## 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。

## 统计代写|线性回归分析代写linear regression analysis代考|EM6613

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。

## 统计代写|线性回归分析代写linear regression analysis代考|Data and Matrix Notation

In this and the next few sections we use matrix notation as a compact way to describe data and perform manipulations of data. Appendix A.6 contains a brief introduction to matrices and linear algebra that some readers may find helpful.

Suppose we have observed data for $n$ cases or units, meaning we have a value of $Y$ and all of the regressors for each of the $n$ cases. We define
$$\mathbf{Y}=\left(\begin{array}{c} y_1 \ y_2 \ \vdots \ y_n \end{array}\right) \quad \mathbf{X}=\left(\begin{array}{cccc} 1 & x_{11} & \cdots & x_{1 p} \ 1 & x_{21} & \cdots & x_{2 p} \ \vdots & \vdots & \vdots & \vdots \ 1 & x_{n 1} & \cdots & x_{n p} \end{array}\right)$$
so $\mathbf{Y}$ is an $n \times 1$ vector and $\mathbf{X}$ is an $n \times(p+1)$ matrix. The $i$ th row of $\mathbf{X}$ will be defined by the symbol $\mathbf{x}_i^{\prime}$, which is a $(p+1) \times 1$ vector for mean functions that include an intercept. Even though $\mathbf{x}_i$ is a row of $\mathbf{X}$, we use the convention that all vectors are column vectors and therefore need to include the transpose on $\mathbf{x}_i^{\prime}$ to represent a row. The first few and the last few rows of the matrix $\mathbf{X}$ and the vector $\mathbf{Y}$ for the fuel data are
$$\mathbf{X}=\left(\begin{array}{ccccc} 1 & 18.00 & 1031.38 & 23.471 & 16.5271 \ 1 & 8.00 & 1031.64 & 30.064 & 13.7343 \ 1 & 18.00 & 908.597 & 25.578 & 15.7536 \ \vdots & \vdots & \vdots & \vdots & \vdots \ 1 & 25.65 & 904.894 & 21.915 & 15.1751 \ 1 & 27.30 & 882.329 & 28.232 & 16.7817 \ 1 & 14.00 & 970.753 & 27.230 & 14.7362 \end{array}\right) \quad \mathbf{Y}=\left(\begin{array}{c} 690.264 \ 514.279 \ 621.475 \ \vdots \ 562.411 \ 581.794 \ 842.792 \end{array}\right)$$

## 统计代写|线性回归分析代写linear regression analysis代考|The Errors e

Define the unobservable random vector of errors e elementwise by $e_i=y_i-\mathrm{E}\left(Y \mid X=\mathbf{x}_i\right)=y_i-\mathbf{x}_i^{\prime} \boldsymbol{\beta}$, and $\mathbf{e}=\left(e_1, \ldots, e_n\right)^{\prime}$. The assumptions concerning the $e_i$ s given in Chapter 2 are summarized in matrix form as
$$\mathrm{E}(\mathbf{e} \mid X)=\mathbf{0} \quad \operatorname{Var}(\mathbf{e} \mid X)=\sigma^2 \mathbf{I}_n$$
where $\operatorname{Var}(\mathbf{e} \mid X)$ means the covariance matrix of $\mathbf{e}$ for a fixed value of $X, \mathbf{I}_n$ is the $n \times n$ matrix with ones on the diagonal and zeroes everywhere else, and $\mathbf{0}$ is a matrix or vector of zeroes of appropriate size. If we add the assumption of normality, we can write
$$(\mathbf{e} \mid X) \sim \mathrm{N}\left(\mathbf{0}, \sigma^2 \mathbf{I}_n\right)$$

