## 统计代写|线性回归分析代写linear regression analysis代考|What does an insignificant estimate tell you

statistics-lab™ 为您的留学生涯保驾护航 在代写线性回归分析linear regression analysis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。我们的专家在代写线性回归分析linear regression analysis代写方面经验极为丰富，各种代写线性回归分析linear regression analysis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|线性回归分析代写linear regression analysis代考|What does an insignificant estimate tell you

The basic reason why the lack of evidence is not proof of non-existence is that there are alternative reasons for the lack of evidence. As mentioned earlier, when a jury in a criminal trial deliberates on whether a defendant is guilty, the jury members are not directed to conclude that the defendant has been proven innocent. Rather, they are supposed to determine whether there is significant evidence (beyond a reasonable doubt) that indicates the defendant was guilty. Thus, one reason why a defendant may be found “not guilty” is that there was not enough evidence.

The same concept is supposed to be used for statistical analysis. We are often testing whether a coefficient estimate is different from zero. Let’s say we are examining how class-size affects elementary-school students’ test scores, and let’s say that we find an insignificant estimate on the variable for class-size. In a study of mine (Arkes 2016), I list four general possible explanations for an insignificant estimate:

1. There is actually no effect of the explanatory variable on the outcome in the population.
2. There is an effect in one direction, but the model is unable to detect the effect due to a modeling problem (e.g., omitted-factors bias or measurement error – see Chapter 6) biasing the coefficient estimate in a direction opposite to the actual effect.
1. There is a small effect that cannot be detected with the available data due to inadequate power i.e., not a large enough sample given the size of the effect.
2. There are varying effects in the population (or sample); some people’s outcomes may be affected positively by the treatment, others’ outcomes may be affected negatively, and others’ outcomes may not be affected; and the estimated effect (which is the average effect) is insignificantly different from zero due to the positive and negative effects canceling each other out or being drowned out by those with zero effects.

So what can you conclude from the insignificant estimate on the class-size variable? You cannot conclude that class size does not affect test scores. Rather, as with the hot hand and the search for aliens, the interpretation should be: “There is no evidence that class-size affects test scores.”

Unfortunately, a very common mistake made in the research world is that the conclusion would be that there is no effect. This is important for issues such as whether there are side effects from pharmaceutical drugs or vaccines. The lack of evidence for a side effect does not mean that there is no effect, particularly if confidence intervals for the estimates include values that would represent meaningful side effects of the drug or vaccine.

All that said, there are sometimes cases in which an insignificant estimate has a $95 \%$ or $99 \%$ confidence interval with a fairly narrow range and outer boundary that, if the boundary were the true population parameter, it would be “practically insignificant” (see Section 5.3.9). If this were the case and the coefficient estimate were not subject to any meaningful bias, then it would be safe to conclude that “there is no meaningful effect.”

## 统计代写|线性回归分析代写linear regression analysis代考|Statistical significance is not the goal

As we conduct research, our ultimate goal should be to advance knowledge. Our goal should not be to find a statistically-significant estimate. Advancing knowledge occurs by conducting objective and honest research.

A statistically insignificant coefficient estimate on a key-explanatory variable is just as valid as a significant coefficient estimate. The problem, many believe, is that an insignificant estimate may not provide as much information as a significant estimate. As described in the previous section, an insignificant estimate does not necessarily mean that there is no meaningful relationship, and so it could have multiple possible interpretations. If the appropriate confidence intervals for the coefficient were narrow (which would indicate adequate power), the methods were convincing for ruling out modeling problems, and the effects would likely go in just one direction, then it would be more reasonable to conclude that an insignificant estimate indicates there is no meaningful effect of the treatment. But meeting all those conditions is rare, and so there are multiple possible conclusions that cannot be distinguished.

As mentioned in the previous section, a statistically-significant estimate could also be subject to the various interpretations of insignificant estimates. But these are often ignored and not deemed as important, to most people, as long as there is statistical significance.

Statistical significance is valued more, perhaps, because it is evidence confirming, to some extent, the researcher’s theory and/or hypothesis. I conducted a quick, informal review of recent issues of leading economic, financial, and education journals. As it has been historically, almost all empirical studies had statistically-significant coefficient estimates on the key-explanatory variable. Indeed, I had a difficult time finding an insignificant estimate. This suggests that the pattern continues that journals are more likely to publish studies with significant estimates on the key-explanatory variables.

The result of statistical significance being valued more is that it incentivizes researchers to make statistical significance the goal of research. This can lead to $\mathbf{p}$-hacking, which involves changing the set of control variables, the method (e.g. Ordinary Least Squares (OLS) vs. an alternative method, such as in Chapters 8 and 9), the sample requirements, or how the variables (including the outcome) are defined until one achieves a p-value below a major threshold. (I describe p-hacking in more detail in Section 13.3.)

It is unfortunate that insignificant estimates are not accepted more. But, hopefully, this book will be another stepping stone for the movement to be more accepting of insignificant estimates. I personally trust insignificant estimates more than significant estimates (except for the hot hand in basketball).

The bottom line is that, as we conduct research, we should be guided by proper modeling strategies and not by what the results are saying.

# 线性回归代写

## 统计代写|线性回归分析代写linear regression analysis代考|What does an insignificant estimate tell you

1. 实际上，解释变量对总体结果没有影响。
2. 在一个方向上有影响，但由于建模问题（例如，遗漏因素偏差或测量误差——参见第 6 章），模型无法检测到影响系数估计值在与实际影响相反的方向上的偏差。
1. 由于功效不足，即没有足够大的样本给定效应大小，因此无法用可用数据检测到一个小效应。
2. 总体（或样本）有不同的影响；某些人的结果可能会受到治疗的积极影响，其他人的结果可能会受到负面影响，而其他人的结果可能不会受到影响；由于正负效应相互抵消或被零效应淹没，因此估计效应（即平均效应）与零无显着差异。

## 广义线性模型代考

statistics-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|线性回归分析代写linear regression analysis代考|What model diagnostics should you do?

statistics-lab™ 为您的留学生涯保驾护航 在代写线性回归分析linear regression analysis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。我们的专家在代写线性回归分析linear regression analysis代写方面经验极为丰富，各种代写线性回归分析linear regression analysis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|线性回归分析代写linear regression analysis代考|What model diagnostics should you do?

None! Well, most of the time, none. This is my view, and I might be wrong. Others (including your professor) may have valid reasons to disagree. But here is the argument why, in most cases, there is no need to perform any model diagnostics.
The two most common model diagnostics that are conducted are:

• checking for heteroskedasticity
• checking for non-normal error terms (Assumption A3 in Section 2.10).
One problem is that the tests are not great. The tests will indicate whether there is statisticallysignificant evidence for heteroskedasticity or non-normal error terms, but they certainly cannot prove that there is not any heteroskedasticity or non-normal error terms.

Regarding heteroskedasticity, your regression probably has heteroskedasticity. And, given that it is costless and painless to fix, you should probably include the heteroskedasticity correction.

