代写|linear regression代写线性回归代考 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

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