## 统计代写|回归分析作业代写Regression Analysis代考|STAT311

statistics-lab™ 为您的留学生涯保驾护航 在代写回归分析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。我们的专家在代写回归分析Regression Analysis代写方面经验极为丰富，各种代写回归分析Regression Analysis相关的作业也就用不着说。

## 统计代写|回归分析作业代写Regression Analysis代考|The Independence Assumption and Repeated Measurements

You know what? All the analyses we did on the charitable contributions prior to the subject/indicator variable model were grossly in error because the independence assumption was so badly violated. You may assume, nearly without question, that these 47 taxpayers are independent of one another. But you may not assume that the repeated observations on a given taxpayer are independent. Charitable behavior in different years is similar for given taxpayers; i.e., the observations are dependent rather than independent. It was wrong for us to assume that there were 470 independent observations in the data set. As you recall, the standard error formula has an ” $n$ ” in the denominator, so it makes a big difference whether you use $n=470$ or $n=47$. In particular, all the standard errors for models prior to the analysis above were too small.

Sorry about that! We would have warned you that all those analyses were questionable earlier, but there were other points that we needed to make. Those were all valid points for cases where the observations are independent, so please do not forget what you learned.
But now that you know, please realize that you must consider the dependence issue carefully. You simply cannot, and must not, treat repeated observations as independent. All of the standard errors will be grossly incorrect when you assume independence; the easiest way to understand the issue is to recognize that $n=470$ is quite a bit different from $n=47$.
Confused? Simulation to the rescue! The following R code simulates and analyzes data where there are 3 subjects, with 100 replications on each, and with a strong correlation (similarity) of the data on each subject.
\begin{aligned} & \mathrm{s}=3 \quad # \text { subjects } \ & r=100 \quad # \text { replications within subject } \ & \mathrm{X}=\operatorname{rnorm}(\mathrm{s}) ; \mathrm{X}=\operatorname{rep}(\mathrm{X}, \text { each }=r) \text { +rnorm }\left(r^{\star} s, 0, .001\right) \ & \mathrm{a}=\operatorname{rnorm}(\mathrm{s}) ; \mathrm{a}=\operatorname{rep}(\mathrm{a}, \text { each }=r) \end{aligned}

$e=\operatorname{rnorm}(s \star r, 0, .001)$
epsilon $=\mathrm{a}+\mathrm{e}$
$\mathrm{Y}=0+0 \star \mathrm{X}+\operatorname{rnorm}\left(\mathrm{S}^* \mathrm{r}\right)$ tepsilon # $\mathrm{Y}$ unrelated to $\mathrm{X}$
sub $=\operatorname{rep}(1: s$, each $=r)$
summary $(\operatorname{lm}(\mathrm{Y} \sim \mathrm{X}))$ # Highly significant $\mathrm{X}$ effect
$\operatorname{summary}(\operatorname{lm}(\mathrm{Y} \sim \mathrm{X}+$ as.factor $($ sub $)))$ # Insignificant $\mathrm{X}$ effect

## 统计代写|回归分析作业代写Regression Analysis代考|Predicting Hans’ Graduate GPA: Theory Versus Practice

Hans is applying for graduate school at Calisota Tech University (CTU). He sends CTU his quantitative score on the GRE entrance examination $\left(X_1=140\right)$, his verbal score on the $\operatorname{GRE}\left(X_2=160\right)$, and his undergraduate GPA $\left(X_3=2.7\right)$. What would be his final graduate GPA at CTU?

Of course, no one can say. But what we do know, from the Law of Total Variance discussed in Chapter 6, is that the variance of the conditional distribution of $Y=$ final CTU GPA is smaller on average when you consider additional variables. Specifically,
$$\mathrm{E}\left{\operatorname{Var}\left(Y \mid X_1, X_2, X_3\right)\right} \leq \mathrm{E}\left{\operatorname{Var}\left(Y \mid X_1, X_2\right)\right} \leq \mathrm{E}\left{\operatorname{Var}\left(Y \mid X_1\right)\right}$$

Figure 11.1 shows how these inequalities might appear, as they relate to Hans. The variation in potentially observable GPAs among students who are like Hans in that they have GRE Math $=140$ is shown in the top panel. Some of that variation is explained by different verbal abilities among students, and the second panel removes that source of variation by considering GPA variation among students who, like Hans, have GRE Math $=140$, and GRE Verbal $=160$. But some of that variation is explained by the general student diligence. Assuming undergraduate GPA is a reasonable measure of such “diligence,” the final panel removes that source of variation by considering GPA variation among students who, like Hans, have GRE Math $=140$, and GRE verbal $=160$, and undergrad GPA $=2.7$. Of course, this can go on and on if additional variables were available, with each additional variable removing a source of variation, leading to distributions with smaller and smaller variances.