Regarding non-normal error terms, recall that, due to the Central Limit Theorem, error terms will be approximately normal if the sample size is large enough (i.e., at least 200 observations at worst, and perhaps only 15 observations would suffice). However, this is not necessarily the case if: (1) the dependent variable is a dummy variable; and (2) there is not a large-enough set of explanatory variables. That said, a problem is that the test for non-normality (which tests for skewness and kurtosis) is highly unstable for small samples.

Having non-normal error terms means that the t-distribution would not apply to the standard errors, so the $t$-stats, standard levels of significance, confidence intervals, and $\mathrm{p}$-values would be a little off-target. The simple solution for cases in which there is the potential for non-normal errors is to require a lower $\mathrm{p}$-value than you otherwise would to conclude that there is a relationship between the explanatory and dependent variables.

I am not overly concerned by problems with non-normal errors because they are small potatoes when weighed against the Bayes critique of $\mathrm{p}$-values and the potential biases from PITFALLS (Chapter 6). If you have a valid study that is pretty convincing in terms of the PITFALLS being unlikely and having low-enough p-values in light of the Bayes critique, then having non-normal error terms would most likely not matter.

One potentially-useful diagnostic would be to check for outliers having large effects on the coefficient estimates. This would likely not be a concern with dependent variables that have a compact range of possible values, such as academic achievement test scores. But it could be the case with dependent variables on individual/family income or corporate profits/revenue, among other such outcomes with potentially large-outlying values of the dependent variable. Extreme values of explanatory variables could also be problematic. In these situations, it could be worth a diagnostic check of outliers for the dependent variable or the residuals. One could estimate the model without the big outliers to see how the results are affected. Of course, the outliers are supposedly legitimate observations, so any results without the outliers are not necessarily more correct. The ideal situation would be that the direction and magnitude of the estimates are consistent between the models with and without the outliers.
Outliers, if based on residuals, could be detected by residual plots. Alternatively, one potential rule that could be used for deleting outliers is based on calculating the standardized residual, which is the actual residual divided by the standard deviation of the residual-there is no need to subtract the mean of the residual since it is zero. The standardized residual indicates how many standard deviations away from zero a residual is. One could use an outlier rule, such as deleting observations with the absolute value of the standardized residual greater than some value, say, 5. With the adjusted sample, one would re-estimate a model to determine how stable the main results are.

## 统计代写|线性回归分析代写linear regression analysis代考|What the research on the hot hand in basketball tells us about

A friend of mine, drawn to the larger questions on life, called me recently and said that we are all alone – that humans are the only intelligent life in the universe. Rather than questioning him on the issue I have struggled with (whether humans, such as myself, should be categorized as “intelligent” life), I decided to focus on the main issue he raised and asked how he came to such a conclusion. Apparently, he had installed one of those contraptions in his backyard that searches for aliens. Honestly, he has so much junk in his backyard that I hadn’t even noticed. He said that he hadn’t received any signals in two years, so we must be alone.

While I have no idea whether we are alone in the universe, I know that my curious friend is not alone in his logic. A recent Wall Street Journal article made a similar logical conclusion in an article with some plausible arguments on why humans may indeed be alone in the universe. One of those arguments was based on the “deafening silence” from the 40-plus-year Search for Extraterrestrial Intelligence (SETI) project, with the conclusion that this is strong evidence that there is no other intelligent life (Metaxas, 2014). Never mind that SETI only searches our galaxy (of the estimated 170-plus billion galaxies in the universe) and that for us to find life on some planet, we have to be aiming our SETI at that planet (instead of the other 100 billion or so planets in our galaxy) at the same time (within the 13.6 billion years our galaxy has been in existence) that the alien geeks on that planet are emitting strong-enough radio signals in our direction (with a 600-plus-year lag for the radio signals to reach us). It may be that some form of aliens sent radio signals our way 2.8 billion years ago (before they went extinct after elininating their Environmental Protection Ageney), purposefully-striked-through and our amoeba-like ancestors had not yet developed the SETI technology to detect the signals.

The flawed logic here, as you have probably determined, is that lack of evidence is not proof of non-existence. This is particularly the case when you have a weak test for what you are looking for.
This logic flaw happens to be very common among academics. One line of research that has been subject to such faulty logic is that on the hot hand in basketball. The “hot hand” is a situation in which a player has a period (often within a single game) with a systematically higher probability of making shots (adjusting for the difficulty of the shot) than the player normally would have. The hot hand can occur in just about any other sport or activity, such as baseball, bowling, dance, test-taking, etc. In basketball, virtually all players and fans believe in the hot hand, based on witnessing players such as Stephen Curry go through stretches in which they make a series of high-difficulty shots. Yet, from 1985 to 2009 , plenty of researchers tested for the hot hand in basketball by using various tests to essentially determine whether a player was more likely to make a shot after a made shot (or consecutive made shots) than after a missed shot. They found no evidence of the hot hand. Their conclusion was “the hot hand is a myth.”
But then a few articles, starting in 2010, found evidence for the hot hand. And, as Stone (2012), Arkes (2013), and Miller and Sanjurjo (2018) show, the tests for the studies in the first 25 years were pretty weak tests for the hot hand because of some modeling problems, one of which I will describe in Box 6.4 in the next chapter.

The conclusions from those pre-2010 studies should not have been “the hot hand is a myth,” but rather “there is no evidence for the hot hand in basketball.” The lack of evidence was not proof of the non-existence of the hot hand. Using the same logic, in the search for aliens, the lack of evidence is not proof of non-existence, especially given that the tests have been weak. ${ }^5 \mathrm{I}$ ‘d bet my friend’s SETI machine that the other life forms out there, if they exist, would make proper conclusions on the basketball hot hand (and that they won’t contact us until we collectively get it right on the hot hand).

# 线性回归代写

## 统计代写|线性回归分析代写linear regression analysis代考|What model diagnostics should you do?

• 检查异方差
• 检查非正态误差项（第 2.10 节中的假设 A3）。
一个问题是测试不是很好。检验将表明是否存在异方差或非正态误差项的统计显着证据，但它们当然不能证明不存在任何异方差或非正态误差项。

## 广义线性模型代考

statistics-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。

## STAT311 Regression Analysis课程简介

This graduate level course offers an introduction into regression analysis. A
Credits 3 researcher is often interested in using sample data to investigate relationships, with an ultimate goal of creating a model to predict a future value for some dependent variable. The process of finding this mathematical model that best fits the data involves regression analysis.
STAT 501 is an applied linear regression course that emphasizes data analysis and interpretation. Generally, statistical regression is collection of methods for determining and using models that explain how a response variable (dependent variable) relates to one or more explanatory variables (predictor variables).

