## 统计代写|linear regression代写线性回归代考|Formulas for the Slope Coefficient and Intercept

statistics-lab™ 为您的留学生涯保驾护航 在代写linear regression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linear regression代写方面经验极为丰富，各种代写linear regression相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|linear regression代写线性回归代考|Formulas for the Slope Coefficient and Intercept

What is the source of the LRM slope coefficient and intercept? How does $\mathrm{R}$ know where to place the linear fit line? Does it plot the data and then try out several lines to see which one does the best job of representing the data? It should come up with a line that is closest, on average, to all the data points in the plot. If we calculate an aggregate measure of distance from the points to the best-fitting line, such as a summary measure of the residuals (see Figure 3.7), it should produce as small a value as possible. Such an exercise is the logic underlying the most common method for fitting the regression line, which $\mathrm{R}$ and other software use-ordinary least squares (OLS) or the principle of least squares. Many researchers refer to the LRM as OLS regression or as an OLS regression model because this estimation technique is used so often. ${ }^{16}$ Other estimation routines, such as weighted least squares (WLS) and maximum likelihood (ML), can also estimate regression models. But we’ll focus

on OLS given its frequent use and because many statistical software routines rely on it.
The goal of OLS is to obtain the minimum value for Equation $3.8$.
$$\mathrm{SSE}=\Sigma\left(y_{i}-\hat{y}{i}\right)^{2}=\Sigma\left(y{i}-\left{\alpha+\beta_{1} x_{i}\right}\right)^{2}$$
SSE is an abbreviation for the sum of squared errors. ${ }^{17}$ The $\left(y_{i}-\hat{y}{i}\right)$ portion represents the residuals, which we learned about in the last section. Thus, the SSE is also the sum of the squared residuals $\left(\sum \hat{\varepsilon}{i}^{2}\right)$. Think once again about the residuals, such as those depicted in Figure 3.7. If the SSE equals zero, then all the data points fall on the fit line. The Pearson’s $r$ is also one or negative one (depending on whether the association is positive or negative).

## 统计代写|linear regression代写线性回归代考|Hypothesis Tests for the Slope Coefficient

H0:b≥0 H一种:b<0

H0:b=0 对比 H一种:b≠0

## 统计代写|linear regression代写线性回归代考|Chapter Summary

1. 计算 AlcoholUse 变量的平均值、中位数、标准差、偏度和峰度。根据此信息，评论其可能的分布。
2. 在中创建核密度图R酒精使用。描述这个变量的分布。
3. 在中创建散点图R将 AlcoholUse 指定为是-轴。在X-轴，使用与酒精使用具有最高皮尔逊相关性（离零最远）的实质性变量（不是行或 ID 变量）。在图中包括一条红色线性拟合线。在图中包含一条蓝色水平线，表示酒精使用的平均值。描述两个变量之间的线性关联。
4. 估计一个 LRM，它使用 AlcoholUse 作为结果变量，作为解释变量，你在X- 练习 3 中的轴。
一种。解释与解释变量相关的截距和斜率系数。
湾。解释p-价值和95%C一世与斜率系数有关。

## 有限元方法代写

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。

## 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。

## 统计代写|linear regression代写线性回归代考|Simple Linear Regression Models

statistics-lab™ 为您的留学生涯保驾护航 在代写linear regression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linear regression代写方面经验极为丰富，各种代写linear regression相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|linear regression代写线性回归代考|Simple Linear Regression Models

Chapter 2 describes a conceptual model as an abstract representation of anticipated associations among concepts or ideas designed to represent broader ideas (such as self-esteem, political ideology, or education). Ideally, statistical models are guided by conceptual models, which are used to delineate hypotheses or research questions. Statistical models outline probabilistic relationships among a set of variables, with the goal of estimating whether there are nonrandom patterns among them. Like conceptual models, these models tend to be simplifications of the complexity that occurs in nature but offer enough detail to predict or understand patterns in the data. A useful way of thinking about statistical models is that they assess ways that a set of data may have been produced, or, in statistical parlance, a data generating process (DGP).

A regression model is a type of statistical model that aims to estimate the association between one or more explanatory variables $(x \mathrm{~s})$ and a single outcome variable $(y)$. An outcome variable is presumed to depend on or to be predicted by the explanatory variables. But the explanatory variables are seen as independent predictors of the outcome variable; hence, they are often called independent variables. Later chapters discuss why this term can be misleading because these variables may, if the model is set up correctly, relate to one another. Many researchers therefore prefer to call those included in a regression model explanatory and outcome variables (used in this book), predictor and response variables, exogenous and endogenous variables, or similar terms. The response or endogenous variable is synonymous with the outcome variable.