The means of the distributions shown in Figure 11.1 are $3.365,3.5$, and 3.44 , respectively. If you were to use one of the distributions to predict Hans, which one would you pick? Clearly, you should pick the one with the smallest variance. His ultimate GPA will be the same number under all three distributions, and since the third distribution has the smallest variance, his GPA will likely be closer to its mean (3.44) than to the other distribution means (3.365 or 3.5).

# 回归分析代写

## 统计代写|回归分析作业代写Regression Analysis代考|The Independence Assumption and Repeated Measurements

\begin{aligned} & \mathrm{s}=3 \quad # \text { subjects } \ & r=100 \quad # \text { replications within subject } \ & \mathrm{X}=\operatorname{rnorm}(\mathrm{s}) ; \mathrm{X}=\operatorname{rep}(\mathrm{X}, \text { each }=r) \text { +rnorm }\left(r^{\star} s, 0, .001\right) \ & \mathrm{a}=\operatorname{rnorm}(\mathrm{s}) ; \mathrm{a}=\operatorname{rep}(\mathrm{a}, \text { each }=r) \end{aligned}

$e=\operatorname{rnorm}(s \star r, 0, .001)$
$=\mathrm{a}+\mathrm{e}$
$\mathrm{Y}=0+0 \star \mathrm{X}+\operatorname{rnorm}\left(\mathrm{S}^* \mathrm{r}\right)$ tempsilon ＃ $\mathrm{Y}$与$\mathrm{X}$无关

$\operatorname{summary}(\operatorname{lm}(\mathrm{Y} \sim \mathrm{X}+$ as。因子$($ sub $)))$ ＃不显著$\mathrm{X}$效应

## 统计代写|回归分析作业代写Regression Analysis代考|Predicting Hans’ Graduate GPA: Theory Versus Practice

$$\mathrm{E}\left{\operatorname{Var}\left(Y \mid X_1, X_2, X_3\right)\right} \leq \mathrm{E}\left{\operatorname{Var}\left(Y \mid X_1, X_2\right)\right} \leq \mathrm{E}\left{\operatorname{Var}\left(Y \mid X_1\right)\right}$$

## 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|回归分析作业代写Regression Analysis代考|STA321

statistics-lab™ 为您的留学生涯保驾护航 在代写回归分析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。我们的专家在代写回归分析Regression Analysis代写方面经验极为丰富，各种代写回归分析Regression Analysis相关的作业也就用不着说。

## 统计代写|回归分析作业代写Regression Analysis代考|Piecewise Linear Regression; Regime Analysis

Usually, it makes sense to model $\mathrm{E}(Y \mid X=x)$ as a continuous function of $x$, but there are cases where a discontinuity is needed. For a hypothetical example, suppose people with less than $\$ 250,000$income are taxed at$28 \%$, and those with$\$250,000$ or more are taxed at $34 \%$. Then a regression model to predict $Y=$ Charitable Contributions will likely have a discontinuity at $X=250,000$, as shown in Figure 10.12.

If you wanted to estimate the model shown in Figure 10.12, you would first create an indicator variable that is 0 for Income $<250$, otherwise 1 , like this:
Ind $=$ ifelse $($ Income $<250,0,1)$
Then you would include that variable in a regression model, with interactions, like this:
$$\text { Charity }=\beta_0+\beta_1 \text { Income }+\beta_2 \text { Ind }+\beta_3 \text { Income } \times \text { Ind }+\varepsilon$$
How can you understand this model? Once again, you must separate the model into the various subgroups. Here there are models in this example:
Group 1: Income $<250$
\begin{aligned} \text { Charity } & =\beta_0+\beta_1 \text { Income }+\beta_2(0)+\beta_3 \text { Income } \times(0)+\varepsilon \ & =\beta_0+\beta_1 \text { Income }+\varepsilon \end{aligned}
Group 2: Income $\geq 250$
\begin{aligned} \text { Charity } & =\beta_0+\beta_1 \text { Income }+\beta_2(1)+\beta_3 \text { Income } \times(1)+\varepsilon \ & =\left(\beta_0+\beta_2\right)+\left(\beta_1+\beta_3\right) \text { Income }+\varepsilon \end{aligned}
Thus, $\beta_0$ and $\beta_1$ are the intercept and slope of the model when Income $<250$, while $\left(\beta_0+\beta_2\right)$ and $\left(\beta_1+\beta_2\right)$ are the intercept and slope of the model when Income $\geq 250$.

