统计代写|线性回归分析代写linear regression analysis代考|STA321

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统计代写|线性回归分析代写linear regression analysis代考|The problem

Jay Leno, in one of his Tonight Show monologues several years ago, mentioned a study that found that $50 \%$ of all academic research is wrong. His punchline: there’s a $50 \%$ chance this study itself is wrong.
The study Leno referred to may actually understate the true percentage of studies that are inaccurate. The major causes of all these errors in research are likely faulty research designs and improper interpretations of the results. These accuracy issues bring into doubt the value of academic research.
Most quantitative academic research, particularly in the social sciences, business, and medicine, rely on regression analyses. The primary objective of regressions is to quantify cause-effect relationships. These cause-effect relationships are part of the knowledge that should guide society to develop good public policies and good strategies for conducting business, educating people, promoting health and general welfare, and more. Regressions are useful for estimating such relationships because they are able to “hold constant” other factors that may confound the cause-effect relationship in question. That is, regressions, if done well, can rule out reasons for two variables to be related, other than the causal-effect reason.
Here are some examples of how regressions can be used to estimate the causal effect of one factor (or a set of factors) on some outcome:

  • How does some new cancer drug affect the probability of a patient surviving 10 years after diagnosis?
  • How does a parental divorce affect children’s test scores?
  • What factors make teachers more effective?
  • What encourages people to save more for retirement?
  • What factors contribute to religious extremism and violence?
  • How does parental cell phone use affect children’s safety?
  • How does oat-bran consumption affect bad cholesterol levels?
  • Do vaccines affect the probability of a child becoming autistic?
  • How much does one more year of schooling increase a person’s earnings?
  • Does smiling when dropping my shirt off at the cleaners affect the probability that my shirt will be ready by Thursday?

A regression is a remarkable tool in its ability to measure how certain variables move together, while holding certain factors constant. A natural human reaction is to be mesmerized by things people do not understand, such as how regressions can produce these numbers. And so, in the roughly 10 times that I have used regression results in briefings to somewhat-high-level officials at the Department of Defense (mostly as a junior researcher, with a senior researcher tagging along to make sure I didn’t say anything dumb), the people I was briefing never asked me whether there were any empirical issues with the regression analysis I had used or how confident I was with the findings. Most of the time, based on the leading official’s response to the research, they would act as if I had just given them the absolute truth on an important problem based on these “magic boxes” called “regressions.” Unfortunately, I was caught up in the excitement of the positive response from these officials, and I wasn’t as forthright as I should have been about the potential pitfalls (and uncertainty) in my findings. And so, I usually let them believe the magic.

统计代写|线性回归分析代写linear regression analysis代考|The purpose of research

To understand where research goes wrong, we first have to understand the overall purpose of research. We conduct research to improve knowledge, which often involves trying to get us closer to understanding cause-effect and other empirical relationships. To demonstrate, let’s start with the highly contentious issue of global warming. You may have some belief on the probability that the following statement is true:
Human activity is contributing to global warming.
And, hopefully that probability of yours lies somewhere between $0.3 \%$ and $99.7 \%-$ that is, you may have your beliefs, but you recognize that you probably are not an expert on the topic and so there is a possibility that you are wrong. I’m guessing that most people would be below $10 \%$ or above $90 \%$ (or, even $5 \%$ and $95 \%$ ). But, for the sake of the argument, let’s say that you have a subjective probability of the statement being true $45 \%$ of the time.

Suppose a study comes out that has new evidence that humans are causing global warming. This may shift your probability upwards. If the new research were reported on cable news channel MSNBC (which leans toward the liberal side of politics) and you tended to watch MSNBC, then let’s say that it would shift your probability up by 7 percentage points (to $52 \%$ ). If you tended to watch Fox News (a more conservative channel) instead, then the news from MSNBC may shift your probability up by some negligible amount, say $0.2$ percentage points (up to $45.2 \%$ ). But, ideally, the amount that your subjective probability of the statement above would shift upwards should depend on:

  • How the study contrasts with prior research on the issue;
  • The validity and extensiveness of the prior research;
  • The extent to which any viable alternative explanations to the current findings can be ruled out – i.e., how valid the methods of the study are.

With regression analysis, it should be the same thinking of shifting beliefs. People have some prior beliefs about some issue, say on whether class size is important for student achievement. Using regression analysis, a new study finds no evidence that class size has an effect on student achievement. This finding should not necessarily be taken as concrete evidence for that side of the issue. Rather, the evidence has to be judged based on the strength of the study relative to the strength of other studies, or the three criteria listed above. And, people would then shift their subjective probability appropriately. The more convincing the analysis, the more it should swing a person’s belief in the direction of the study’s conclusions.

This is where it is up to researchers, the media, and the public to properly scrutinize research to assess how convincing it is. As I will describe below, you cannot always rely on the peer-review process that determines what research gets published in journals.