# 线性回归代写

## 统计代写|线性回归分析代写linear regression analysis代考|Data and Matrix Notation

$$\mathbf{Y}=\left(\begin{array}{c} y_1 \ y_2 \ \vdots \ y_n \end{array}\right) \quad \mathbf{X}=\left(\begin{array}{cccc} 1 & x_{11} & \cdots & x_{1 p} \ 1 & x_{21} & \cdots & x_{2 p} \ \vdots & \vdots & \vdots & \vdots \ 1 & x_{n 1} & \cdots & x_{n p} \end{array}\right)$$

$$\mathbf{X}=\left(\begin{array}{ccccc} 1 & 18.00 & 1031.38 & 23.471 & 16.5271 \ 1 & 8.00 & 1031.64 & 30.064 & 13.7343 \ 1 & 18.00 & 908.597 & 25.578 & 15.7536 \ \vdots & \vdots & \vdots & \vdots & \vdots \ 1 & 25.65 & 904.894 & 21.915 & 15.1751 \ 1 & 27.30 & 882.329 & 28.232 & 16.7817 \ 1 & 14.00 & 970.753 & 27.230 & 14.7362 \end{array}\right) \quad \mathbf{Y}=\left(\begin{array}{c} 690.264 \ 514.279 \ 621.475 \ \vdots \ 562.411 \ 581.794 \ 842.792 \end{array}\right)$$

## 统计代写|线性回归分析代写linear regression analysis代考|The Errors e

$$\mathrm{E}(\mathbf{e} \mid X)=\mathbf{0} \quad \operatorname{Var}(\mathbf{e} \mid X)=\sigma^2 \mathbf{I}_n$$

$$(\mathbf{e} \mid X) \sim \mathrm{N}\left(\mathbf{0}, \sigma^2 \mathbf{I}_n\right)$$

## 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|STAT108

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。

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

Estimates of $\operatorname{Var}\left(\hat{\beta}_0 \mid X\right)$ and $\operatorname{Var}\left(\hat{\beta}_1 \mid X\right)$ are obtained by substituting $\hat{\sigma}^2$ for $\sigma^2$ in (2.11). We use the symbol $\widehat{\operatorname{Var}}(\mathrm{)}$ for an estimated variance. Thus
\begin{aligned} & \widehat{\operatorname{Var}}\left(\hat{\beta}_1 \mid X\right)=\hat{\sigma}^2 \frac{1}{\mathrm{SXX}} \ & \widehat{\operatorname{Var}}\left(\hat{\beta}_0 \mid X\right)=\hat{\sigma}^2\left(\frac{1}{n}+\frac{\bar{x}^2}{\mathrm{SXX}}\right) \end{aligned}
The square root of an estimated variance is called a standard error, for which we use the symbol se( ). The use of this notation is illustrated by
$$\operatorname{se}\left(\hat{\beta}_1 \mid X\right)=\sqrt{\widehat{\operatorname{Var}}\left(\hat{\beta}_1 \mid X\right)}$$
The terms standard error and standard deviation are sometimes used interchangeably. In this book, an estimated standard deviation always refers to the variability between values of an observable random variable like the response $y_i$ or an unobservable random variance like the errors $e_i$. The term standard error will always refer to the square root of the estimated variance of a statistic like a mean $\bar{y}$, or a regression coefficient $\hat{\beta}_1$.