An LRM seeks to account for or explain differences in values of the outcome variable with information about values of the explanatory variables. The LRM also seeks, to varying degrees, answers to the following questions:

1. What are the predicted mean levels of the outcome variable for particular values of the explanatory variables?
2. What is the most appropriate equation for representing the association between each explanatory variable and the outcome variable? This includes assessing the direction (positive? negative?) and magnitude of each association.Which explanatory variables are good predictors of the outcome and which are not? The answer is based on several results from the LRM, including the size of the coefficients, differences in predicted means, the $p$-values, and the CIs, but each has limitations. ${ }^{1}$

## 统计代写|linear regression代写线性回归代考|Assumptions of Simple LRMs

The LRM rests on several assumptions that dictate how well it operates. Most of these concern characteristics of the population data and focus on the errors of prediction $\left(\varepsilon_{i}\right)$. But having access to information from a population is unusual, so we must assess, roughly or indirectly, the assumptions of LRMs with information from a sample. In other words, since we do not have information from the $Y$, we cannot compute $\varepsilon_{i}$ directly. The sample includes only the $x$ s and $y$, so we must use an estimate of $\varepsilon_{i}$. This estimate, depicted as the error term $\left(\hat{\varepsilon}{i}\right)$ in Equation $3.5$, is represented by the residuals ${ }^{6}$ from the model, which are computed as $\left(y{i}-\hat{y}{i}\right)$. Rather than distinguishing the errors of prediction from the population and the sample, however, we’ll take for granted that the sample provides a good estimate of $\bar{Y}{i}$ with $\hat{y}{i}$ so that $\left(y{i}-\hat{y}{i}\right) \cong\left(y{i}-\bar{Y}_{i}\right)$.
Here are the key assumptions of simple LRMs:

1. Independence: the errors of prediction $\left(\varepsilon_{i}\right)$ are statistically independent of one another. Using the example from the Nations2018 dataset, we assume that the errors in predicting public expenditures across nations are independent. In practice, this often implies that the observations are independent. One way to (almost) guarantee this is to use simple random sampling. (However, in this example we should ask ourselves: are the economic conditions of these nations likely to be independent?) Chapters 8 and 15 outline additional ways to understand the independence assumption.
2. Homoscedasticity (constant variance): the errors of prediction have equivalent variance for all possible values of $X$. In other words, the variance of the errors is assumed to be constant across the distribution of X. At this point it may be simpler, yet imprecise, to think about the $Y$ values and ask whether their variability is equivalent at different values of $X$. Chapter 9 discusses the homoscedasticity assumption.

## 统计代写|linear regression代写线性回归代考|An Example of an LRM Using $R$

You may be confused at this point, though let’s hope not. An example using some data should be beneficial. The dataset StateData2018.csv includes a number of variables from all 50 states in the U.S. These data include population characteristics, crime rates, substance use rates, and various economic and social factors. We’ll treat the data as a sample, even though one might argue that they represent a population. Similar to the code that produces Figure 3.2, the following $\mathrm{R}$ code creates a scatter plot and overlays a linear fit line with the number of opioid deaths per 100,000 residents (OpioidoDDeathRate) as the outcome (y) variable and average life satisfaction (LifeSatis), which is based on state-specific survey data ${ }^{8}$ that gauges happiness and satisfaction with one’s family life and health among adult residents, as the explanatory $(x)$ variable.
R code for Figure $3.4$
plot (StateData2018\$LifeSatis, StateData2018 \$OpioidoDdeathRate, xlab=”Average life
satisfaction”, ylab=”Opioid overdose deaths per
100,000 population”, pch=1)
abline (1m (StateData2018\$OpioidodDeathRate StateData2018\$LifeSatis), col=”red”)
R code for Figure $3.4$
plot (StateData2018\$LifeSatis, StateData2018 \$OpioidoDDeathRate, xlab=”Average life
satisfaction”, ylab= “Opioid overdose deaths per
100,000 population”, pch=1)
abline ( $1 \mathrm{~m}$ (StateData2018\$OpioidoDDeathRate$~$StateData2018\$LifeSatis), col= “red”)
Figure $3.4$ displays a negative slope. Yet the points diverge from the line;
only a few are relatively close to it. Do you see any other patterns in the data
relative to the line?
We’ll now estimate a simple LRM using these two variables. As you may
have already determined given R’s abline function that created the linear
fit lines in Figures $3.2$ and 3.4, an LRM is estimated in R using the lm func-
tion. The abbreviation signifies “linear model.”
Figure $3.4$ displays a negative slope. Yet the points diverge from the line; only a few are relatively close to it. Do you see any other patterns in the data relative to the line?

