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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写线性回归linear regression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linear regression代写方面经验极为丰富，各种代写线性回归linear regression相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|线性回归代写linear regression代考|The Partial F Test

Suppose that there is data on variables $Z, w_1, \ldots, w_r$ and that a useful MLR model has been made using $Y=t(Z), x_1 \equiv 1, x_2, \ldots, x_p$ where each $x_i$ is some function of $w_1, \ldots, w_r$. This useful model will be called the full model. It is important to realize that the full model does not need to use every variable $w_j$ that was collected. For example, variables with outliers or missing values may not be used. Forming a useful full model is often very difficult, and it is often not reasonable to assume that the candidate full model is good based on a single data set, especially if the model is to be used for prediction.
Even if the full model is useful, the investigator will often be interested in checking whether a model that uses fewer predictors will work just as well. For example, perhaps $x_p$ is a very expensive predictor but is not needed given that $x_1, \ldots, x_{p-1}$ are in the model. Also a model with fewer predictors tends to be easier to understand.

Definition 2.21. Let the full model use $Y, x_1 \equiv 1, x_2, \ldots, x_p$ and let the reduced model use $Y, x_1, x_{i_2}, \ldots, x_{i_q}$ where $\left{i_2, \ldots, i_q\right} \subset{2, \ldots, p}$.
The partial $F$ test is used to test whether the reduced model is good in that it can be used instead of the full model. It is crucial that the reduced model be selected before looking at the data. If the reduced model is selected after looking at output and discarding the worst variables, then the $\mathrm{p}$-value for the partial $F$ test will be too high. For (ordinary) least squares, usually a constant is used, and we are assuming that both the full model and the reduced model contain a constant. The partial $F$ test has null hypothesis $H o: \beta_{i_{q+1}}=\cdots=\beta_{i_p}=0$, and alternative hypothesis $H_A:$ at least one of the $\beta_{i_j} \neq 0$ for $j>q$. The null hypothesis is equivalent to Ho: “the reduced model is good.” Since only the full model and reduced model are being compared, the alternative hypothesis is equivalent to $H_A$ : “the reduced model is not as good as the full model, so use the full model,” or more simply, $H_A$ : “use the full model.”

## 统计代写|线性回归代写linear regression代考|The Wald t Test

Often investigators hope to examine $\beta_k$ in order to determine the importance of the predictor $x_k$ in the model; however, $\beta_k$ is the coefficient for $x_k$ given that the other predictors are in the model. Hence $\beta_k$ depends strongly on the other predictors in the model. Suppose that the model has an intercept:

$x_1 \equiv 1$. The predictor $x_k$ is highly correlated with the other predictors if the OLS regression of $x_k$ on $x_1, \ldots, x_{k-1}, x_{k+1}, \ldots, x_p$ has a high coefficient of determination $R_k^2$. If this is the case, then often $x_k$ is not needed in the model given that the other predictors are in the model. If at least one $R_k^2$ is high for $k \geq 2$, then there is multicollinearity among the predictors.

As an example, suppose that $Y=$ height, $x_1 \equiv 1, x_2=$ left leg length, and $x_3=$ right leg length. Then $x_2$ should not be needed given $x_3$ is in the model and $\beta_2=0$ is reasonable. Similarly $\beta_3=0$ is reasonable. On the other hand, if the model only contains $x_1$ and $x_2$, then $x_2$ is extremely important with $\beta_2$ near 2. If the model contains $x_1, x_2, x_3, x_4=$ height at shoulder, $x_5=$ right arm length, $x_6=$ head length, and $x_7=$ length of back, then $R_i^2$ may be high for each $i \geq 2$. Hence $x_i$ is not needed in the MLR model for $Y$ given that the other predictors are in the model.

Definition 2.23. The $100(1-\delta) \%$ CI for $\beta_k$ is $\hat{\beta}k \pm t{n-p, 1-\delta / 2} \operatorname{se}\left(\hat{\beta}k\right)$. If the degrees of freedom $d=n-p \geq 30$, the $\mathrm{N}(0,1)$ cutoff $z{1-\delta / 2}$ may be used.
Know how to do the 4 step Wald $t$-test of hypotheses.
i) State the hypotheses Ho: $\beta_k=0$ Ha: $\beta_k \neq 0$.
ii) Find the test statistic $t_{o, k}=\hat{\beta}k / \operatorname{se}\left(\hat{\beta}_k\right)$ or obtain it from output. iii) Find pval from output or use the $t$-table: pval $=$ $$2 P\left(t{n-p}<-\left|t_{o, k}\right|\right)=2 P\left(t_{n-p}>\left|t_{o, k}\right|\right)$$

# 线性回归代写

## 统计代写|线性回归代写linear regression代考|The Wald t Test

$x_1 \equiv 1$. 预测器 $x_k$ 如果 OLS 回归与其他预测变量高度相关 $x_k$ 上 $x_1, \ldots, x_{k-1}, x_{k+1}, \ldots, x_p$ 决定系数高 $R_k^2$. 如果是这种情况，那么通常 $x_k$ 鉴于其他预 测变量在模型中，因此模型中不需要。如果至少有一个 $R_k^2$ 是高的 $k \geq 2$ ，则预测变量之间存在多重共线性。

i) 陈述假设 $\mathrm{Ho}: \beta_k=0$ 他有: $\beta_k \neq 0$.
(ii) 找到检验统计量 $t_{o, k}=\hat{\beta} k / \mathrm{se}\left(\hat{\beta}k\right)$ 或从输出中获取。iii) 从输出中查找 pval 或使用 $t$-表: pval= $$2 P\left(t n-p<-\left|t{o, k}\right|\right)=2 P\left(t_{n-p}>\left|t_{o, k}\right|\right)$$

## 有限元方法代写

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## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师