# 统计代写|回归分析作业代写Regression Analysis代考|STA4210

## 统计代写|回归分析作业代写Regression Analysis代考|Exact Inferences: Prediction Intervals

Notice that the range of the confidence interval, $1,303.753$ and $1,560.912$, is around 250 Cost units, much narrower than the range shown by the vertical bar in Figure 3.5, which is around 1,000 Cost units. Why? Is this yet another approximation? No. The reason for the big difference is that the mean of all potentially observable values of the Cost variable for jobs with any fixed number of widgets, is very much different than a single potentially observable value of the Cost variable.
It makes sense, intuitively and by the Law of Large Numbers, that you can estimate a mean value more and more precisely, with a margin of error tending towards 0 , when you increase your sample size. However, you cannot estimate a single value with such precision, no matter how large is your sample size.

To understand the distinction between a single value of $Y$ and the mean value of the potentially observable $Y^{\prime}$ s, suppose you have a model for how stock returns behave:
(Return on Company A’s stock) $=\beta_0+\beta_1($ Return on the $S \& P 500$ index $)+\varepsilon$.
(Return on Company A’s stock) $=0.0032+0.67$ (Return on the $S \& P 500$ index) $+e$
Now, suppose we tell you that the return on the SEPP 500 index was $0.005(0.5 \%)$ yesterday. What can you tell us about the return on Company A’s stock? Was it exactly $0.0032+0.67(0.005)=0.00655(0.655 \%)$ ? We hope you can see that the answer is no, it was not $0.655 \%$. In all likelihood, it was not even very close to $0.655 \%$. It might even have been a negative number-it is quite common that individual stock prices move in a direction counter to the market. You cannot predict the actual value of company A’s stock return with precision using this model, because company A’s stock return is not a deterministic function of the $S \mathcal{E} P 500$ return. There are unique features of Company A that make it differ from the market, sometimes substantially, on any given day.

Having a large sample size here means that the estimate of the mean of all potentially observable returns of Company A’s stock, given the SEPP 500 market return is $0.005$, is very close to $0.0032+0.67(0.005)=0.00655$. However, the mean of all potentially observable returns is very different from a single potentially observable return: The individual return differs from the conditional mean (which is approximately $0.00655$ ), by the random error term $e$. This error term can be quite large, leading possibly to a negative Company A return when the $S \mathcal{E P} 500$ return is positive.

## 统计代写|回归分析作业代写Regression Analysis代考|Hypothesis Testing and p-Values

Some researchers will do nearly anything to get a publication. The incentives are great: Fame, tenure, promotion, annual salary, raises, prime class assignments, and clout in one’s department are a function of quality and quantity of publications.

Historically, statistical results were required to be “statistically significant” to be publishable. In terms of confidence intervals, this means that the interval for the effect (e.g., the $\beta$ ) in question must exclude 0 so that you can confidently state the direction of the effect (positive or negative) of the given $X$ variable on $Y$.

Researchers used the $p$-values that are reported routinely by regression software to determine “statistical significance.” But p-values are easily manipulated, and unscrupulous researchers can analyze data “creatively” to get nearly any $p$-value they would like to see. This has led to an unfortunate practice known as p-hacking, where researchers try analyses many different ways until they get a $p$-value that is statistically significant, and then try to publish the results. Because of their potential for misuse, there is a strong movement in the scientific community away from use of $p$-values, as well as the phrase “statistical significance,” in favor of other statistics and characterizations.

When interpreted correctly and not misused, the $p$-value does provide interesting and somewhat useful information. Thus, we insist that you understand $p$-values very well, so that you can use them correctly and effectively, and so that you will not become a “p-hacker.”

To interpret the $p$-value correctly, you must consider the question, “Is the estimate of the effect of $X$ on $Y$ explainable by chance alone?” But to answer that question, you must first understand what it means for an estimated effect to be explained by chance alone. The following example explains this concept.

# 回归分析代考

## 统计代写|回归分析作业代写回归分析代考|精确推论:预测区间

(a公司股票的回报)$=\beta_0+\beta_1($$S \& P 500$指数的回报$)+\varepsilon$ .
(a公司股票的回报)$=0.0032+0.67$ ($S \& P 500$指数的回报)$+e$假设我们告诉你，昨天SEPP 500指数的回报率是$0.005(0.5 \%)$。你能告诉我们A公司股票的回报率吗?确切地说是$0.0032+0.67(0.005)=0.00655(0.655 \%)$吗?我们希望你能看到答案是否定的，它不是$0.655 \%$。十有八九，它甚至不太接近$0.655 \%$。这甚至可能是一个负数——个股价格与市场走势相反是很常见的。使用该模型无法精确预测A公司股票收益的实际值，因为A公司股票收益不是$S \mathcal{E} P 500$收益的确定函数。A公司有其独特的特点，使其在任何一天都与市场不同，有时甚至有很大的不同

## 统计代写|回归分析作业代写回归分析代考|假设检验和p-值

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