We’ll now estimate a simple LRM using these two variables. As you may have already determined given R’s abline function that created the linear fit lines in Figures $3.2$ and 3.4, an LRM is estimated in R using the $1 \mathrm{~m}$ function. The abbreviation signifies “linear model.”

## 统计代写|linear regression代写线性回归代考|Simple Linear Regression Models

LRM 旨在利用有关解释变量值的信息来解释或解释结果变量值的差异。LRM 还在不同程度上寻求以下问题的答案：

1. 对于解释变量的特定值，结果变量的预测平均水平是多少？
2. 什么是表示每个解释变量和结果变量之间关联的最合适的方程？这包括评估每个关联的方向（正面？负面？）和幅度。哪些解释变量可以很好地预测结果，哪些不是？答案基于 LRM 的几个结果，包括系数的大小、预测均值的差异、p-values 和 CI，但每个都有局限性。1

## 统计代写|linear regression代写线性回归代考|Assumptions of Simple LRMs

LRM 依赖于几个假设，这些假设决定了它的运作情况。其中大多数关注人口数据的特征，并关注预测的错误(e一世). 但是从人群中获取信息是不寻常的，因此我们必须粗略或间接地评估 LRM 的假设与来自样本的信息。换句话说，由于我们没有来自是，我们无法计算e一世直接地。该样本仅包括X沙是, 所以我们必须使用一个估计e一世. 这个估计，描述为误差项(e^一世)在方程3.5, 由残差表示6从模型，计算为(是一世−是^一世). 然而，我们不会将预测误差与总体和样本区分开来，而是理所当然地认为样本提供了一个很好的估计是¯一世和是^一世以便(是一世−是^一世)≅(是一世−是¯一世).

1. 独立性：预测的错误(e一世)在统计上相互独立。使用 Nations2018 数据集中的示例，我们假设预测各国公共支出的错误是独立的。在实践中，这通常意味着观察是独立的。（几乎）保证这一点的一种方法是使用简单的随机抽样。（然而，在这个例子中，我们应该问自己：这些国家的经济状况是否可能是独立的？）第 8 章和第 15 章概述了理解独立假设的其他方法。
2. Homoscedasticity（常数方差）：预测的误差对于所有可能的值具有等价的方差X. 换句话说，假设误差的方差在 X 的分布中是恒定的。在这一点上，考虑是并询问它们的可变性在不同的值下是否相等X. 第 9 章讨论了同方差性假设。

## 统计代写|linear regression代写线性回归代考|An Example of an LRM Using R

plot (StateData2018 $LifeSatis, StateData2018$ OpioidoDdeathRate, xlab=”平均生活

100,000 人口”, pch=1)
abline (1m (StateData2018 $OpioidodDeathRate StateData2018$ LifeSatis), col=”red” )

plot (StateData2018 $LifeSatis, StateData2018$ OpioidoDDeathRate, xlab=”平均生活

100,000 人中阿片类药物过量死亡人数”, pch=1)
abline (1 米（StateData2018 $OpioidoDDeathRate StateData2018$ LifeSatis), col= “red”)

。该缩写表示“线性模型”。

## 有限元方法代写

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。

## 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。

## 统计代写|linear regression代写线性回归代考|Comparing Means from Two Groups

statistics-lab™ 为您的留学生涯保驾护航 在代写linear regression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linear regression代写方面经验极为丰富，各种代写linear regression相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|linear regression代写线性回归代考|Comparing Means from Two Groups

We referred to a mean-comparison test, the $t$-test, earlier in the chapter when comparing the weights of two litters of puppies. Let’s review this test in more detail. First, recall that we may compare many statistics from distributions, including standard deviations and standard errors. A common exercise, however, is to assess, in an inferential sense, whether the mean from one population is likely different from the mean of another population. If we draw samples from two populations, we should consider sampling error. Our samples probably have different means than the true population means,

so we should take this likely variation into account. A $t$-test is designed to evaluate whether two means are likely different across populations by, first, taking the difference between the sample means and, second, evaluating the presumed sampling error.