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

The intercept is used to illustrate the general form of confidence intervals for normally distributed estimates. The standard error of the intercept is $\operatorname{se}\left(\beta_0 \mid X\right)=\hat{\sigma}\left(1 / n+\bar{x}^2 / \mathrm{SXX}\right)^{1 / 2}$. Hence, a $(1-\alpha) \times 100 \%$ confidence interval for the intercept is the set of points $\beta_0$ in the interval
$$\hat{\beta}_0-t(\alpha / 2, n-2) \operatorname{se}\left(\hat{\beta}_0 \mid X\right) \leq \beta_0 \leq \hat{\beta}_0+t(\alpha / 2, n-2) \operatorname{se}\left(\hat{\beta}_0 \mid X\right)$$
For Forbes’s data, $\operatorname{se}\left(\hat{\beta}_0 \mid X\right)=0.379\left(1 / 17+(202.953)^2 / 530.724\right)^{1 / 2}=3.340$. For a $90 \%$ confidence interval, $t(0.05,15)=1.753$, and the interval is
\begin{aligned} -42.138-1.753(3.340) & \leq \beta_0 \leq-42.138+1.753(3.340) \ -47.99 & \leq \beta_0 \leq-36.28 \end{aligned}
Ninety percent of such intervals will include the true value.
A hypothesis test of
$\mathrm{NH}: \quad \beta_0=\beta_0^, \quad \beta_1$ arbitrary $\mathrm{AH}: \quad \beta_0 \neq \beta_0^, \quad \beta_1$ arbitrary is obtained by computing the $t$-statistic
$$t=\frac{\hat{\beta}_0-\beta_0^*}{\operatorname{se}\left(\hat{\beta}_0 \mid X\right)}$$
and referring this ratio to the $t$-distribution with $d f=n-2$, the number of $d f$ in the estimate of $\sigma^2$. For example, in Forbes’s data, consider testing the $\mathrm{NH}$ $\beta_0=-35$ against the alternative that $\beta_0 \neq-35$. The statistic is
$$t=\frac{-42.138-(-35)}{3.34}=-2.137$$
Since AH is two-sided, the $p$-value corresponds to the probability that a $t(15)$ variable is less than -2.137 or greater than +2.137 , which gives a $p$-value that rounds to 0.05 , providing some evidence against $\mathrm{NH}$. This hypothesis test for these data is not one that would occur to most investigators and is used only as an illustration.

# 线性回归代写

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

\begin{aligned} & \widehat{\operatorname{Var}}\left(\hat{\beta}_1 \mid X\right)=\hat{\sigma}^2 \frac{1}{\mathrm{SXX}} \ & \widehat{\operatorname{Var}}\left(\hat{\beta}_0 \mid X\right)=\hat{\sigma}^2\left(\frac{1}{n}+\frac{\bar{x}^2}{\mathrm{SXX}}\right) \end{aligned}

$$\operatorname{se}\left(\hat{\beta}_1 \mid X\right)=\sqrt{\widehat{\operatorname{Var}}\left(\hat{\beta}_1 \mid X\right)}$$

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

$$\hat{\beta}_0-t(\alpha / 2, n-2) \operatorname{se}\left(\hat{\beta}_0 \mid X\right) \leq \beta_0 \leq \hat{\beta}_0+t(\alpha / 2, n-2) \operatorname{se}\left(\hat{\beta}_0 \mid X\right)$$

\begin{aligned} -42.138-1.753(3.340) & \leq \beta_0 \leq-42.138+1.753(3.340) \ -47.99 & \leq \beta_0 \leq-36.28 \end{aligned}
90％的这样的间隔将包含真实值。

$\mathrm{NH}: \quad \beta_0=\beta_0^, \quad \beta_1$任意$\mathrm{AH}: \quad \beta_0 \neq \beta_0^, \quad \beta_1$任意通过计算$t$ -统计量得到
$$t=\frac{\hat{\beta}_0-\beta_0^*}{\operatorname{se}\left(\hat{\beta}_0 \mid X\right)}$$