## 统计代写|回归分析作业代写Regression Analysis代考|Relationship Between Commodity Price and Commodity Stockpile

The following data set contains government-reported annual numbers for price (Price) and stockpiles (Stocks) of a particular agricultural commodity in an Asian country.
URA-DataSets/master/Comm_Price.txt”)
attach(Comm)
Comm = read.table $($ https $: / /$ raw.githubusercontent. com/andrea $2719 /$
URA-DataSets/master/Comm_Price.txt”)
attach (Comm)
Figure 10.13 shows how the Stocks and Price have changed over time. Something happened in 2002 to the Stocks variable; perhaps a re-definition of the measurement in response to a policy change.

This abrupt shift in 2002 causes trouble in estimating the relationship between Price and Stocks, which would ordinarily be considered a negative one because of the laws of supply and demand. Figure 10.14 shows the (Stocks, Price) scatter, with data values before 2002 indicated by circles, as well as global and separate least-squares fits.

$\mathrm{R}$ code for Figure 10.14
pch = ifelse $($ Year $<2002,1,2)$ par (mfrow=c $(1,2))$ plot (Stocks, Price, pch=pch) abline (lsfit (Stocks, Price)) plot (Stocks, Price, pch=pch) abline (lsfit (Stocks [Year $<2002$ ], Price [Year<2002]), 1ty=1) abline (Isfit (Stocks [Year $>=2002$ ], Price [Year $>=2002$ ]), Ity=2)

# 回归分析代写

## 统计代写|回归分析作业代写Regression Analysis代考|Piecewise Linear Regression; Regime Analysis

Ind $=$如果没有$($收入$<250,0,1)$

$$\text { Charity }=\beta_0+\beta_1 \text { Income }+\beta_2 \text { Ind }+\beta_3 \text { Income } \times \text { Ind }+\varepsilon$$

\begin{aligned} \text { Charity } & =\beta_0+\beta_1 \text { Income }+\beta_2(0)+\beta_3 \text { Income } \times(0)+\varepsilon \ & =\beta_0+\beta_1 \text { Income }+\varepsilon \end{aligned}

\begin{aligned} \text { Charity } & =\beta_0+\beta_1 \text { Income }+\beta_2(1)+\beta_3 \text { Income } \times(1)+\varepsilon \ & =\left(\beta_0+\beta_2\right)+\left(\beta_1+\beta_3\right) \text { Income }+\varepsilon \end{aligned}

## 统计代写|回归分析作业代写Regression Analysis代考|Relationship Between Commodity Price and Commodity Stockpile

“URA-DataSets/master/Comm＿Price.txt”)

Comm = read。表$($ HTTPS $: / /$ raw.githubusercontent。com andrea $2719 /$
“URA-DataSets/master/Comm＿Price.txt”)

2002年的这种突然转变给估计价格和股票之间的关系带来了麻烦，由于供求规律，这种关系通常被认为是负相关的。图10.14显示了(股票，价格)散点，2002年之前的数据值用圆圈表示，以及全局和单独的最小二乘拟合。

$\mathrm{R}$ 代码见图10.14
pch= ifelse $($ Year $<2002,1,2)$ par (mfrow=c $(1,2))$ plot (Stocks, Price, pch=pch) abline (lsfit (Stocks, Price)) plot (Stocks, Price, pch=pch) abline (lsfit (Stocks [Year $<2002$]， Price [Year<2002])， 1ty=1) abline (Isfit (Stocks [Year $>=2002$]， Price [Year $>=2002$])， Ity=2)

## 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|回归分析作业代写Regression Analysis代考|ST430

statistics-lab™ 为您的留学生涯保驾护航 在代写回归分析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。我们的专家在代写回归分析Regression Analysis代写方面经验极为丰富，各种代写回归分析Regression Analysis相关的作业也就用不着说。