The name $t$-test is used because the $t$-value that is the basis of the test follows a Student’s $t$-distribution. ${ }^{32}$ This distribution is almost indistinguishable from the normal distribution when the sample size is greater than 50 . At smaller sample sizes, the $t$-distribution has fatter tails and is a bit flatter in the middle than the normal distribution.

Equations $2.13$ and $2.14$ demonstrate how to compute a conventional $t$-test that assumes the means are drawn from two independent populations.
$$\begin{gathered} t=\frac{\bar{x}-\bar{y}}{s_{p} \sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}} \ \text { where } s_{p}=\sqrt{\frac{\left(n_{1}-1\right) s_{1}^{2}+\left(n_{2}-1\right) s_{2}^{2}}{\left(n_{1}+n_{2}\right)-2}} \end{gathered}$$
The $s_{p}$ in the equations is the pooled standard deviation, which estimates the sampling error. The $n$ s denote the sample sizes and the $s^{2} s$ are the variances for the two groups. A key assumption of this test is that the variances from the two groups are equal. Some researchers are uncomfortable making this assumption-or it may not be tenable-so they use the estimator shown in Equation 2.15, which is called Welch’s $t$-test. ${ }^{33}$
$$t^{\prime}=\frac{\bar{x}-\bar{y}}{\sqrt{\frac{\operatorname{var}(x)}{n_{1}}+\frac{\operatorname{var}(y)}{n_{2}}}}$$
Since the $t^{\prime}$ does not follow the $t$-distribution, we must rely on special tables to determine the probability of a difference between the two means when using Welch’s test. Fortunately, $R$ and other statistical software provide both versions of the $t$-test.

Here’s an example of a $t$-test that uses litters 3 and 4 from the earlier puppy samples. As a reminder, the weights in ounces are

Litter 3: $[39,55,56,58,61,66,69]$
Litter 4: $[42,44,48,55,57,60,66]$
The means are $57.7$ and $53.1$, with a difference of 4.6. A t-test returns a $t$-value of $0.92$ with a $p$-value of $0.37$ and a CI of ${-6.2,15.4}$. The interpretations of the two inferential measures are:
$p$-value: if we take many, many samples from the two populations of puppies and the difference in the population means is zero, we expect to find a difference in sample means of $4.6$ ounces or more approximately 37 times, on average, out of every 100 pairs of samples we examine.
$95 \%$ CI: given a difference of $4.6$ ounces, we are $95 \%$ confident that the difference in the population means falls in the interval $-6.2$ and $15.4$.

## 统计代写|linear regression代写线性回归代考|Examples Using $R$

The file Nations2018.csv ${ }^{37}$ is a small dataset that contains data from eight nations. The variables are public expenditures (expend), a measure of government expenditures on individual and collective goods and services as a percentage of the nation’s gross domestic product, openness to trade with other nations (econopen), and the percentage of the labor force that is unionized (perlabor). Let’s use $R$ to compute some of the statistics discussed in this chapter. To begin, after importing the dataset and installing the $R$ package psych, ${ }^{38}$ use the following code to obtain descriptive statistics for the public expenditures variable:

R code
library (psych) # to activate the package
describe (Nations2018\$expend) R output (abbreviated)$\begin{array}{llllllll} & 8 & 19.79 & 2.87 & 19.8 & 19.8 & 1.85 & 14.1\end{array}$range skew kurtosis se$9.3-0.6-0.62 \quad 1.01$The describe function provides various statistics, including the mean, standard deviation (sd), median, trimmed mean, median absolute deviation (mad), range, skewness, kurtosis, and standard error of the mean (se). The$95 \%$CI for the mean is simple to calculate using the t.test function (e.g., t.test (Nations 2018 sexpend)). R also has several user-written packages that include CI functions (e.g., Hmisc). For public expenditures, the$95 \%$CI from the t.test function is$17.39$and 22.19. How should we interpret it? Compute the correlation and covariance between public expenditures and economic openness (hint: see the earlier$\mathrm{R}$function, but you might also wish to review the documentation for the psych package for similar functions). You should find a correlation of$0.64$and a covariance of$36.36$. Let’s examine another dataset. Open the data file GSS2018.csv.${ }^{39}$The dataset contains a variable called female, which includes two categories: male and female.${ }^{40}$We’ll use it to compare personal income (labeled pincome) for these two groups using a$t$-test.$R$code t.test (GSS2018\$pincome GSS2018\$female) What does the output show? What is the$t$-value? What is the$p$-value? The$95 \%$CI? How should we interpret the$95 \%$CI? Suppose we wish to test a conceptual model that proposes that males have higher incomes than females in the U.S. Are the results consistent with this model? Let’s practice building some graphs using the variables pincome and sei in the GSS2018 dataset. What do kernel density plots show about them?$?^{4}$Box-and-whisker plots? 12 What measures of central tendency are most appropriate for these variables? If one of them is skewed, can you find a transformation that normalizes its distribution? ## 统计代写|linear regression代写线性回归代考|Chapter Exercises The dataset called American.csv consists of data from a 2004 national survey of adults in the U.S. Our objective is to examine some variables from this dataset. In addition to an identification variable (id), they include: • educate: years of formal education. • american: a continuous measure of what the respondent thinks it means to be “an American” that ranges from believing that being an American means being a Christian, speaking English only, and being born in the U.S. (high end of the scale) to not seeing these as indicators of being an American (low end of the scale). • group: a binary variable that indicates whether or not the respondent is an immigrant to the U.S. After importing the dataset into$R$, complete the following exercises: 1. Compute the means, medians, standard deviations, variances, skewnesses, and standard errors of the means for the variables educate and american. 2. Furnish the number of respondents in each category of the group variable, followed by the percentage of respondents in each category of this variable. What percentage of the sample is in the “Not immigrant” category? What percentage of the sample is in the “Immigrant” category? 1. Conduct a$t$-test (Welch’s version) that compares the means of the variable american for those in the “Not immigrant” group and those in the “Immigrant” group. Report the means for the two groups, the$p$-value from the$t$-test, and the$95 \%$CI from the$t$-test. Interpret the$p$-value and the$95 \%$CI. 2. What is the Pearson’s correlation of educate and american? What is the$95 \%$CI of the correlation? Provide a brief interpretation of the Pearson’s correlation. 3. Create a kernel density plot and a box plot of the variable american. Describe its distribution. 4. Challenge: use R’s plot function to create a scatter plot with educate on the$x$-axis and american on the$y$-axis. Describe the pattern shown by the scatter plot. Why is a scatter plot limited in this situation? Search within$R$or online for the R function jitter. Use this function to modify the scatter plot. Why is the scatter plot still of limited use for understanding the association between the two variables? ## linear regression代写 ## 统计代写|linear regression代写线性回归代考|Comparing Means from Two Groups 我们提到了均值比较检验，吨-测试，在本章前面比较两窝小狗的重量时。让我们更详细地回顾一下这个测试。首先，回想一下，我们可以比较分布中的许多统计数据，包括标准偏差和标准误差。然而，一个常见的练习是从推断的意义上评估一个群体的平均值是否可能不同于另一个群体的平均值。如果我们从两个总体中抽取样本，我们应该考虑抽样误差。我们的样本可能具有与真实总体均值不同的均值， 所以我们应该考虑到这种可能的变化。一种吨-test 旨在通过首先获取样本均值之间的差异，然后评估假定的抽样误差来评估两种均值在总体中是否可能不同。 名字吨使用 -test 是因为吨-作为测试基础的值遵循学生的吨-分配。32当样本量大于 50 时，这种分布与正态分布几乎无法区分。在较小的样本量下，吨-分布的尾部较粗，中间比正态分布更平。 方程2.13和2.14演示如何计算常规吨-假设平均值来自两个独立总体的测试。 吨=X¯−是¯sp1n1+1n2 在哪里 sp=(n1−1)s12+(n2−1)s22(n1+n2)−2 这sp方程中是汇总标准偏差，它估计了抽样误差。这ns 表示样本大小和s2s是两组的方差。该检验的一个关键假设是两组的方差相等。一些研究人员对做出这个假设感到不舒服——或者它可能站不住脚——所以他们使用方程 2.15 中显示的估计量，称为 Welch’s吨-测试。33 吨′=X¯−是¯曾是⁡(X)n1+曾是⁡(是)n2 由于吨′不遵循吨-分布，我们在使用韦尔奇检验时必须依靠特殊的表格来确定两个均值之间存在差异的概率。幸运的是，R和其他统计软件提供两个版本的吨-测试。 这是一个示例吨- 使用早期小狗样本中的第 3 和第 4 窝的测试。提醒一下，以盎司为单位的重量是 垃圾3：[39,55,56,58,61,66,69] 垃圾4：[42,44,48,55,57,60,66] 手段是57.7和53.1，相差 4.6。t 检验返回一个吨-的价值0.92与p-的价值0.37和一个 CI−6.2,15.4. 两种推论测度的解释是： p-value：如果我们从两个小狗群体中抽取很多很多样本，并且群体均值的差异为零，我们希望找到样本均值的差异4.6在我们检查的每 100 对样品中，平均大约 37 次。 95%CI：给定一个差异4.6盎司，我们是95%确信总体均值的差异落在区间内−6.2和15.4. ## 统计代写|linear regression代写线性回归代考|Examples Using R 文件 Nations2018.csv37是一个包含来自八个国家的数据的小型数据集。变量是公共支出（支出），衡量政府在个人和集体商品和服务上的支出占国家国内生产总值的百分比，与其他国家的贸易开放度（econopen），以及劳动力的百分比工会（perlabor）。让我们使用R计算本章讨论的一些统计数据。首先，在导入数据集并安装R包装心理，38使用以下代码获取公共支出变量的描述性统计数据： R代码 库（psych）#激活包 describe（Nations2018$ expend）
R输出（略）
819.792.8719.819.81.8514.1