## PREREQUISITES

This graduate level course covers the following topics:

• Understanding the context for simple linear regression.
• How to evaluate simple linear regression models
• How a simple linear regression model is used to estimate and predict likely values
• Understanding the assumptions that need to be met for a simple linear regression model to be valid
• How multiple predictors can be included into a regression model
• Understanding the assumptions that need to be met when multiple predictors are included in the regression model for the model to be valid
• How a multiple linear regression model is used to estimate and predict likely values
• Understanding how categorical predictors can be included into a regression model
• How to transform data in order to deal with problems identified in the regression model
• Strategies for building regression models
• Distinguishing between outliers and influential data points and how to deal with these
• Handling problems typically encountered in regression contexts
• Alternative methods for estimating a regression line besides using ordinary least squares
• Understanding regression models in time dependent contexts
• Understanding regression models in non-linear contexts

## STAT311 Regression Analysis HELP（EXAM HELP， ONLINE TUTOR）

Use the cig_1st_diff data set. This is based on the changes from 1990 to 2000 , and it is extracted from the data set used in Question #3. Estimate a first-difference model, as follows: regress cigch on taxch, uratech, and beertaxch. Weight the model by pop 2000 , and use robust standard errors. Interpret the estimate on taxch.

From the example in Section 8.5 from Card and Krueger (1994) on estimating the effects of minimum-wage increases on employment, write out the regression equation for the difference-in-difference model.

Use the data set oecd_gas_demand. From Question #7 in Chapter 3, add fixed effects for the country, along with a heteroskedasticity correction.
a. How does the coefficient estimate on lrpmg change from Question #7 in Chapter 3 with the fixed effects added?
b. How does this change which observations are compared to which observations?

Return to the tv-bmi-ecls data set used for Exercise $# 5$ in Chapter 6 . From that exercise, along with other descriptions of the research issue, there is much potential omitted-factors bias.
a. Explore the data description and variable list (from the file “Exercises data set descriptions” on the book’s website). Design a model to address the omitted-factors bias.
b. Are there any shortcomings to your approach?

## Textbooks

• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.

Statistics-lab™可以为您提供metrostate.edu STAT311 Regression Analysis回归分析的代写代考辅导服务！ 请认准Statistics-lab™. Statistics-lab™为您的留学生涯保驾护航。

## 经济代写|计量经济学代写Econometrics代考|Dummy Variables

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics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

## 经济代写|计量经济学代写Econometrics代考|The nature of qualitative information

So far, we have examined the equation specifications employed in econometric analysis, as well as techniques used to obtain estimates of the parameters in an equation and procedures for assessing the significance, accuracy and precision of those estimates. An assumption made implicitly up to this point has been that we can always obtain a set of numerical values for all the variables we want to use in our models. However, there are variables that can play a very important role in the explanation of an econometric model but are not numerical or easy to quantify. Examples of these are:
(a) gender may be very important in determining salary levels;
(b) different ethnic groups may follow diverse patterns regarding consumption and savings;
(c) educational levels can affect earnings from employment; and/or
(d) being a member of a labour union may imply different treatment/attitudes than not belonging to the union.
All these are cases for cross-sectional analysis.
Not easily quantifiable (or, in general, qualitative) information could also arise within a time series econometric framework. Consider the following examples:
(a) changes in a political regime may affect production processes or employment conditions;
(b) a war can have an impact on all aspects of economic activity;
(c) certain days in a week or certain months in a year can have different effects on stock prices; and
(d) seasonal effects are frequently observed in the demand for particular products; for example, ice cream in the summer, furs during the winter.

The aim of this chapter is to show the methods used to include information from qualitative variables in econometric models. This is done by using ‘dummy’ or ‘dichotomous’ variables. The next section presents the possible effects of qualitative variables in regression equations and how to use them. We then present special cases of dummy variables and the Chow test for structural stability.

## 经济代写|计量经济学代写Econometrics代考|Constant dummy variables

Consider the following cross-sectional regression equation:
$$Y_i=\beta_1+\beta_2 X_{2 i}+u_i$$

The constant term $\left(\beta_1\right)$ in this equation measures the mean value of $Y_i$ when $X_{2 i}$ is equal to zero. The important thing here is that this regression equation assumes that the value of $\beta_0$ will be the same for all the observations in the data set. However, the coefficient might be different, depending on different aspects of the data set. For example, regional differences might exist in the values of $Y_i ;$ or $Y_i$ might represent the growth of GDP for European Union (EU) countries. Differences in growth rates are quite possible between core and peripheral countries. The question is, how can we quantify this information in order to enter it in the regression equation and check for the validity of this possible difference? The answer is: with the use of a special type of variable – a dummy (or fake) that captures qualitative effects by coding the different possible outcomes with numerical values.

This can usually be done quite simply by dichotomizing the possible outcomes and arbitrarily assigning the values of 0 and 1 to the two possibilities. So, for the EU countries example, we can have a new variable, $D$, which can take the following values:
$$D= \begin{cases}1 & \text { for core country } \ 0 & \text { for peripheral country }\end{cases}$$
Note that the choice of which of the alternative outcomes is to be assigned the value of 1 does not alter the results in an important way, as we shall show later.

Thus, entering this dummy variable in the regression model in Equation (9.1) we get:
$$Y_i=\beta_1+\beta_2 X_{2 i}+\beta_3 D_i+u_i$$
and in order to obtain the interpretation of $D_i$, consider the two possible values of $D$ and how these will affect the specification of Equation (9.3). For $D=0$ we have:
\begin{aligned} Y_i & =\beta_1+\beta_2 X_{2 i}+\beta_3(0)i+u_i \ & =\beta_1+\beta_2 X{2 i}+u_i \end{aligned}

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|The nature of qualitative information

(a) 性别在决定工资水平方面可能非常重要；
(b) 不同族裔群体可能遵循不同的消费和储蓄模式；
(c) 教育水平会影响就业收入；和/或
(d) 加入工会可能意味着与不加入工会不同的待遇/态度。

(a) 政治体制的变化可能影响生产过程或就业条件；
(b) 战争会对经济活动的各个方面产生影响；
(c) 一周中的某些天或一年中的某些月会对股票价格产生不同的影响；( d
) 在特定产品的需求中经常观察到季节性影响；例如，夏天的冰淇淋，冬天的皮草。

## 经济代写|计量经济学代写Econometrics代考|Constant dummy variables

$$Y_i=\beta_1+\beta_2 X_{2 i}+u_i$$

$D={1 \quad$ for core country 0 for peripheral country

$$Y_i=\beta_1+\beta_2 X_{2 i}+\beta_3 D_i+u_i$$

$$Y_i=\beta_1+\beta_2 X_{2 i}+\beta_3(0) i+u_i \quad=\beta_1+\beta_2 X 2 i+u_i$$

## 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。

## 经济代写|计量经济学代写Econometrics代考|Approaches in choosing an appropriate model

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics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

## 经济代写|计量经济学代写Econometrics代考|The traditional view: average economic regression

In the past, the traditional approach to econometric modelling was to start by formulating the simplest possible model to obey the underlying economic theory and, after estimating that model, to perform various tests in order to determine whether it was satisfactory.

A satisfactory model in that sense would be: (a) one having significant coefficients (that is high $t$-ratios), and coefficients whose signs correspond with the theoretical predictions; (b) one with a good fit (that is high $R^2$ ); and (c) one having residuals that do not suffer from autocorrelation or heteroskedasticity.

