如果你也在 怎样代写回归分析Regression Analysis 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。回归分析Regression Analysis回归中的概率观点具体体现在给定X数据的特定固定值的Y数据的可变性模型中。这种可变性是用条件分布建模的;因此，副标题是:“条件分布方法”。回归的整个主题都是用条件分布来表达的;这种观点统一了不同的方法，如经典回归、方差分析、泊松回归、逻辑回归、异方差回归、分位数回归、名义Y数据模型、因果模型、神经网络回归和树回归。所有这些都可以方便地用给定特定X值的Y条件分布模型来看待。

回归分析Regression Analysis条件分布是回归数据的正确模型。它们告诉你，对于变量X的给定值，可能存在可观察到的变量Y的分布。如果你碰巧知道这个分布，那么你就知道了你可能知道的关于响应变量Y的所有信息，因为它与预测变量X的给定值有关。与基于R^2统计量的典型回归方法不同，该模型解释了100%的潜在可观察到的Y数据，后者只解释了Y数据的一小部分，而且在假设几乎总是被违反的情况下也是不正确的。

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统计代写|回归分析作业代写Regression Analysis代考|The Regression Model in Matrix Form

The model representation $Y=\mathbf{X} \beta+\varepsilon$ is not complete because it states nothing about the assumptions. The following expression is a complete representation of the classical model; notice how simple the model looks when expressed in matrix form.
The classical model in matrix form
$$
\boldsymbol{Y} \mid \mathbf{X}=\mathbf{x} \sim \mathrm{N}_n\left(\mathbf{x} \boldsymbol{\beta}, \sigma^2 \mathbf{I}\right)
$$
Here, the $\mathbf{X}=\mathbf{x}$ condition refers to a specific realized matrix $\mathbf{x}$ of the random matrix $\mathbf{X}$ and is a simple generalization of the $X=x$ condition we have used repeatedly to its matrix form. The matrix $\mathbf{X}$ contains potentially observable (random) $X$ values, as well as fixed values for any non-random $X$ data. The first column of $\mathbf{X}$ is ordinarily the column of 1 ‘s needed to capture the intercept term $\beta_0$, and this column is not random.
In Appendix A of Chapter 1, we introduced the bivariate normal distribution, which is a distribution of two variables. Here, the symbol ” $\mathrm{N}_n\left(\mathbf{x} \boldsymbol{\beta}, \sigma^2 \mathbf{I}\right)$ ” refers to a multivariate normal distribution. The ” $n$ ” subscript identifies that it is a distribution of the $n$ variables $Y_1, Y_2, \ldots$, $Y_n$. The $\mathbf{x} \boldsymbol{\beta}$ term refers to the mean vector of the distribution, and the term $\sigma^2 \mathbf{I}$ refers to its covariance matrix (explained in detail below).
All assumptions in the classical regression model are embodied in the concise matrix form of the model: The correct functional specification assumption is embodied in the mean vector $(\mathbf{x} \boldsymbol{\beta})$ specification, the constant variance and independence assumptions are implied by specification of $\sigma^2 \mathbf{I}$ as covariance matrix, as will be described below, and the normality assumption is embodied in the multivariate normal specification.
A covariance matrix is a matrix that contains all the variances and covariances among a set of random variables. For example, if $\left(W_1, W_2, W_3\right)$ are jointly distributed random variables, then the covariance matrix of $\boldsymbol{W}=\left(W_1, W_2, W_3\right)$ is given by
$$
\operatorname{Cov}(W)=\left[\begin{array}{ccc}
\operatorname{Var}\left(W_1\right) & \operatorname{Cov}\left(W_1, W_2\right) & \operatorname{Cov}\left(W_1, W_3\right) \
\operatorname{Cov}\left(W_2, W_1\right) & \operatorname{Var}\left(W_2\right) & \operatorname{Cov}\left(W_2, W_3\right) \
\operatorname{Cov}\left(W_3, W_1\right) & \operatorname{Cov}\left(W_3, W_2\right) & \operatorname{Var}\left(W_3\right)
\end{array}\right]
$$
Notice that the row/column combination tells you which pair of variables are involved, or which variable is involved in the case of the diagonal elements. Note also that the covariance of a variable with itself is just the variance of that variable, which explains why the variances are on the diagonal of the covariance matrix.

统计代写|回归分析作业代写Regression Analysis代考|Unbiasedness of the OLS Estimator $\hat{\beta}$ Under the Gauss-Markov Model

Strangely, it is easier to prove the unbiasedness of the estimators $\hat{\beta}$ using their matrix form. We will assume the Gauss-Markov model, thus the mathematical theorem is stated as follows: If the data are produced by the Gauss-Markov model, then the OLS $\hat{\boldsymbol{\beta}}$ is an unbiased estimator of $\boldsymbol{\beta}$. Since the Gauss-Markov model includes the (normality-assuming) classical model as a special case, the proof of unbiasedness of the estimators $\hat{\beta}$ in the Gauss-Markov model implies, a fortiori, unbiasedness of the estimators $\hat{\beta}$ in the classical model as well.
There are two parts to the unbiasedness argument. The first is that the estimates are unbiased, conditional on the observed values of the random $X$ variables. The second is to note that, by the law of total expectation, the estimates are also unbiased when considered over all possible samples of random $X$ data.

