英语翻译For undergraduates,I do not do most of the derivations in this chapter,at least not in detail.Rather,I focus on interpreting the assumptions,which mostly concern the population.Other than random sampling,the only assumption that involves

英语翻译For undergraduates,I do not do most of the derivations in this chapter,at least not in detail.Rather,I focus on interpreting the assumptions,which mostly concern the population.Other than random sampling,the only assumption that involves
英语翻译
For undergraduates,I do not do most of the derivations in this chapter,at least not in detail.Rather,I focus on interpreting the assumptions,which mostly concern the population.Other than random sampling,the only assumption that involves more than population considerations is the assumption about no perfect collinearity,where the possibility of perfect collinearity in the sample (even if it does not occur in the population) should be touched on.The more important issue is perfect collinearity in the population,but this is fairly easy to dispense with via examples.These come from my experiences with the kinds of model specification issues that beginners have trouble with.
The comparison of simple and multiple regression estimates – based on the particular sample at hand,as opposed to their statistical properties – usually makes a strong impression.Sometimes I do not bother with the “partialling out” interpretation of multiple regression.
As far as statistical properties,notice how I treat the problem of including an irrelevant variable:no separate derivation is needed,as the result follows form Theorem 3.1.
I do like to derive the omitted variable bias in the simple case.This is not much more difficult than showing unbiasedness of OLS in the simple regression case under the first four Gauss-Markov assumptions.It is important to get the students thinking about this problem early on,and before too many additional (unnecessary) assumptions have been introduced.
I have intentionally kept the discussion of multicollinearity to a minimum.This partly indicates my bias,but it also reflects reality.It is,of course,very important for students to understand the potential consequences of having highly correlated independent variables.But this is often beyond our control,except that we can ask less of our multiple regression analysis.If two or more explanatory variables are highly correlated in the sample,we should not expect to precisely estimate their ceteris paribus effects in the population.
I find extensive treatments of multicollinearity,where one “tests” or somehow “solves” the multicollinearity problem,to be misleading,at best.Even the organization of some texts gives the impression that imperfect multicollinearity is somehow a violation of the Gauss-Markov assumptions:they include multicollinearity in a chapter or part of the book devoted to “violation of the basic assumptions,” or something like that.I have noticed that master’s students who have had some undergraduate econometrics are often confused on the multicollinearity issue.It is very important that students not confuse multicollinearity among the included explanatory variables in a regression model with the bias caused by omitting an important variable.
I do not prove the Gauss-Markov theorem.Instead,I emphasize its implications.Sometimes,and certainly for advanced beginners,I put a special case of Problem 3.12 on a midterm exam,where I make a particular choice for the function g(x).Rather than have the students directly compare the variances,they should appeal to the Gauss-Markov theorem for the superiority of OLS over any other linear,unbiased estimator.

英语翻译For undergraduates,I do not do most of the derivations in this chapter,at least not in detail.Rather,I focus on interpreting the assumptions,which mostly concern the population.Other than random sampling,the only assumption that involves
对于大学生,我不要在这一章中,大部分的推导,至少不详细.相反,我将重点解释的假设,它主要关注的人口.除随机抽样,涉及的唯一前提是比人口的考虑更多的是关于没有完美的线性,那里的样品中（即使它没有发生在人口）的可能性应该是完美的线性提及的假设.更重要的问题是在人口完美的线性,但是这是相当容易,免除通过的例子.这些来自我的经验与问题的各种型号规格的初学者有麻烦.
而简单的和多元回归估计的比较 - 基于手头特定样本,而不是他们的统计性质 - 通常带有强烈的印象.有时候,我也懒得与“partialling出”多元回归解释.
据,统计物业通知我如何对待一个不相关的变数的问题包括：没有单独的推导是必要的,作为结果如下形式定理3.1.
我不喜欢,推导出了简单的情况下遗漏变量偏差.这不是比显示在第一个四高斯马尔可夫假设的情况下简单回归母机无偏难.重要的是让学生对这个问题的思考早,之前太多额外的（不必要的）假设相继出台.
我特意保留了多重共线性的讨论到最低限度.这部分说明我的偏见,但它也反映了现实.这是,当然是非常重要的,让学生了解有高度相关自变量的潜在后果.但是,这往往是我们无法控制,但我们可以请我们的多元回归分析少.如果两个或更多的解释变量高度相关的样品,我们不应该指望他们准确地估计,在其他条件不变的人口条件不变的影响.
我发现广泛的共线性处理,其中一个“测试”或以某种方式“解决”的共线性问题,是误导,最好的.即使是一些文本组织给人的印象是不完美的多重共线性在某种程度上是高斯马尔可夫假设冲突：他们包括多重共线性在一章或专门讨论“违反了基本假设”,或类似的东西书的一部分.我注意到,主是谁已经取得了一些经常上的多重共线性问题混为一谈本科计量经济学的学生.这是非常重要的是学生之间的多重共线性不能混为一谈包括在回归模型的解释变量与被省略的一个重要变量所造成的偏差.
我不能证明高斯马尔可夫定理.相反,我要强调的影响.有时,当然也为先进的初学者,我把一期中考试的一个问题3.12特殊情况,我在那里做一个特别的选择函数g（x）的.而不是让学生直接比较的差异,他们应该呼吁高斯马尔可夫定理的母机对任何其他线性,无偏估计的优越性.