统计代写|linear regression代写线性回归代考|Review of Elementary Statistical Concepts

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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|Review of Elementary Statistical Concepts

统计代写|linear regression代写线性回归代考|Review of Elementary Statistical Concepts

You were probably introduced to statistics in a pre-algebra course. But your initial introduction may have occurred in elementary or primary school. When was the first time you heard the word mean used to indicate the average of a set of numbers? What about the term median? Perhaps in an early math class. Do you recall doing graphing exercises: being given two sets of numbers and plotting them on the $x$ – and $y$-axes (also called the coordinate axes)? You may remember that the set of numbers for $x$ and $y$ are called variables because they can take on different values (e.g., $[12,14,17])$. Contrast these to constants: sets of numbers that contain single values only $\left(\mathrm{e} \cdot \mathrm{g}_{-}[2,2,2]\right.$, $[17,17,17])$.

At some point, you were likely introduced to the concepts of elementary probability. ${ }^{1}$ Your introduction might have included a motivating question such as, “What is the probability or chance that, if you choose one ball from a closed container that includes one red and five blue balls, it will be the red ball?” You were instructed to first count the number of possible outcomes (since the container includes six balls, any one of which could be chosen, six possible outcomes exist), which served as a denominator. You then counted the particular outcome-choosing the red ball. Only one red ball is in the container, so the count of this outcome is one. This was a numerator. Putting these two counts together in a fraction resulted in a probability of choosing the red ball of $1 / 6$, or about $0.167$. The latter number is also called a proportion. Probabilities and proportions fall between zero and one; this constitutes the first rule of probability. ${ }^{2}$ Multiplying them by 100 creates percentages $(0.167 \times$ $100=16.7 \%$. But what does a probability of $0.167$ mean? One interpretation is that we expect to choose a red ball about $16.7 \%$ of the time when we pick balls one at a time over and over (don’t forget that we need to replace the chosen ball each time-this is called sampling with replacement). Each selection is called an experiment, so selecting the balls over and over again composes multiple experiments. But is it realistic to expect to choose a red ball $16.7 \%$ of the time? We could test this assumption by repeating the experiment again and

again and keeping a lengthy record. Statisticians refer to this approach-the theoretical idea rather than the actual tedious counting-as frequentist probability or frequentism since it examines, but actually assumes, what happens when something countable is repeated over and over. ${ }^{3}$

Probabilities are presented using, not surprisingly, the letter $P$. One way to symbolize the probability of choosing a red ball is with $P($ red). We may write $P($ red $)=0.167$ or $P($ red $)=1 / 6$. You might recall that some statistical tests, such as $t$-tests or analysis of variance (ANOVA)s, are accompanied by $p$-values. As we shall learn, $p$-values are a type of probability used in many statistical tests.

The basic foundations of statistical analysis are established by combining the principles of probability and elementary statistical concepts. Among a variety of descriptions, statistics may be defined as the analysis of data and the use of such data to make decisions in the presence of uncertainty. This two-pronged definition is useful for delineating two general types of statistical analyses: descriptive and inferential. Researchers use descriptive methods to analyze one or more variables in order to describe or summarize their characteristics, often with measures of central tendency and measures of dispersion. Descriptive methods are also employed to visualize variables, such as with histograms, density plots, stem-and-leaf plots, and box-and-whisker plots. We’ll see examples of some of these later in the chapter.

Inferential statistics are designed to infer or deduce something about a population from a sample and are useful for decision making, policy analysis, and gaining an understanding of patterns of associations among people, states, companies, or other units of interest. But uncertainty is a key issue since inferring something about a population requires acknowledgment that any sample contains limited information about that population. We’ll return to the issue of inferential statistics once we’ve reviewed some tools for describing variables.

统计代写|linear regression代写线性回归代考|Measures of Central Tendency

Now that we have some background information about statistics, let’s turn to some statistical measures, including how they are used and computed. We’ll begin with measures of central tendency. Suppose we collect data on the weights (in ounces) of several puppies in a litter. We place each puppy on a digital scale, trying to hold them still so we can record their weights. What is your best guess of the average weight of the puppies in the litter? Perhaps