9.3−0.6−0.621.01

Rcode
t.test (GSS2018 $pincome GSS2018$ female)

## 统计代写|linear regression代写线性回归代考|Chapter Exercises

• 教育：多年的正规教育。
• 美国人：对受访者认为成为“美国人”意味着什么的连续衡量，范围从相信成为美国人意味着成为基督徒、只会说英语、出生在美国（量表的高端）到不相信将这些视为作为美国人的指标（规模的低端）。
• group：一个二元变量，表示受访者是否是美国移民 将
数据集导入到R，完成以下练习：
1. 计算变量education 和american 的均值、中位数、标准差、方差、偏度和标准误。
2. 提供组变量的每个类别中的受访者数量，然后是该变量的每个类别中的受访者百分比。样本的百分比在“不”中

1. 进行一次吨-test（Welch 的版本）比较“非移民”组和“移民”组的变量 American 的均值。报告两组的均值，p-值来自吨-测试，并且95%来自 CI吨-测试。解释p-价值和95%那里。
2. 皮尔逊教育与美国的相关性是什么？是什么95%CI 的相关性？提供 Pearson 相关性的简要解释。
3. 创建变量美国的核密度图和箱线图。描述其分布。
4. 挑战：使用 R 的 plot 函数创建散点图，并在X-轴和美国是-轴。描述散点图显示的模式。为什么散点图在这种情况下受到限制？内搜索R或在线获取R函数抖动。使用此功能修改散点图。为什么散点图对于理解两个变量之间的关联仍然有限？

## 有限元方法代写

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。

## 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。

## 统计代写|linear regression代写线性回归代考|Unbiasedness and Efficiency

statistics-lab™ 为您的留学生涯保驾护航 在代写linear regression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linear regression代写方面经验极为丰富，各种代写linear regression相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|linear regression代写线性回归代考|Unbiasedness and Efficiency

As noted earlier, assembling a good sample is key to obtaining suitable estimates of parameters. This raises the general issue of what makes a good statistical estimator, or formula for finding an estimate such as a mean, a median, or, as discussed in later chapters, a regression coefficient. Developing estimates that are accurate and that do not fluctuate too much from one sample to the next is important. Two properties of estimators that are vital for obtaining such estimates are unbiasedness and efficiency.

Unbiasedness refers to whether the mean of the sampling distribution of a statistic equals the population parameter it estimates. For example, is the arithmetic mean estimated from the sample a good estimate of the corresponding mean in the population? Recall that the formula for the sample standard deviation includes the term ${n-1}$ in the denominator. This is necessary to obtain an unbiased estimate of the sample standard deviation, but it presents a slight degree of bias when estimating the population standard deviation.
Efficiency refers to how stable a statistic is from one sample to the next. A more efficient statistic has less variability across samples and is thus, on average, more precise. The estimators for the mean of the normal distribution and probabilities from binomial distributions are considered efficient. Finally, consistency refers to whether the statistic converges to the population

parameter as the sample size increases. Thus, it combines characteristics of both unbiasedness and efficiency. ${ }^{29}$

A common way to represent unbiasedness and efficiency is with an archery target. As shown in Figure 2.3, estimators from statistical models can be visualized as trying to “hit” the parameter in the population. Estimators can be unbiased and efficient, biased but efficient, unbiased but inefficient, or neither. The benefits of having unbiased and efficient statistics should be clear.