If one or more of these points is violated, researchers try to find better methods of estimation (that is the Cochrane-Orcutt iterative method of estimation for the case of serial correlation) or to check other possible causes of bias such as whether important variables have been omitted from the model or whether redundant variables have been included, or to consider alternative functional forms, and so on.

This approach, which essentially starts with a simple model and then ‘builds up’ the models as the situation demands, is called the ‘simple to general approach’ or the ‘average economic regression (AER)’, a term coined by Gilbert (1986), because this was the method that most traditional econometric research was following in practice.
The AER approach has been subject to major criticisms:
1 One obvious criticism is that the procedure followed in the AER approach suffers from data mining. Since generally only the final model is presented by the researcher, no information is available regarding the number of variables used in the model before obtaining the ‘final’ model results.
2 Another criticism is that the alterations to the original model are carried out in an arbitrary manner, based mainly on the beliefs of the researcher. It is therefore quite possible for two different researchers examining the same case to arrive at totally different conclusions.
3 By definition, the initial starting model is incorrect as it has omitted variables. This means that all the diagnostic tests on this model are incorrect, so we may consider important variables to be insignificant and exclude them.

## 经济代写|计量经济学代写Econometrics代考|The Hendry ‘general to specific approach’

Following from these three major criticisms of the AER, an alternative approach has been developed called the ‘general to specific approach’ or the Hendry approach, because it was developed mainly by Professor Hendry of the London School of Economics (see Hendry and Richard, 1983). The approach is to start with a general model that contains – nested within it as special cases – other, simpler, models. Let’s use an example to understand this better. Assume that we have a variable $Y$ that can be affected by two explanatory variables $X$ and $Z$. The general to specific approach proposes as a starting point the estimation of the following regression equation:
\begin{aligned} Y_t= & a+\beta_0 X_t+\beta_1 X_{t-1}+\beta_2 X_{t-2}+\cdots+\beta_m X_{t-m} \ & +\gamma_0 Z_t+\gamma_1 Z_{t-1}+\gamma_2 Z_{t-2}+\cdots+\gamma_m Z_{t-m} \ & +\delta_1 Y_{t-1}+\delta_2 Y_{t-2}+\cdots+\delta_m Y_{t-m}+u_t \end{aligned}
that is, to regress $Y_t$ on contemporaneous and lagged terms $X_t$ and $Z_t$ as well as lagged values of $Y_t$. This model is called an autoregressive (because lagged values of the dependent variable appear as regressors as well) distributed lag (because the effect of $X$ and $Z$ on $Y$ is spread over a period of time from $t-m$ to $t$ ) model (ARDL). Models such as that shown in Equation (8.69) are known as dynamic models because they examine the behaviour of a variable over time.

The procedure then is, after estimating the model, to apply appropriate tests and to narrow down the model to the simpler ones that are nested with the previously estimated model.

Consider the above example for $m=2$ to see how to proceed in practice with this approach. We have the original model:
\begin{aligned} Y_t= & a+\beta_0 X_t+\beta_1 X_{t-1}+\beta_2 X_{t-2} \ & +\gamma_0 Z_t+\gamma_1 Z_{t-1}+\gamma_2 Z_{t-2}+\delta_1 Y_{t-1}+\delta_2 Y_{t-2}+u_t \end{aligned}
where one restriction may be that all the $X$ s are non-important in the determination of $Y$. For this we have the hypothesis $H_0: \beta_0=\beta_1=\beta_2=0$; and if we accept that, we have a simpler model such as:
$$Y_t=a+\gamma_0 Z_t+\gamma_1 Z_{t-1}+\gamma_2 Z_{t-2}+\delta_1 Y_{t-1}+\delta_2 Y_{t-2}+u_t$$
Another possible restriction may be that the second lagged term of each variable is insignificant; that is hypothesis $H_0: \beta_2=\gamma_2=\delta_2=0$. Accepting this restriction will give the following model:
$$Y_t=a+\beta_0 X_t+\beta_1 X_{t-1}+\gamma_0 Z_t+\gamma_1 Z_{t-1}+\delta_1 Y_{t-1}+u_t$$
It should be clear by now that the models in Equations (8.71) and ( 8.72$)$ are both nested versions of the initial model in Equation (8.70); but Equation ( 8.72$)$ is not a nested model of Equation (8.71) and therefore we cannot proceed to Equation (8.72) after estimating Equation (8.71).

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|The traditional view: average economic regression

AER 方法一直受到重大批评：
1 一个明显的批评是 AER 方法中遵循的过程受到数据挖掘的影响。由于研究人员通常只提供最终模型，因此在获得“最终”模型结果之前，没有关于模型中使用的变量数量的信息。
2 另一个批评是，对原始模型的改动主要基于研究人员的信念，以任意方式进行。因此，两个不同的研究人员研究同一个案例很可能得出完全不同的结论。
3 根据定义，初始模型是不正确的，因为它遗漏了变量。这意味着在这个模型上的所有诊断测试都是不正确的，所以我们可以认为重要的变量是无关紧要的并排除它们。

## 经济代写|计量经济学代写Econometrics代考|The Hendry ‘general to specific approach’

$$Y_t=a+\beta_0 X_t+\beta_1 X_{t-1}+\beta_2 X_{t-2}+\cdots+\beta_m X_{t-m} \quad+\gamma_0 Z_t+\gamma_1 Z_{t-1}+\gamma_2 Z_{t-2}+\cdots+$$

$$Y_t=a+\beta_0 X_t+\beta_1 X_{t-1}+\beta_2 X_{t-2} \quad+\gamma_0 Z_t+\gamma_1 Z_{t-1}+\gamma_2 Z_{t-2}+\delta_1 Y_{t-1}+\delta_2 Y_{t-2}+u_t$$

$$Y_t=a+\gamma_0 Z_t+\gamma_1 Z_{t-1}+\gamma_2 Z_{t-2}+\delta_1 Y_{t-1}+\delta_2 Y_{t-2}+u_t$$

$$Y_t=a+\beta_0 X_t+\beta_1 X_{t-1}+\gamma_0 Z_t+\gamma_1 Z_{t-1}+\delta_1 Y_{t-1}+u_t$$

## 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。

## ECON335 Econometrics课程简介

The objective of this course is to provide the basic knowledge of econometrics that is essential equipment for any serious economist or social scientist. The course introduces statistical tools including regression analysis and its application using cross-sectional data.
The second week onwards will be focused on how various technical problems inherent in economic analysis, including heteroskedasticity, autocorrelation, and endogeneity should be handled. This section of the course will pay special attention to the application of the regression model to time-series data – both stationary and non-stationary.
Using the theories and their application in economics, you will participate in daily workshops to get hands-on experience implementing the various estimators and testing procedures in Stata using real-world data. As a result, you will consider how the theory can be applied to a wide range of questions of economic interest (For example, modelling long-term relationships between prices and exchange rates).
By the end of the course, you will be able to provide proof of the unbiasedness or biasedness and consistency or inconsistency of least squares, and instrumental variable estimators using simple models.