not always the best, but the most common measure is the arithmetic mean, ${ }^{6}$ which is computed using the formulas in Equation 2.1.
$$
\mathrm{E}[\mathrm{X}]=\mu=\frac{\sum X_{i}}{N} \text { (population) or } \bar{x}=\frac{\sum x_{i}}{n} \text { (sample) }
$$
The term on the left-hand side of the first equation, $E[X]$, is a symbolic way of expressing the expected value of variable $X$, which is often used to represent the mean. We could also list this term as E[weight in ounces], but, as long as it’s clear that $X=$ weight in ounces, using $E[X]$ is satisfactory. The Greek letter $\mu$ represents the population mean, whereas $\bar{x}$ in the second part of the equation is the sample mean. The formula for computing the mean is simple. Add all the values of the variable and divide the sum by the number of observations. The cumbersome symbol that looks like an overgrown $E$ in the numerator of Equation $2.1$ is the summation sign; it tells us to add whatever is next to it. The symbol $X_{i}$ or $x_{i}$ signifies specific values of the variable, or the individual puppy weights we’ve recorded. The subscript $i$ indicates each observation. The letter $N$ or $n$ is the number of observations. This may be represented as $i \ldots n$. If $n=5$, then five individual observations are in the sample. Uppercase Roman letters represent population values and lowercase Roman letters represent sample values. $E[X]=\bar{x}$ implies that the sample mean is designed to estimate the population expected value or the population mean. Here’s a simple example. Our Siberian Husky, Steppenwolf, sires a litter of puppies. We weigh them and record the following: $[48,52,58,62,70]$. The sum of this set is $[48+52+58+62+70]=290$, with a sample mean of $290 / 5=58$ ounces. The mean is also called the center of gravity. Suppose we have a plank of wood that is of uniform weight across its span. We order the puppies from lightest to heaviest-trying to space them out proportional to their weights-and place them on the plank of wood. The mean is the point of balance, or the point at which we would place a fulcrum underneath the plank to balance the puppies.
The mean has a couple of interesting features:

  1. It is measured in the same units as the observations. If the observations are not all measured in the same unit (e.g., some puppies’ weights are in grams, others in ounces), then the mean is not interpretable.
  2. The mean provides a suitable measure of central tendency if the variable is measured continuously and is normally distributed.

统计代写|linear regression代写线性回归代考|Measures of Dispersion

Knowing a variable’s central tendency is just part of the story. As suggested by Figures $2.1$ and 2.2, depicting how much a variable fluctuates around the mean is also important. The objective of measures of dispersion is to indicate the spread of the distribution of a variable. You should be familiar with the term standard deviation, the most common dispersion measure for continuous variables. $.^{12}$ Before seeing the formula for this measure, however, let’s consider some other measures of dispersion. The most basic for a continuous

variable is the sum of squares, or $S S[x]$. Assuming a sample, the formula is supplied in Equation 2.3.
$$
\operatorname{SS}[\mathrm{x}]=\Sigma\left(x_{i}-\bar{x}\right)^{2}
$$
We first compute deviations from the mean $\left(x_{i}-\bar{x}\right)$ for each observation, square each, and then add them. If you’ve learned about ANOVA models, the sum of squares should be familiar. Perhaps you even recall the various forms of the sum of squares. We’ll learn more about these in Chapter 5 .
The second measure of dispersion, and one you should recognize, is the variance, which is labeled $s^{2}$ for samples and $\sigma^{2}$ (sigma-squared) for populations. The sample formula is shown in Equation 2.4.
$$
\operatorname{var}[x]=s^{2}=\frac{\sum\left(x_{i}-\bar{x}\right)^{2}}{n-1}
$$
The variance is the sum of squares divided by the sample size minus one and is measured in squared units of the variable. The standard deviation (symbolized as $s$ (sample) or $\sigma$ (population)), however, is measured in the same units as the variable (see Equation 2.5).
$$
\mathrm{sd}[\mathrm{x}]=s=\sqrt{\frac{\sum\left(x_{i}-\bar{x}\right)^{2}}{n-1}}
$$
A variable’s distribution is often represented by its mean and standard deviation (or variance). A variable that follows a normal distribution, for instance, is symbolized as $X \sim N(\mu, \sigma)$ or $x \sim N(\bar{x}, \mathrm{~s})$ (the wavy line means “distributed as”). When two variables are measured in the same units and have the same mean, one is less dispersed than the other if its standard deviation is smaller. Recall that the means for the two litters of puppies are 55 and 70 . Their standard deviations are $10.8$ and 47.1. The weights in the second litter have a much larger standard deviation, which is not surprising given their range. Another useful measure of dispersion is the coefficient of variation (CV), which is computed as $s / \bar{x}$ and is usually then multiplied by 100 . The CV is valuable for comparing distributions because it shows how much a variable fluctuates about its mean. The CVs for the two litters are $19.6$ and 67.1.