## 统计代写|linear regression代写线性回归代考|The Standard Normal Distribution and Z-Scores

Recall that we mentioned z-values in the discussion of CIs. These values are drawn from a standard normal distribution-also called a z-distributionwhich has a mean of zero and a standard deviation of one. The standard normal distribution is useful in a couple of situations. First, as discussed earlier, the formula for the large-sample CI utilizes z-values.

Second, they provide a useful transformation for continuous variables that are measured in different units. For instance, suppose we wish to compare the distributions of weights of two litters of puppies, but one is from the U.S. and the weights are measured in ounces and the other is from Germany and the weights are measured in grams. Converting ounces into grams is simple

(1 ounce $=28.35$ grams), but we may also transform the different measurement units using z-scores. This results in a comparable measurement scale. A $z$-score transformation is based on Equation $2.9$.
$$z \text {-score }=\frac{\left(x_{i}-\bar{x}\right)}{s}$$
Each observation of a variable is entered into this formula to yield its z-score, or what are sometimes called standardized values. The unit of measurement for $z$-scores is standard deviations. In $R$, the scale function computes them for each observation of a variable (the function may also be used to transform variables into other units in addition to z-scores). Let’s see how to use it on one of the samples of puppy weights along with a new sample of weights measured in grams.

## 统计代写|linear regression代写线性回归代考|Covariance and Correlation

We’ve seen a couple of examples of comparing variables from different sources (e.g., puppy weights from different litters); we now assess whether two variables shift or change together. For instance, is it fair to say that the length and the weight of puppies shift together? Are longer puppies, on average, heavier than shorter puppies? The answer is, on average, most likely yes. In statistical language, we say that length and weight covary or are correlated. The two measures used most often to assess the association between two continuous variables are, not surprisingly, called the covariance and the correlation. To be precise, the most common type of correlation is the Pearson’s product-moment correlation. ${ }^{30}$

A covariance is a measure of the joint variation of two continuous variables. Two variables covary when large values of one are accompanied by large or small values of the other. For instance, puppy length and weight covary because large values of one tend to accompany large values of the other in a population or in most samples, though the association is not uniform because of the substantial variation in the lengths and weights of puppies. Equation $2.10$ furnishes the formula for the covariance.
$$\operatorname{cov}(x, y)=\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{n-1}$$
The covariance formula multiplies deviations from the means of both variables, adds them across the observations, and then divides the sum by the sample size minus one. Don’t forget that this implies the $x$ s and $y$ s come from the same unit, whether a puppy, person, place, or thing.

A limitation of the covariance is its dependence on the measurement units of both variables, so its interpretation is not intuitive. It would be helpful to have a measure of association that offered a way to compare various associations of different combinations of variables. The Pearson’s product-moment correlation-often shortened to Pearson’s $r$-accomplishes this task. Among several formulas for the correlation, Equations $2.11$ and $2.12$ are the easiest to understand.
$$\begin{gathered} \operatorname{corr}(x, y)=r=\frac{\operatorname{cov}(x, y)}{\sqrt{\operatorname{var}(x) \times \operatorname{var}(y)}} \ \operatorname{corr}(x, y)=r=\frac{\sum\left(z_{x}\right)\left(z_{y}\right)}{n-1} \end{gathered}$$
Equation $2.11$ shows that the correlation is the covariance divided by the pooled standard deviation. Equation $2.12$ displays the relationship between z-scores and correlations. It shows that the correlation may be interpreted as a standardized measure of association. Some characteristics of correlations include:

1. Correlations range from $-1$ and $+1$, with positive numbers indicating a positive association and negative numbers indicating a negative association (as one variable increases the other tends to decrease).
2. A correlation of zero implies no statistical association, at least not one that can be measured assuming a straight-line association, between the two variables.
3. The correlation does not change if we add a constant to the values of the variables or if we multiply the values by some constant number. However, these constants must have the same sign, negative or positive.