## PREREQUISITES

It seems like you are describing a course in econometrics that aims to equip students with basic knowledge and skills in statistical analysis, with a focus on regression analysis and its application to cross-sectional and time-series data in economics. The course also covers various technical problems that can arise in econometric analysis, such as heteroskedasticity, autocorrelation, and endogeneity, and how to address them.

In addition to theoretical instruction, the course provides practical workshops to give students hands-on experience using statistical software (such as Stata) to implement various estimators and testing procedures on real-world data. The course aims to help students apply econometric theory to a wide range of economic questions, such as modelling long-term relationships between prices and exchange rates.

By the end of the course, students should be able to evaluate the unbiasedness or biasedness and consistency or inconsistency of least squares and instrumental variable estimators using simple models.

## ECON335 Econometrics HELP（EXAM HELP， ONLINE TUTOR）

Run the following auxiliary regression:
$$\ln \left(\hat{u}i^2\right)=a_1+a_2 Z{2 i}+a_3 Z_{3 i}+\cdots+a_p Z_{p i}+v_i$$

Formulate the null and the alternative hypotheses. The null hypothesis of homoskedasticity is:
$$\mathrm{H}_0: \quad a_1=a_2=\cdots=a_p=0$$
while the alternative is that at least one of the $a$ is different from zero.

Compute the $L M=n R^2$ statistic, where $n$ is the number of observations used in order to estimate the auxiliary regression in Step 2, and $R^2$ is the coefficient of determination of this regression. The $L M$ statistic follows the $\chi^2$ distribution with $p-1$ degrees of freedom.

Reject the null and conclude that there is significant evidence of heteroskedasticity when $L M$-statistical is greater than the critical value (LM-stat > $\left.\chi_{p-1, \alpha}^2\right)$. Alternatively, compute the $p$-value and reject the null if the $p$-value is less than the level of significance $\alpha$ (usually $\alpha=0.05$ ).

## Textbooks

• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.

Statistics-lab™可以为您提供colostate.edu ECON335 Econometrics计量经济学课程的代写代考辅导服务！ 请认准Statistics-lab™. Statistics-lab™为您的留学生涯保驾护航。

## 物理代写|流体力学代写Fluid Mechanics代考|One-Equation Model by Prandtl

statistics-lab™ 为您的留学生涯保驾护航 在代写流体力学Fluid Mechanics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。我们的专家在代写流体力学Fluid Mechanics代写方面经验极为丰富，各种代写流体力学Fluid Mechanics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

## 物理代写|流体力学代写Fluid Mechanics代考|One-Equation Model by Prandtl

A one-equation model is an enhanced version of the algebraic models we discussed in previous sections. This model utilizes one turbulent transport equation originally developed by Prandtl. Based on purely dimensional arguments, Prandtl proposed a relationship between the dissipation and the kinetic energy that reads
$$\varepsilon=C_D k^{3 / 2} / l_t$$
where the turbulence length scale $\ell_{\mathrm{t}}$ is set proportional to the mixing length, $\ell_{\mathrm{m}}$, the boundary layer thickness $\delta$ or a wake or a jet width. The velocity scale in Eq. (9.132) is set proportional to the turbulent kinetic energy $V_t \propto k^{1 / 2}$ as suggested independently by Kolmogorov [95] and Prandtl [96]. Thus, the expression for the turbulent viscosity becomes:
$$\mu_t=C_\mu \ell_m k^{0.5}$$
with the constant $C_\mu$ to be determined from the experiment. The turbulent kinetic energy, $k$, as a transport equation is taken from Sect. 9.2.2 in the form of Eqs. (9.111) or (9.126) where the dissipation is implemented. For simple two-dimensional flows where no separation occurs, with the mean-flow component $\overline{V_1} \equiv \bar{U}$ as the significant velocity in $x_1 \equiv x$-direction, and the distance from the wall $x_2 \equiv y$, the following approximation by Launder and Spalding [97] may be used
$$\rho \frac{\mathrm{D} k}{\mathrm{D} t}=\mu_t\left(\frac{\partial \bar{U}}{\partial y}\right)^2+\frac{\partial}{\partial y}\left(\frac{\mu_t}{\sigma_k} \frac{\partial k}{\partial y}\right)-C_D \frac{\rho k^{3 / 2}}{\ell_m},$$
where $\sigma_k=1$ and $C_D=0.08$ are coefficients determined from experiments utilizing simple flow configurations. The one-equation model provides a better assumption for the velocity scale $V_{\mathrm{t}}$ than $\ell_m|\partial \bar{U} / \partial y|$. Similar to the algebraic model, the oneequation one is not applicable to the general three-dimensional flow cases since a general expression for the mixing length does not exist. Therefore the use of a oneequation model does not offer any improvement compared with the algebraic one. The one-equation models discussed above are based on kinetic energy equations. There are a variety of one-equation models that are based on Prandtl’s concept and discussed in [88].

## 物理代写|流体力学代写Fluid Mechanics代考|Two-Equation k − ε Model

The two equations utilized by this model are the transport equations of kinetic energy $k$ and the transport equation for dissipation $\varepsilon$. These equations are used to determine the turbulent kinematic viscosity $v_t$. For fully developed high Reynolds number turbulence, the exact transport equations for $k(9.126)$ can be used. The transport equation for $\varepsilon(9.129)$ includes triple correlations that are almost impossible to measure. Therefore, relative to $\varepsilon$, we have to replace it with a relationship that approximately resembles the terms in Eq. (9.129). To establish such a purely empirical relationship, dimensional analysis is heavily used. Launder and Spalding [98] used the following equations for kinetic energy
$$\frac{\mathrm{D} k}{\mathrm{D} t}=\frac{1}{\rho} \frac{\partial}{\partial x_j}\left(\frac{\mu_t}{\sigma_k} \frac{\partial k}{\partial x_j}\right)+\frac{\mu_t}{\rho}\left(\frac{\partial \bar{V}i}{\partial x_j}+\frac{\partial \bar{V}_j}{\partial x_i}\right) \frac{\partial \bar{V}_i}{\partial x_j}-\varepsilon$$ and for dissipation $$\frac{\mathrm{D} \varepsilon}{\mathrm{D} t}=\frac{1}{\rho} \frac{\partial}{\partial x_j}\left(\frac{\mu_t}{\sigma{\varepsilon}} \frac{\partial \varepsilon}{\partial x_j}\right)+C_{\varepsilon 1} \frac{\mu_t}{\rho} \frac{\varepsilon}{k}\left(\frac{\partial \bar{V}i}{\partial x_j}+\frac{\partial \bar{V}_j}{\partial x_i}\right) \frac{\partial \bar{V}_i}{\partial x_j}-\frac{C{\varepsilon 2} \varepsilon^2}{k},$$
and the turbulent viscosity, $\mu_t$, can be expressed as
$$\mu_t=v_t \rho=\frac{C_\mu \rho k^2}{\varepsilon}$$
The constants $\sigma_{\mathrm{k}}, \sigma_{\varepsilon}, C_{\varepsilon_1}, C_{\varepsilon_2}$ and $C_\mu$ listed in Table 9.2 are calibration coefficients that are obtained from simple flow configurations such as grid turbulence. The models are applied to such flows and the coefficients are determined to make the model simulate the experimental behavior. The values of the above constants recommended by Launder and Spalding [83] are given in Table 9.2.
As seen, the simplified Eqs. (9.165) and (9.166) do not contain the molecular viscosity. They may be applied to free turbulence cases where the molecular viscosity is negligibly small compared to the turbulence viscosity. However, one cannot expect to obtain reasonable results by simulation of the wall turbulence using these equations.