统计代写|线性回归分析代写linear regression analysis代考|STA321

线性回归分析代考

统计代写|线性回归分析代写linear regression analysis代考|The problem

杰雷诺 (Jay Leno) 几年前在他的《今夜秀》(Tonight Show) 独白中提到了一项研究,该研究发现50%所有的学术研究都是错误的。他的妙语:有一个50%机会这项研究本身是错误的。
Leno 提到的研究实际上可能低估了不准确研究的真实百分比。所有这些研究错误的主要原因可能是错误的研究设计和对结果的不正确解释。这些准确性问题使学术研究的价值受到质疑。
大多数定量学术研究,特别是在社会科学、商业和医学领域,都依赖于回归分析。回归的主要目标是量化因果关系。这些因果关系是知识的一部分,应该指导社会制定良好的公共政策和良好的战略来开展业务、教育人们、促进健康和普遍福利等。回归对于估计此类关系很有用,因为它们能够“保持不变”可能混淆所讨论的因果关系的其他因素。也就是说,回归,如果做得好,可以排除两个变量相关的原因,而不是因果关系原因。
以下是一些示例,说明如何使用回归来估计一个因素(或一组因素)对某些结果的因果影响:

  • 一些新的抗癌药物如何影响患者在诊断后 10 年存活的可能性?
  • 父母离婚如何影响孩子的考试成绩?
  • 哪些因素使教师更有效率?
  • 是什么鼓励人们为退休储蓄更多?
  • 哪些因素助长了宗教极端主义和暴力?
  • 父母使用手机如何影响孩子的安全?
  • 食用燕麦麸如何影响坏胆固醇水平?
  • 疫苗会影响孩子患自闭症的概率吗?
  • 一个人多上一年学能增加多少收入?
  • 把我的衬衫丢在洗衣店时微笑会影响我的衬衫在星期四之前准备好的可能性吗?

回归是一种卓越的工具,因为它能够衡量某些变量如何一起移动,同时保持某些因素不变。人类的自然反应是被人们不理解的事物迷住,例如回归如何产生这些数字。因此,在大约 10 次的情况下,我在向国防部高级官员的简报中使用了回归结果(主要是作为一名初级研究员,一名高级研究员跟随以确保我没有说任何话愚蠢),我做简报的人从来没有问过我使用的回归分析是否存在任何经验问题,或者我对这些发现的信心如何。大多数时候,根据领导官员对研究的反应,他们会表现得好像我刚刚根据这些称为“回归”的“魔盒”给了他们关于一个重要问题的绝对真理。不幸的是,我被这些官员的积极回应所吸引,对于我的发现中的潜在陷阱(和不确定性),我没有像我应该的那样直率。所以,我通常让他们相信魔法。

统计代写|线性回归分析代写linear regression analysis代考|The purpose of research

要了解研究哪里出了问题,我们首先必须了解研究的总体目的。我们进行研究以增进知识,这通常涉及试图让我们更接近于理解因果关系和其他经验关系。为了证明这一点,让我们从备受争议的全球变暖问题开始。您可能会相信以下陈述为真的概率:
人类活动导致全球变暖。
而且,希望你的概率介于两者之间0.3%和99.7%−也就是说,您可能有自己的信念,但您认识到自己可能不是该主题的专家,因此您有可能错了。我猜大多数人会在下面10%或以上90%(甚至5%和95%). 但是,为了论证,假设您有一个主观概率认为该陈述为真45%的时间。

假设一项研究有新的证据表明人类正在导致全球变暖。这可能会提高您的概率。如果新研究在有线新闻频道 MSNBC(倾向于政治自由派)上进行了报道,并且您倾向于观看 MSNBC,那么假设它会将您的概率提高 7 个百分点(到52%). 如果您倾向于观看 Fox News(一个更保守的频道),那么来自 MSNBC 的新闻可能会将您的概率提高一些可以忽略不计,比如说0.2个百分点(高达45.2%). 但是,理想情况下,您对上述陈述的主观概率向上移动的数量应取决于:

  • 该研究如何与之前对该问题的研究进行对比;
  • 先前研究的有效性和广泛性;
  • 可以排除对当前发现的任何可行替代解释的程度——即研究方法的有效性。

与回归分析,应该是相同的信念转移思维。人们对某些问题有一些先验的信念,比如班级规模对学生成绩是否重要。使用回归分析,一项新研究没有发现班级规模对学生成绩有影响的证据。这一发现不一定被视为问题这一方面的具体证据。相反,必须根据研究相对于其他研究的强度或上述三个标准来判断证据。然后,人们会适当地改变他们的主观概率。分析越有说服力,就越应该使人相信研究结论的方向。

这是由研究人员、媒体和公众适当审查研究以评估其说服力的地方。正如我将在下面描述的,您不能总是依赖同行评审过程来决定哪些研究会在期刊上发表。

统计代写|线性回归分析代写linear regression analysis代考

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