Y=\mathrm{X} \beta+\varepsilon
$$This concise form covers all the n observations and all the X variables ( k of them) in one simple equation. Note that there are boldface non-italic terms and boldface italic terms in the expression. To make the material easier to read, we use the convention that boldface means a matrix, while boldface italic refers to a vector, which is a matrix with a single column. Thus \boldsymbol{Y}, \boldsymbol{\beta}, and \varepsilon, are vectors (single-column matrices), while \mathbf{X} is a matrix having multiple columns. ## 统计代写|回归分析作业代写Regression Analysis代考|The Least Squares Estimates in Matrix Form One use of matrix algebra is to display the model for all n observations and all X variables succinctly as shown above. Another use is to identify the OLS estimates of the \beta ‘s. There is simply no way to display the OLS estimates other than by using matrix algebra, as follows:$$
\hat{\boldsymbol{\beta}}=\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}} Y
$$(The ” \mathrm{T} ” symbol denotes transpose of the matrix.) To see why the OLS estimates have this matrix representation, recall that in the simple, classical regression model, the maximum likelihood (ML) estimates must minimize the sum of squared “errors” called SSE. The same is true in multiple regression: The ML estimates must minimize the function$$
\operatorname{SSE}\left(\beta_0, \beta_1, \ldots, \beta_k\right)=\sum_{i=1}^n\left{y_i-\left(\beta_0+\beta_1 x_{i 1}+\cdots+\beta_k x_{i k}\right)\right}^2
$$In the case of two X variables (k=2), you are to choose \hat{\beta}0, \hat{\beta}_1, and \hat{\beta}_2 that define the plane, f\left(x_1, x_2\right)=\hat{\beta}_0+\hat{\beta}_1 x_1+\hat{\beta}_2 x_2, such as the one shown in Figure 6.3 , that minimizes the sum of squared vertical deviations from the 3-dimensional point cloud \left(x{i 1}, x_{i 2}, y_i\right), i=1,2, \ldots, n. Figure 7.1 illustrates the concept. # 回归分析代写 ## 统计代写|回归分析作业代写Regression Analysis代考|Multiple Regression from the Matrix Point of View 在简单回归的情况下，您看到斜率的OLS估计有一个简单的形式:它是(X, Y)分布的估计协方差除以X分布或\hat{\beta}1=\hat{\sigma}{x y} / \hat{\sigma}_x^2的估计方差。在多元回归中没有这样简单的公式。相反，你必须使用矩阵代数，包括矩阵乘法和矩阵逆。如果您不熟悉基本的矩阵代数，包括乘法、加法、减法、转置、单位矩阵和矩阵逆，那么在继续阅读之前，您应该花一些时间熟悉这些特定的概念。(也许你可以找到一个“矩阵代数初学者”类型的网页。) 搞定了?好吧，继续读下去。 我们在回归中首先使用矩阵代数是为了给出回归模型的简明表示。多元回归模型涉及n观测值和k变量，这两个变量都可以是数千甚至数百万。该模型的以下矩阵形式提供了一种非常方便的速记方式来表示所有这些信息。$$
Y=\mathrm{X} \beta+\varepsilon
$$这个简洁的形式在一个简单的方程中涵盖了所有的n观测值和所有的X变量(其中的k变量)。请注意，表达式中有黑体非斜体项和黑体斜体项。为了使材料更容易阅读，我们使用约定，黑体表示矩阵，而黑体斜体表示向量，这是一个具有单列的矩阵。因此\boldsymbol{Y}, \boldsymbol{\beta}和\varepsilon是向量(单列矩阵)，而\mathbf{X}是具有多列的矩阵。 ## 统计代写|回归分析作业代写Regression Analysis代考|The Least Squares Estimates in Matrix Form 矩阵代数的一种用法是简洁地显示所有n观测值和所有X变量的模型，如上所示。另一个用途是识别\beta的OLS估计。除了使用矩阵代数之外，根本没有办法显示OLS估计，如下所示:$$
\hat{\boldsymbol{\beta}}=\left(\mathbf{X}^{\mathrm{T}} \mathbf{X}\right)^{-1} \mathbf{X}^{\mathrm{T}} Y
$$(“\mathrm{T}”符号表示矩阵的转置。)要了解为什么OLS估计具有这种矩阵表示，请回忆一下，在简单的经典回归模型中，最大似然(ML)估计必须最小化称为SSE的平方“误差”的总和。在多元回归中也是如此:机器学习估计必须最小化函数$$
\operatorname{SSE}\left(\beta_0, \beta_1, \ldots, \beta_k\right)=\sum_{i=1}^n\left{y_i-\left(\beta_0+\beta_1 x_{i 1}+\cdots+\beta_k x_{i k}\right)\right}^2
$$在有两个X变量(k=2)的情况下，您将选择\hat{\beta}0, \hat{\beta}1和\hat{\beta}_2来定义平面f\left(x_1, x_2\right)=\hat{\beta}_0+\hat{\beta}_1 x_1+\hat{\beta}_2 x_2，如图6.3所示，它最小化与三维点云\left(x{i 1}, x{i 2}, y_i\right), i=1,2, \ldots, n垂直偏差的平方和。图7.1说明了这个概念。 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 ## 统计代写|线性回归分析代写linear regression analysis代考|SAMPLING FROM A NORMAL POPULATION 如果你也在 怎样代写线性回归Linear Regression 这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。线性回归Linear Regression在统计学中，是对标量响应和一个或多个解释变量（也称为因变量和自变量）之间的关系进行建模的一种线性方法。一个解释变量的情况被称为简单线性回归；对于一个以上的解释变量，这一过程被称为多元线性回归。这一术语不同于多元线性回归，在多元线性回归中，预测的是多个相关的因变量，而不是一个标量变量。 线性回归Linear Regression在线性回归中，关系是用线性预测函数建模的，其未知的模型参数是根据数据估计的。最常见的是，假设给定解释变量（或预测因子）值的响应的条件平均值是这些值的仿生函数；不太常见的是，使用条件中位数或其他一些量化指标。像所有形式的回归分析一样，线性回归关注的是给定预测因子值的反应的条件概率分布，而不是所有这些变量的联合概率分布，这是多元分析的领域。 statistics-lab™ 为您的留学生涯保驾护航 在代写线性回归分析linear regression analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写线性回归分析linear regression analysis代写方面经验极为丰富，各种代写线性回归分析linear regression analysis相关的作业也就用不着说。 ## 统计代写|线性回归分析代写linear regression analysis代考|SAMPLING FROM A NORMAL POPULATION Much of the intuition for the use of least squares estimation is based on the assumption that the observed data are a sample from a multivariate normal population. While the assumption of multivariate normality is almost never tenable in practical regression problems, it is worthwhile to explore the relevant results for normal data, first assuming random sampling and then removing that assumption. Suppose that all of the observed variables are normal random variables, and the observations on each case are independent of the observations on each other case. In a two-variable problem, for the i th case observe \left(x_i, y_i\right), and suppose that$$