# 流体力学代写

## 物理代写|流体力学代写Fluid Mechanics代考|One-Equation Model by Prandtl

$$\varepsilon=C_D k^{3 / 2} / l_t$$

$$\mu_t=C_\mu \ell_m k^{0.5}$$

$$\rho \frac{\mathrm{D} k}{\mathrm{D} t}=\mu_t\left(\frac{\partial \bar{U}}{\partial y}\right)^2+\frac{\partial}{\partial y}\left(\frac{\mu_t}{\sigma_k} \frac{\partial k}{\partial y}\right)-C_D \frac{\rho k^{3 / 2}}{\ell_m},$$

## 物理代写|流体力学代写Fluid Mechanics代考|Two-Equation k − ε Model

$$\frac{\mathrm{D} k}{\mathrm{D} t}=\frac{1}{\rho} \frac{\partial}{\partial x_j}\left(\frac{\mu_t}{\sigma_k} \frac{\partial k}{\partial x_j}\right)+\frac{\mu_t}{\rho}\left(\frac{\partial \bar{V} i}{\partial x_j}+\frac{\partial \bar{V}j}{\partial x_i}\right) \frac{\partial \bar{V}_i}{\partial x_j}-\varepsilon$$ 和消散 $$\frac{\mathrm{D} \varepsilon}{\mathrm{D} t}=\frac{1}{\rho} \frac{\partial}{\partial x_j}\left(\frac{\mu_t}{\sigma \varepsilon} \frac{\partial \varepsilon}{\partial x_j}\right)+C{\varepsilon 1} \frac{\mu_t}{\rho} \frac{\varepsilon}{k}\left(\frac{\partial \bar{V} i}{\partial x_j}+\frac{\partial \bar{V}j}{\partial x_i}\right) \frac{\partial \bar{V}_i}{\partial x_j}-\frac{C \varepsilon 2 \varepsilon^2}{k},$$ 和湍流粘度， $\mu_t$ ，可以表示为 $$\mu_t=v_t \rho=\frac{C\mu \rho k^2}{\varepsilon}$$

## 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。

## 物理代写|流体力学代写Fluid Mechanics代考|Cebeci–Smith Model

statistics-lab™ 为您的留学生涯保驾护航 在代写流体力学Fluid Mechanics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。我们的专家在代写流体力学Fluid Mechanics代写方面经验极为丰富，各种代写流体力学Fluid Mechanics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

## 物理代写|流体力学代写Fluid Mechanics代考|Cebeci–Smith Model

Another algebraic model is the Cebeci-Smith [92] which has been used primarily in external high speed aerodynamics with attached thin boundary layer. It is a two-layer algebraic zero-equation model which gives the eddy viscosity by separate expressions in each layer, as a function of the local boundary layer velocity profile. The model is not suitable for cases with large separated regions and significant curvature/rotation effects. The turbulent kinematic viscosity for the inner layer is calculated from
$$v_{t i}=l_m^2\left[\left(\frac{\partial U}{\partial y}\right)^2+\left(\frac{\partial U}{\partial x}\right)^2\right]^{\frac{1}{2}} .$$
For the outer layer kinematic viscosity is
$$v_{t_0}=\alpha U_e \delta_1 F_{K l}(y ; \delta)$$
with
$$F_{K l}(y ; \delta)=\left[1+5.5\left(\frac{y}{\delta}\right)^6\right]^{-1} \text { and } \delta_1=\int_0^\delta\left(1-U / U_e\right) d y$$
$\alpha=0.0168, U_e$ the velocity at the edge of the boundary layer, $\delta_1$ the boundary layer displacement thickness and $F_{K l}$ as the Klebanoff intermittency function [93]. The mixing length in Eq. (9.151) is determined by combining Eqs. (9.143) and (9.144)
$$l_m=\kappa y\left(1-e^{-y^{+} / A^{+}}\right)$$
with $\kappa=0.4$ and $A^{+}=26\left(1+y \frac{d p / d x}{\rho u_\tau^2}\right)^{-1 / 2}$.

## 物理代写|流体力学代写Fluid Mechanics代考|Baldwin–Lomax Algebraic Model

The third algebraic model is the Baldwin-Lomax model [94]. The basic structure of this model is essentially the same as the Cebeci-Smith model with the exception of a few minor changes. Similar to Cebeci-Smith, this model is a two-layer algebraic zero-equation model which gives the eddy kinematic viscosity $v_t$ as a function of the local boundary layer velocity profile. The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace and turbomachinery applications. While this model is quite robust and provides quick results, it is not capable of capturing details of the flow field. Since this model is not suitable for calculating flow situations with separation, its applicability is limited. We briefly summarize the structure of this model as follows. The kinematic viscosity for the inner layer is
$$v_{t_i}=l_m^2|\Omega|$$
with
$$l_m=\kappa y\left(1-e^{-y^{+} / A_0}\right)$$
and $\Omega=e_i e_j \omega_{i j}$ as the rotation tensor. The outer layer is described by
$$v_{t 0}=\alpha C_{\mathrm{cp}} F_{\mathrm{wake}} F_{\mathrm{kl}}\left(y, y_{\max } / C_{\mathrm{Kleb}}\right)$$
with the wake function $F_{\text {wake }}$
$$F_{\text {wake }}=\min \left(y_{\max } F_{\max } ; C_{\mathrm{wk}} y_{\max } U_{\mathrm{diff}} / F_{\max }\right)$$
and $F_{\max }$ and $y_{\max }$ as the maximum of the function
$$F(y)=y|\Omega|\left(1-e^{-y^{+} / A_0}\right)$$
The velocity difference $U_{\text {diff }}$ is defined as the difference of the velocity at $y_{\max }$ and $y_{\min }$ :
$$U_{\mathrm{diff}}=\operatorname{Max}\left(\sqrt{U_i U_i}\right)-\operatorname{Min}\left(\sqrt{U_i U_i}\right)$$
with the closure coefficients listed in Table 9.1.
The above zero-equation models are applied to cases of free turbulent flow such as wake flow, jet flow, and jet boundaries.