## 统计代写|linear regression代写线性回归代考|The Standard Normal Distribution and Z-Scores

（1盎司=28.35克），但我们也可以使用 z 分数来转换不同的测量单位。这导致了可比较的测量规模。一种和- 分数转换基于方程式2.9.

## 统计代写|linear regression代写线性回归代考|Covariance and Correlation

1. 相关范围从−1和+1，正数表示正关联，负数表示负关联（随着一个变量的增加，另一个变量趋于减少）。
2. 相关性为零意味着两个变量之间没有统计关联，至少不是可以假设为直线关联来测量的关联。
3. 如果我们将一个常数添加到变量的值或将这些值乘以某个常数，则相关性不会改变。但是，这些常数必须具有相同的符号，无论是负号还是正号。

## 有限元方法代写

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。

## 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。

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

statistics-lab™ 为您的留学生涯保驾护航 在代写linear regression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linear regression代写方面经验极为丰富，各种代写linear regression相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|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|Sampling Error and Standard Errors

I hope readers of subsequent chapters will be comfortable thinking about the results of quantitative studies as they consider this material and as they embark on their own studies. In fact, I never wish to underemphasize the importance of careful reasoning among those assessing and using statistical techniques. Nor should we suspend our common sense and knowledge of the research literature simply because a set of numbers supports some unusual conclusion. This is not to say that statistical analysis is not valuable or that the results are generally misleading. Numerous findings from research studies that did not comport with accepted knowledge have been shown valid in subsequent studies. Statistical analyses have also led to many noteworthy discoveries in social, behavioral, and health sciences, as well as informed policy in a productive way. The point I wish to impart is that we need a combination of tools-including statistical methods, a clear comprehension of previous research, and our own ideas and reasoning abilities-to help us understand social and behavioral issues.

## 统计代写|linear regression代写线性回归代考|Our Doubts are Traitors and Make Us Lose the Good We Oft Might Win 2

1. 一项研究永远不会结束。在我们能够（或应该）就社会和行为现象得出合理的结论之前，需要进行多项研究。
2. 在考虑研究结果时，消费者和研究人员需要接受健康的怀疑态度。5他们应该询问有关如何收集数据、如何测量变量以及是否使用了适当的统计方法的问题。我们还应该认识到，即使是设计最好的研究，随机或抽样“误差”（见第 2 章）也会影响结果。
3. 应该鼓励人们在评估数据和分析结果时使用他们的常识和推理能力。尽管最大限度地减少确认偏差和类似的认知倾向（错误）影响我们处理和解释信息的方式很重要，但我们仍然应该考虑研究结果是否基于合理的前提，并遵循我们已经了解的现象的逻辑模式。

## 统计代写|linear regression代写线性回归代考|Best Statistical Practices 6

1. 尽早且经常地绘制数据。
2. 了解您的数据集只是可以观察到的许多可能的数据集之一。
3. 了解您的数据集的背景——什么是背景科学以及如何进行测量（例如，调查问题或直接测量）？用于收集数据的测量工具有哪些限制？是否缺少某些数据？为什么？
4. 在选择汇总统计数据时要深思熟虑。
5. 尽早确定分析的哪些部分是探索性的，哪些部分是确认性的，并预先注册7您的假设，如果不是正式的，那么至少在您自己的脑海中。
6. 如果你使用p-价值观，8可以提供一些关于统计结果的证据，遵循以下原则
：报告效应量和置信区间 (CI)；
湾。考虑提供预测值或效应大小的图形证据，以向您的听众展示分析提供的差异幅度；
C。报告您进行的测试数量（正式和非正式）；
d。解释p-根据您的样本量（和功率）的值；
e. 不要使用p- 声称没有差异的原假设为真的值；和

F。考虑p- 充其量仅将价值视为关于您的结论的一种证据来源，而不是结论本身。

1. 考虑创建定制的、基于模拟的统计测试，以使用您的特定数据集回答您的特定问题。
2. 使用模拟来了解您的统计计划在像您这样的数据集上的性能，并测试各种假设。
3. 以怀疑的态度阅读结果，记住模式很容易偶然出现（尤其是对于小样本），并且基于小样本量的意外结果通常是错误的。
4. 将数据中的统计结果或模式解释为与概念模型或假设一致或不一致，而不是声称它们揭示或证明了某些现象或关系（有关该建议的详细说明，请参见第 2 章）。

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。