\left(\begin{array}{c}
x_i \
y_i
\end{array}\right) \sim \mathrm{N}\left(\left(\begin{array}{c}
\mu_x \
\mu_y
\end{array}\right),\left(\begin{array}{cc}
\sigma_x^2 & \rho_{x y} \sigma_x \sigma_y \
\rho_{x y} \sigma_x \sigma_y & \sigma_y^2
\end{array}\right)\right)
$$Equation (4.9) says that x_i and y_i are each realizations of normal random variables with means \mu_x and \mu_y, variances \sigma_x^2 and \sigma_y^2 and correlation \rho_{x y}. Now, suppose we consider the conditional distribution of y_i given that we have already observed the value of x_i. It can be shown (see e.g., Lindgren, 1993; Casella and Berger, 1990 ) that the conditional distribution of y_i given x_i, is normal and,$$
y_i \mid x_i \sim \mathrm{N}\left(\mu_y+\rho_{x y} \frac{\sigma_y}{\sigma_x}\left(x_i-\mu_x\right), \sigma_y^2\left(1-\rho_{x y}^2\right)\right)
$$If we define$$
$$then the conditional distribution of y_i given x_i is simply$$
y_i \mid x_i \sim \mathrm{N}\left(\beta_0+\beta_1 x_i, \sigma^2\right)
$$which is essentially the same as the simple regression model with the added assumption of normality. ## 统计代写|线性回归分析代写linear regression analysis代考|Simple Linear Regression and R2 In simple regression linear problems, we can always determine the appropriateness of R^2 as a summary by examining the summary graph of the response versus the predictor. If the plot looks like a sample from a bivariate normal population, as in Figure 4.2 \mathrm{a}, then R^2 is a useful measure. The less the graph looks like this figure, the less useful is R^2 as a summary measure. Figure 4.3 shows six summary graphs. Only for the first three of them is R^2 a useful summary of the regression problem. In Figure 4.3e, the mean function appears curved rather than straight so correlation is a poor measure of dependence. In Figure 4.3 \mathrm{~d} the value of R^2 is virtually determined by one point, making R^2 necessarily unreliable. The regular appearance of the remaining plot suggests a different type of problem. We may have several identifiable groups of points caused by a lurking variable not included in the mean function, such that the mean function for each group has a negative slope, but when groups are combined the slope becomes positive. Once again R^2 is not a useful summary of this graph. In multiple linear regression, R^2 can also be interpreted as the square of the correlation in a summary graph, this time of Y versus fitted values \hat{Y}. This plot can be interpreted exactly the same way as the plot of the response versus the single term in simple linear regression to decide on the usefulness of R^2 as a summary measure. For other regression methods such as nonlinear regression, we can define R^2 to be the square of the correlation between the response and the fitted values, and use this summary graph to decide if R^2 is a useful summary. # 线性回归代写 ## 统计代写|线性回归分析代写linear regression analysis代考|SAMPLING FROM A NORMAL POPULATION Much of the intuition for the use of least squares estimation is based on the assumption that the observed data are a sample from a multivariate normal population. While the assumption of multivariate normality is almost never tenable in practical regression problems, it is worthwhile to explore the relevant results for normal data, first assuming random sampling and then removing that assumption. Suppose that all of the observed variables are normal random variables, and the observations on each case are independent of the observations on each other case. In a two-variable problem, for the i th case observe \left(x_i, y_i\right), and suppose that$$
\left(\begin{array}{c}
x_i \
y_i
\end{array}\right) \sim \mathrm{N}\left(\left(\begin{array}{c}
\mu_x \
\mu_y
\end{array}\right),\left(\begin{array}{cc}
\sigma_x^2 & \rho_{x y} \sigma_x \sigma_y \
\rho_{x y} \sigma_x \sigma_y & \sigma_y^2
\end{array}\right)\right)
$$Equation (4.9) says that x_i and y_i are each realizations of normal random variables with means \mu_x and \mu_y, variances \sigma_x^2 and \sigma_y^2 and correlation \rho_{x y}. Now, suppose we consider the conditional distribution of y_i given that we have already observed the value of x_i. It can be shown (see e.g., Lindgren, 1993; Casella and Berger, 1990 ) that the conditional distribution of y_i given x_i, is normal and,$$
y_i \mid x_i \sim \mathrm{N}\left(\mu_y+\rho_{x y} \frac{\sigma_y}{\sigma_x}\left(x_i-\mu_x\right), \sigma_y^2\left(1-\rho_{x y}^2\right)\right)
$$If we define$$
$$then the conditional distribution of y_i given x_i is simply$$
y_i \mid x_i \sim \mathrm{N}\left(\beta_0+\beta_1 x_i, \sigma^2\right)