## 统计代写|回归分析作业代写Regression Analysis代考|Does Location Affect House Price, Controlling for House Size?

Even though the realtors say “location, location, location!”, the observed effects of location on house price might simply be due to the fact that bigger homes tend to be in some locations. After all, square footage is a strong determinant of house price. To compare prices in different locations for homes of the same size, simply add “sqfeet” to the model like this:
attach(house)
fit.main = lm(sell $~$ location + sqfeet, data=house)
summary (fit.main)
house $=$ read.csv $($ https: $/ /$ raw.githubusercontent.com/andrea $2719 /$
attach (house)
fit.main $=1 \mathrm{~m}($ sell $\sim$ location + sqfeet, data=house)
summary (fit.main)
The results are as follows:
Coefficients :
Estimate std. Error $t$ value $\operatorname{Pr}(>|t|)$
$\begin{array}{lllll}\text { (Intercept) } 25.898669 & 5.060777 \quad 5.118 \quad 3.67 \mathrm{e}-06 * * *\end{array}$
locationB $-21.106407 \quad 2.152655-9.8056 .41 \mathrm{e}-14 * \star *$
locationd $-21.431288 \quad 3.579304 \quad-5.988 \quad 1.43 e-07 \star \star * *$
locationd $-24.846429 \quad 2.574269 \quad-9.6521 .13 \mathrm{e}-13 \star \star *$
locatione $-27.304759 \quad 2.538505-10.7561 .94 \mathrm{e}-15 * k *$
sqfeet $\quad 0.0412240 .002578 \quad 15.993<2 e-16 * k$ Signif. Codes: 0 ‘‘ 0.001 ‘‘ 0.01 ‘*’ $0.05 ‘ y^{\prime} 0.1$ ‘ 1
Residual standard error: 6.638 on 58 degrees of freedom
Multiple R-squared: 0.874, Adjusted R-squared: 0.8631
F-statistic: 80.47 on 5 and 58 DF, p-value: $<2.2 e-16$

## 统计代写|回归分析作业代写Regression Analysis代考|Full Model versus Restricted Model $F$ Tests

As we have mentioned repeatedly, tests of hypotheses are not the best way to evaluate models and assumptions. However, the $F$ test that was introduced in Chapter 8 is so common in the history of ANOVA, ANCOVA, and regression that we would be remiss not to mention it.

Models such as those shown in Figures 10.7 and 10.6 are often compared by using the $F$ test, which is a test to compare “full” versus “restricted” classical regression models. (For models other than the classical regression model, full/restricted model comparison is more commonly done using the likelihood ratio test, which is used starting in Chapter 12 of this book.)
In the usual regression analysis, a full model typically has the form:
$$Y=\beta_0+\beta_1 X_1+\beta_2 X_2+\ldots+\beta_k X_k+\varepsilon$$
Here, the parameters $\beta_0, \beta_1, \beta_2, \ldots$, and $\beta_k$ are unconstrained; that is, each parameter can possibly take any value whatsoever between $-\infty$ and $\infty$, and the value that one $\beta$ parameter takes is not dependent on (or constrained by) the value that any other $\beta$ parameter takes.
A restricted model is the same model, but with constraints on the parameters. The most common restrictions are constraints such as $\beta_1=\beta_2=0$, although other constraints such as $\beta_2=1$, or $\beta_1-\beta_2=0$, or $\beta_0+15 \beta_2=100$ are also possible.

The separate slope model graphed in Figure 10.7 is a full model relative to the restricted model that constrains all the interaction $\beta^{\prime}$ s to be zero, shown in Figure 10.6. The $F$ test can be used to compare these models. To construct the $F$ test, let $\mathrm{SSE}{\mathrm{F}}$ denote the error sum of squares in the full model, and let $\mathrm{SSE}{\mathrm{R}}$ denote the error sum of squares in the restricted model. It is a mathematical fact that
$$\mathrm{SSE}{\mathrm{F}} \leq \mathrm{SSE}{\mathrm{R}}$$

# 回归分析代写

## 统计代写|回归分析作业代写Regression Analysis代考|Does Location Affect House Price, Controlling for House Size?

House $=$ read.csv $($ https: $/ /$ raw.githubusercontent.com/andrea $2719 /$

$\begin{array}{lllll}\text { (Intercept) } 25.898669 & 5.060777 \quad 5.118 \quad 3.67 \mathrm{e}-06 * * *\end{array}$
locationB $-21.106407 \quad 2.152655-9.8056 .41 \mathrm{e}-14 * \star *$

sqfeet $\quad 0.0412240 .002578 \quad 15.993<2 e-16 * k$标志。代码:0“0.001”0.01“*”$0.05 ‘ y^{\prime} 0.1$

f统计量在5和58 DF上为80.47,p值: $<2.2 e-16$

## 统计代写|回归分析作业代写Regression Analysis代考|Full Model versus Restricted Model $F$ Tests

$$Y=\beta_0+\beta_1 X_1+\beta_2 X_2+\ldots+\beta_k X_k+\varepsilon$$

$$\mathrm{SSE}{\mathrm{F}} \leq \mathrm{SSE}{\mathrm{R}}$$

## 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。