# 流体力学代写

## 物理代写|流体力学代写Fluid Mechanics代考|Cebeci–Smith Model

$$v_{t i}=l_m^2\left[\left(\frac{\partial U}{\partial y}\right)^2+\left(\frac{\partial U}{\partial x}\right)^2\right]^{\frac{1}{2}}$$

$$v_{t_0}=\alpha U_e \delta_1 F_{K l}(y ; \delta)$$

$$F_{K l}(y ; \delta)=\left[1+5.5\left(\frac{y}{\delta}\right)^6\right]^{-1} \text { and } \delta_1=\int_0^\delta\left(1-U / U_e\right) d y$$
$\alpha=0.0168, U_e$ 边界层边缘的速度， $\delta_1$ 边界层位移厚度和 $F_{K l}$ 作为 Klebanoff 间歇函数 [93]。方程式中的 混合长度。(9.151) 是通过结合等式来确定的。(9.143) 和 (9.144)
$$l_m=\kappa y\left(1-e^{-y^{+} / A^{+}}\right)$$
$$\text { 和 } \kappa=0.4 \text { 和 } A^{+}=26\left(1+y \frac{d p / d x}{\rho u_\tau^2}\right)^{-1 / 2} \text {. }$$

## 物理代写|流体力学代写Fluid Mechanics代考|Baldwin–Lomax Algebraic Model

$$v_{t_i}=l_m^2|\Omega|$$

$$l_m=\kappa y\left(1-e^{-y^{+} / A_0}\right)$$

$$v_{t 0}=\alpha C_{\mathrm{cp}} F_{\text {wake }} F_{\mathrm{kl}}\left(y, y_{\max } / C_{\mathrm{Kleb}}\right)$$

$$F_{\text {wake }}=\min \left(y_{\max } F_{\max } ; C_{\mathrm{wk}} y_{\max } U_{\mathrm{diff}} / F_{\max }\right)$$

$$F(y)=y|\Omega|\left(1-e^{-y^{+} / A_0}\right)$$

$$U_{\mathrm{diff}}=\operatorname{Max}\left(\sqrt{U_i U_i}\right)-\operatorname{Min}\left(\sqrt{U_i U_i}\right)$$

## 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。

## 物理代写|广义相对论代写General relativity代考|Derivation of Hubble’s Law

statistics-lab™ 为您的留学生涯保驾护航 在代写广义相对论General relativity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。我们的专家在代写广义相对论General relativity代写方面经验极为丰富，各种代写广义相对论General relativity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

## 物理代写|广义相对论代写General relativity代考|Derivation of Hubble’s Law

Consider a light ray propagation from a distant galaxy at $\left(r_1, \theta_1, \phi_1\right)$ towards $r=0$. The equations of a null geodesic imply that this light ray moves along the path $\theta=\theta_1, \phi=\phi_1$. Suppose the present epoch is denoted by $t=t_0$ and let a right ray leave the source at $t=t_1$. Then the condition for the ray to reach at $r=0$, at $t=t_0$
$$\int_{t_1}^{t_0} \frac{c d t}{a(t)}=\int_0^{r_1} \frac{d r}{\sqrt{1-k r^2}}=f\left(r_1\right) .$$
Assuming that $r_1$ is small for nearby objects, we then get approximately,
$$f\left(r_1\right) \cong r_1 \cong \frac{c\left(t_0-t_1\right)}{a\left(t_0\right)}$$

Now Taylor’s expansion near $t_0$,
\begin{aligned} a\left(t_1\right) & \cong a\left(t_0\right)+\left(t_1-t_0\right) \dot{a}\left(t_0\right)=a\left(t_0\right)\left[1-\left(t_0-t_1\right) \frac{\dot{a}\left(t_0\right)}{a\left(t_0\right)}\right], \ & =a\left(t_0\right)\left[1-\left(t_0-t_1\right) H_0\right] \text { where } H_0=\frac{\dot{a}\left(t_0\right)}{a\left(t_0\right)} . \end{aligned}
Also, we know
$$(1+z)^{-1}=\frac{a\left(t_1\right)}{a\left(t_0\right)} \cong 1-\left(t_0-t_1\right) H_0 .$$
For, small redshift $z$, we have
$$1-z \cong 1-\left(t_0-t_1\right) H_0$$
This implies
$$\begin{gathered} c z \cong r_1 a\left(t_0\right) H_0=D_1 H_0, \ \text { where } D_1=r_1 a\left(t_0\right), \end{gathered}$$
may be defined as a proper distance at the epoch $t_0$.
From a Doppler shift point of view, cz may be identified with the velocity of recession of a galaxy in proportion to its distance from us. This is Hubble’s law and $H_0$ is the Hubble’s constant given by
$$H_0=\frac{\dot{a}\left(t_0\right)}{a\left(t_0\right)}$$

## 物理代写|广义相对论代写General relativity代考|Angular Size

The angular measurement describing how a large sphere or circle looks from a given point of view is the angular diameter or angular size. In Euclidean geometry, the diameter $d$ is related to the observed angle $\Delta \theta$ as
$$\Delta \theta=\frac{d}{r},$$
where $r$ is its distance. However, for curved spacetime, one needs to use $\mathrm{R}-\mathrm{W}$ spacetime.
Let us consider a galaxy $G_1$ having linear extend $d(\overline{A B})$ and the angle subtended by this galaxy $G_1$ at the observer $\mathrm{O}$ is $\Delta \theta_1$ (see Fig. 101). Consider two neighboring null geodesics (representing light rays) from the two points $A, B$ at the two extremities of $G_1$. Without any loss of generality, we can select the coordinates of $A$ and $B$ as $\left(\theta_1, \phi_1\right)$ and $\left(\theta_1+\Delta \theta_1, \phi_1\right)$, respectively. For the curved space, we use R-W line element to find the proper distance between $A$ and $B$. Now, plugging $t=t_1=$ constant, $r=r_1=$ constant, $\phi=\phi_1=$ constant, and $d \theta=\Delta \theta_1$ in the R-W line element, we get
$$d s^2=-r_1^2 a^2\left(t_1\right)\left(\Delta \theta_1\right)^2=-d^2$$
[in $G_1$, the space-like separation $A B=d$, which is a rest frame] Thus,
\begin{aligned} \Delta \theta_1 & =\frac{d}{r_1 a\left(t_1\right)}=\frac{d(1+z)}{r_1 a\left(t_0\right)}, \quad \text { (using Eq. (11.30)) } \ & =\frac{d(1+z)}{D_1} .[\text { using Eq. (11.36)] } \end{aligned}
Note that in Euclidean space, $\Delta \theta_1$ is decreasing with an increase in the distance of the galaxy from us. However, in curved space, the result is different. For expanding universe, the scale factor $a(t)$ is increasing with time and consequently, $z$ will be increasing (by Eq. (11.31)). Therefore, it is not always true that $\Delta \theta_1$ decreases with time. Light from a galaxy takes much time to reach us for expanding universe.