which is essentially the same as the simple regression model with the added assumption of normality.

## 统计代写|线性回归分析代写linear regression analysis代考|Simple Linear Regression and R2

In simple regression linear problems, we can always determine the appropriateness of $R^2$ as a summary by examining the summary graph of the response versus the predictor. If the plot looks like a sample from a bivariate normal population, as in Figure $4.2 \mathrm{a}$, then $R^2$ is a useful measure. The less the graph looks like this figure, the less useful is $R^2$ as a summary measure.

Figure 4.3 shows six summary graphs. Only for the first three of them is $R^2$ a useful summary of the regression problem. In Figure 4.3e, the mean function appears curved rather than straight so correlation is a poor measure of dependence. In Figure $4.3 \mathrm{~d}$ the value of $R^2$ is virtually determined by one point, making $R^2$ necessarily unreliable. The regular appearance of the remaining plot suggests a different type of problem. We may have several identifiable groups of points caused by a lurking variable not included in the mean function, such that the mean function for each group has a negative slope, but when groups are combined the slope becomes positive. Once again $R^2$ is not a useful summary of this graph.

In multiple linear regression, $R^2$ can also be interpreted as the square of the correlation in a summary graph, this time of $Y$ versus fitted values $\hat{Y}$. This plot can be interpreted exactly the same way as the plot of the response versus the single term in simple linear regression to decide on the usefulness of $R^2$ as a summary measure.

For other regression methods such as nonlinear regression, we can define $R^2$ to be the square of the correlation between the response and the fitted values, and use this summary graph to decide if $R^2$ is a useful summary.

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## MATLAB代写

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