Earlier we discussed the median and trimmed mean as robust alternatives to the mean. Robust measures of dispersion are also available, such as the interquartile range (75th $-25$ th quartile) and the median absolute deviation (MAD): median ( $\left.\left|x_{i}-\tilde{x}\right|\right)$, or the median of the absolute values of the observed $x$ s minus the median. Whereas the standard deviations and CVs of the two puppy litters are far apart, the MADs are the same: 14.8. The one extreme value in litter 2 does not affect this robust measure of dispersion.

统计代写|linear regression代写线性回归代考|Review of Elementary Statistical Concepts

linear regression代写

统计代写|linear regression代写线性回归代考|Review of Elementary Statistical Concepts

您可能在预代数课程中被介绍过统计学。但是您最初的介绍可能发生在小学或小学。您第一次听到用于表示一组数字的平均值的平均值这个词是什么时候?中位数这个词怎么样?也许在早期的数学课上。你还记得做图形练习吗:给出两组数字并将它们绘制在X- 和是-axes(也称为坐标轴)?你可能还记得一组数字X和是被称为变量是因为它们可以取不同的值(例如,[12,14,17]). 将这些与常量进行对比:仅包含单个值的数字集(和⋅G−[2,2,2], [17,17,17]).

在某些时候,您可能已经了解了基本概率的概念。1你的介绍可能包括一个激励性的问题,例如,“如果你从一个包含一个红色和五个蓝色球的封闭容器中选择一个球,它是红球的概率或几率是多少?” 你被要求首先计算可能结果的数量(因为容器包括六个球,其中任何一个都可以选择,所以存在六个可能的结果),它作为分母。然后你计算特定的结果——选择红球。容器中只有一个红球,因此该结果的计数为 1。这是一个分子。将这两个计数放在一个分数中导致选择红球的概率1/6,或大约0.167. 后一个数字也称为比例。概率和比例介于零和一之间;这构成了概率的第一条规则。2将它们乘以 100 创建百分比(0.167× 100=16.7%. 但是概率是多少0.167意思是?一种解释是,我们期望选择一个关于16.7%在我们一次又一次地挑选一个球的时候(不要忘记我们每次都需要更换所选择的球——这被称为带更换的采样)。每次选择都称为一个实验,因此一遍又一遍地选择球构成了多个实验。但是期望选择一个红球是否现实16.7%的时间?我们可以通过再次重复实验来检验这个假设

再次并保持冗长的记录。统计学家将这种方法(理论思想而不是实际繁琐的计数)称为频率论概率或频率论,因为它检查但实际上假设当可数的事情一遍又一遍地重复时会发生什么。3

毫不奇怪,使用字母来表示概率磷. 一种表示选择红球概率的方法是磷(红色的)。我们可以写磷(红色的)=0.167或者磷(红色的)=1/6. 您可能还记得一些统计测试,例如吨- 检验或方差分析 (ANOVA),伴随着p-价值观。正如我们将要学习的,p-值是许多统计测试中使用的一种概率。

统计分析的基本基础是通过结合概率原理和基本统计​​概念而建立的。在各种描述中,统计可以定义为对数据的分析以及在存在不确定性的情况下使用这些数据做出决策。这个双管齐下的定义对于描述两种一般类型的统计分析很有用:描述性和推理性。研究人员使用描述性方法来分析一个或多个变量,以描述或总结它们的特征,通常使用集中趋势的度量和分散的度量。描述性方法也用于可视化变量,例如直方图、密度图、茎叶图和盒须图。我们将在本章后面看到其中一些示例。

推论统计旨在从样本中推断或推断出有关人口的某些信息,可用于决策、政策分析以及了解人、州、公司或其他利益单位之间的关联模式。但不确定性是一个关键问题,因为推断人口的某些事情需要承认任何样本都包含关于该人口的有限信息。一旦我们回顾了一些描述变量的工具,我们将回到推论统计的问题。

统计代写|linear regression代写线性回归代考|Measures of Central Tendency

现在我们有了一些关于统计的背景信息,让我们转向一些统计度量,包括它们是如何使用和计算的。我们将从集中趋势的度量开始。假设我们收集了一窝小狗的重量数据(以盎司为单位)。我们将每只小狗放在一个数字秤上,试图让它们保持静止,这样我们就可以记录它们的重量。您对垫料中幼犬平均体重的最佳猜测是多少?也许