# 广义相对论代考

## 物理代写|广义相对论代写General relativity代考|Derivation of Hubble’s Law

$$\int_{t_1}^{t_0} \frac{c d t}{a(t)}=\int_0^{r_1} \frac{d r}{\sqrt{1-k r^2}}=f\left(r_1\right)$$

$$f\left(r_1\right) \cong r_1 \cong \frac{c\left(t_0-t_1\right)}{a\left(t_0\right)}$$

$$a\left(t_1\right) \cong a\left(t_0\right)+\left(t_1-t_0\right) \dot{a}\left(t_0\right)=a\left(t_0\right)\left[1-\left(t_0-t_1\right) \frac{\dot{a}\left(t_0\right)}{a\left(t_0\right)}\right], \quad=a\left(t_0\right)\left[1-\left(t_0-t_1\right) H_0\right]$$

$$(1+z)^{-1}=\frac{a\left(t_1\right)}{a\left(t_0\right)} \cong 1-\left(t_0-t_1\right) H_0$$

$$1-z \cong 1-\left(t_0-t_1\right) H_0$$

$$c z \cong r_1 a\left(t_0\right) H_0=D_1 H_0, \text { where } D_1=r_1 a\left(t_0\right),$$

$$H_0=\frac{\dot{a}\left(t_0\right)}{a\left(t_0\right)}$$

## 物理代写|广义相对论代写General relativity代考|Angular Size

$$\Delta \theta=\frac{d}{r}$$

$$d s^2=-r_1^2 a^2\left(t_1\right)\left(\Delta \theta_1\right)^2=-d^2$$
[在 $G_1$ ，类似空间的分离 $A B=d$ ，这是一个休息框架]因此，
$$\Delta \theta_1=\frac{d}{r_1 a\left(t_1\right)}=\frac{d(1+z)}{r_1 a\left(t_0\right)}, \quad \text { (using Eq. (11.30)) } \quad=\frac{d(1+z)}{D_1} \cdot[\text { using Eq. (11.36)] }$$

## 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。

## 物理代写|广义相对论代写General relativity代考|Newtonian Cosmology

statistics-lab™ 为您的留学生涯保驾护航 在代写广义相对论General relativity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。我们的专家在代写广义相对论General relativity代写方面经验极为丰富，各种代写广义相对论General relativity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

## 物理代写|广义相对论代写General relativity代考|Newtonian Cosmology

Let us consider the universe to be an immensely large sphere of gas (that means larger than we can imagine but not infinite). Treating the gas particles as galaxies, i.e., the universe is a huge sphere filled with the gas of galaxies and its volume is very large. Further, we consider that the gaseous sphere is isotropic and homogeneous. An observer or a point which is carried along with the expansion is said to be comoving. As the sphere is isotropic and homogeneous, the expansion is regulated by a single function of time and as a result, we can write the distance between any two comoving points at a time $t$ as
$$r(t)=R(t) r_0$$
where $r_0$ is a constant for the pair and $R(t)$, called the scale factor, is the universal expansion factor. Differentiating (11.18) with respect to time, we get,
$$v(t)=\dot{r}(t)=H(t) r(t)$$
where
$$H(t)=\frac{\dot{R}(t)}{R(t)}$$
$H(t)$ is called the Hubble’s parameter. Equation (11.19) is called Hubble’s law. Note that $H$ is a function of time.
It is customary to denote its present value by $H_0$, i.e.,
$$H_0=\frac{\dot{R}\left(t_0\right)}{R\left(t_0\right)}$$
where $t_0$ is the present moment.
Hubble’s law is consistent with the observation that all other galaxies are moving away from us. This indicates that the distance between two galaxies is increasing with the time that means the velocity of separation $v$ is a function of time. Let at the present time the separation distance be $r$, then there must have been a time $\tau$ in the past when the distance between them was very small. Thus, according to Eq. (11.19), we have
$$\tau=\frac{r}{v}=\frac{1}{H_0}$$

## 物理代写|广义相对论代写General relativity代考|Cosmological Redshift

The observed wavelengths of the spectral lines from a star are not the same as the original wavelengths of the spectral lines of the star. The lines are shifted to the red or blue due to the relative velocity between the earth and the star. If the star is approaching the earth then we get blue-shift and if the star is receding then one gets redshift. We will discuss how the shifted spectral lines are related to the scale factor.

Consider a distant galaxy situated at a point whose coordinates are $\left(r_1, \theta_1, \phi_1\right)$. It emits a light ray that propagates and reaches us $(r=0$ ). Light ray travels along a null geodesic. Without any loss of generality, we consider that the path of the light lies on the plane $\left(\theta=\theta_1, \phi=\phi_1\right)$. Suppose the present epoch is denoted by $t=t_0$ and let a light ray leave the source at $t=t_1$. For null geodesic, we have $d s=0$. Now using $d \theta=0, d \phi=0$, the R-W metric yields the following condition for the ray to arrive at $r=0$ at $t=t_0$
$$\int_{t_1}^{t_0} \frac{c d t}{a(t)}=\int_0^{r_1} \frac{d r}{\left(1-k r^2\right)^{\frac{1}{2}}} .$$
[In the null geodesics (with $d s=0, d \theta=d \phi=0$ ),
$$\frac{c d t}{a(t)}= \pm \frac{d r}{\left(1-k r^2\right)^{\frac{1}{2}}}$$
we should take minus sign in this relation as $r$ decreases as $t$ increases along this null geodesic]
Light wave starts at $r=r_1$ and reaches us at $r=0$. Let two successive crests of the wave leave at $t_1$ and $t_1+\Delta t_1$ and arrive at $t_0$ and $t_0+\Delta t_0$, respectively. Equation (11.27) yields
$$\int_{t_1+\Delta t_1}^{t_0+\Delta t_0} \frac{c d t}{a(t)}=\int_0^{t_1} \frac{d r}{\sqrt{1-k r^2}}=\int_{t_1}^{t_0} \frac{c d t}{a(t)}$$

# 广义相对论代考

## 物理代写|广义相对论代写General relativity代考|Newtonian Cosmology

$$r(t)=R(t) r_0$$

$$v(t)=\dot{r}(t)=H(t) r(t)$$

$$H(t)=\frac{\dot{R}(t)}{R(t)}$$
$H(t)$ 称为哈勃参数。方程 (11.19) 称为哈勃定律。注意 $H$ 是时间的函数。 通常用以下方式表示其现值 $H_0$ ，那是，
$$H_0=\frac{\dot{R}\left(t_0\right)}{R\left(t_0\right)}$$

$$\tau=\frac{r}{v}=\frac{1}{H_0}$$

## 物理代写|广义相对论代写General relativity代考|Cosmological Redshift

$$\int_{t_1}^{t_0} \frac{c d t}{a(t)}=\int_0^{r_1} \frac{d r}{\left(1-k r^2\right)^{\frac{1}{2}}} .$$
[在零测地线（与 $d s=0, d \theta=d \phi=0 ） ，$
$$\frac{c d t}{a(t)}= \pm \frac{d r}{\left(1-k r^2\right)^{\frac{1}{2}}}$$

$$\int_{t_1+\Delta t_1}^{t_0+\Delta t_0} \frac{c d t}{a(t)}=\int_0^{t_1} \frac{d r}{\sqrt{1-k r^2}}=\int_{t_1}^{t_0} \frac{c d t}{a(t)}$$

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## MATLAB代写

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