The $\mathbf{X}$ matrix has random and fixed elements; the first column of the ones, for example, contains fixed (non-random) elements. Also, if there are $X$ variables that are fixed in advance of observing the $Y$ data, as occurs for example in designed experiments and in some kinds of stratified sampling, then these $X$ variables are also fixed, not random.

回归分析代写

统计代写|回归分析作业代写Regression Analysis代考|The Regression Model in Matrix Form

模型表示$Y=\mathbf{X} \beta+\varepsilon$是不完整的，因为它没有说明任何假设。下面的表达式是经典模型的完整表示;注意，当用矩阵形式表示模型时，它看起来是多么简单。
经典的矩阵模型
$$
\boldsymbol{Y} \mid \mathbf{X}=\mathbf{x} \sim \mathrm{N}_n\left(\mathbf{x} \boldsymbol{\beta}, \sigma^2 \mathbf{I}\right)
$$
这里，$\mathbf{X}=\mathbf{x}$条件是指随机矩阵$\mathbf{X}$的一个特定的已实现矩阵$\mathbf{x}$，是我们多次使用的$X=x$条件对其矩阵形式的简单推广。矩阵$\mathbf{X}$包含潜在的可观察(随机)$X$值，以及任何非随机$X$数据的固定值。$\mathbf{X}$的第一列通常是捕获截取项$\beta_0$所需的1的列，并且这一列不是随机的。
在第一章的附录A中，我们介绍了二元正态分布，它是两个变量的分布。这里，符号“$\mathrm{N}_n\left(\mathbf{x} \boldsymbol{\beta}, \sigma^2 \mathbf{I}\right)$”表示多元正态分布。“$n$”下标表示它是$n$变量$Y_1, Y_2, \ldots$、$Y_n$的分布。$\mathbf{x} \boldsymbol{\beta}$项是指分布的均值向量，$\sigma^2 \mathbf{I}$项是指其协方差矩阵(下文将详细解释)。
经典回归模型中的所有假设都体现在模型简洁的矩阵形式中:正确的功能规范假设体现在均值向量$(\mathbf{x} \boldsymbol{\beta})$规范中，恒定方差和独立性假设通过规范$\sigma^2 \mathbf{I}$作为协方差矩阵隐含，如下文所述，正态性假设体现在多元正态规范中。
协方差矩阵是包含一组随机变量之间的所有方差和协方差的矩阵。例如，$\left(W_1, W_2, W_3\right)$为联合分布随机变量，则$\boldsymbol{W}=\left(W_1, W_2, W_3\right)$的协方差矩阵为
$$
\operatorname{Cov}(W)=\left[\begin{array}{ccc}
\operatorname{Var}\left(W_1\right) & \operatorname{Cov}\left(W_1, W_2\right) & \operatorname{Cov}\left(W_1, W_3\right) \
\operatorname{Cov}\left(W_2, W_1\right) & \operatorname{Var}\left(W_2\right) & \operatorname{Cov}\left(W_2, W_3\right) \
\operatorname{Cov}\left(W_3, W_1\right) & \operatorname{Cov}\left(W_3, W_2\right) & \operatorname{Var}\left(W_3\right)
\end{array}\right]
$$
注意，行/列组合告诉您涉及到哪对变量，或者对角线元素的情况下涉及到哪个变量。还要注意，一个变量与自身的协方差就是这个变量的方差，这就解释了为什么方差在协方差矩阵的对角线上。

统计代写|回归分析作业代写Regression Analysis代考|Unbiasedness of the OLS Estimator $\hat{\beta}$ Under the Gauss-Markov Model

奇怪的是，用它们的矩阵形式证明估计量$\hat{\beta}$的无偏性更容易。假设采用高斯-马尔可夫模型，则数学定理表述如下:如果数据是由高斯-马尔可夫模型产生的，则OLS $\hat{\boldsymbol{\beta}}$是$\boldsymbol{\beta}$的无偏估计。由于高斯-马尔可夫模型包含(正态假设)经典模型作为一种特殊情况，高斯-马尔可夫模型中估计量$\hat{\beta}$的无偏性证明也意味着经典模型中估计量$\hat{\beta}$的无偏性。
不偏不倚的论点有两个部分。首先，估计是无偏的，以随机变量X的观测值为条件。其次是要注意，根据总期望定律，当考虑随机X数据的所有可能样本时，估计也是无偏的。

$\mathbf{X}$矩阵具有随机和固定的元素;例如，1的第一列包含固定(非随机)元素。同样，如果在观察Y数据之前有X变量是固定的，例如在设计实验和某些分层抽样中，那么这些X变量也是固定的，而不是随机的。

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