并不总是最好的,但最常见的衡量标准是算术平均值,6使用公式 2.1 中的公式计算得出。
和[X]=μ=∑X一世ñ (人口)或 X¯=∑X一世n (样本) 
第一个等式左边的项,和[X], 是表示变量期望值的符号方式X,通常用于表示均值。我们也可以将此术语列为 E[重量单位为盎司],但是,只要清楚X=以盎司为单位的重量,使用和[X]是令人满意的。希腊字母μ代表总体平均值,而X¯等式的第二部分是样本均值。计算平均值的公式很简单。将变量的所有值相加,然后将总和除以观察数。看起来像杂草丛生的笨重符号和在方程的分子中2.1是求和符号;它告诉我们添加它旁边的任何内容。符号X一世或者X一世表示变量的特定值,或我们记录的个体小狗体重。下标一世表示每个观察。信ñ或者n是观察次数。这可以表示为一世…n. 如果n=5,则样本中有五个单独的观察值。大写罗马字母代表总体值,小写罗马字母代表样本值。和[X]=X¯意味着样本均值旨在估计总体预期值或总体均值。这是一个简单的例子。我们的西伯利亚雪橇犬 Steppenwolf 育有一窝小狗。我们称重并记录以下内容:[48,52,58,62,70]. 这组的总和是[48+52+58+62+70]=290, 样本均值为290/5=58盎司。平均值也称为重心。假设我们有一块在其跨度上重量均匀的木板。我们将幼犬从最轻到最重排序——试图按照它们的重量成比例地把它们分开——然后把它们放在木板上。平均值是平衡点,或者我们将在木板下方放置一个支点以平衡幼犬的点。
均值有几个有趣的特征:

  1. 它的测量单位与观测值相同。如果观察结果并非全部以相同的单位测量(例如,一些幼犬的体重以克为单位,另一些以盎司为单位),则平均值无法解释。
  2. 如果变量是连续测量的并且是正态分布的,则平均值提供了一种合适的集中趋势度量。

统计代写|linear regression代写线性回归代考|Measures of Dispersion

了解变量的集中趋势只是故事的一部分。如图所示2.1和 2.2,描述变量围绕平均值波动的程度也很重要。离散度量的目的是表明变量分布的扩展。您应该熟悉术语标准差,这是最常见的连续变量离散度度量。.12然而,在看到这个度量的公式之前,让我们考虑一些其他的分散度量。最基本的连续

变量是平方和,或小号小号[X]. 假设一个样本,公式在公式 2.3 中提供。
党卫军⁡[X]=Σ(X一世−X¯)2
我们首先计算与平均值的偏差(X一世−X¯)对于每个观察,将每个观察平方,然后将它们相加。如果您了解 ANOVA 模型,那么平方和应该很熟悉。也许您甚至还记得平方和的各种形式。我们将在第 5 章中详细了解这些内容。
离散度的第二个度量,你应该认识到的,是方差,它被标记为s2对于样品和σ2(西格玛平方)的人口。示例公式如公式 2.4 所示。
曾是⁡[X]=s2=∑(X一世−X¯)2n−1
方差是平方和除以样本量减一,并以变量的平方单位测量。标准差(符号为s(样本)或σ但是,(人口))以与变量相同的单位进行测量(参见公式 2.5)。
sd[X]=s=∑(X一世−X¯)2n−1
变量的分布通常由其均值和标准差(或方差)表示。例如,服从正态分布的变量用符号表示为X∼ñ(μ,σ)或者X∼ñ(X¯, s)(波浪线表示“分布为”)。当两个变量以相同的单位测量并且具有相同的均值时,如果其标准差较小,则一个变量的分散程度低于另一个变量。回想一下,两窝小狗的平均值是 55 和 70 。它们的标准差是10.8和 47.1。第二窝的重量有更大的标准偏差,考虑到它们的范围,这并不奇怪。离散度的另一个有用度量是变异系数 (CV),其计算公式为s/X¯然后通常乘以 100 。CV 对于比较分布很有价值,因为它显示了变量对其均值的波动程度。两窝的简​​历是19.6和 67.1。

早些时候,我们讨论了中位数和修剪后的平均值作为平均值的稳健替代方案。还可以使用可靠的分散度量,例如四分位距(第 75−25th 四分位数)和中位数绝对偏差(MAD):中位数(|X一世−X~|),或观察到的绝对值的中位数Xs 减去中位数。尽管两窝幼犬的标准差和 CV 相差甚远,但 MAD 相同:14.8。垃圾 2 中的一个极值不会影响这种稳健的分散测量。

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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