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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 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: $\beta_k=0 \quad$ 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 $=$ $$2 P\left(t{n-p}<-\left|t_{o, k}\right|\right)=2 P\left(t_{n-p}>\left|t_{o, k}\right|\right) .$$
Use the normal table or the $d=Z$ line in the $t$-table if the degrees of freedom $d=n-p \geq 30$. Again pval is the estimated p-value.
iv) State whether you reject Ho or fail to reject Ho and give a nontechnical sentence restating your conclusion in terms of the story problem.

统计代写|线性回归代写linear regression代考|Two Important Special Cases

When studying a statistical model, it is often useful to try to understand the model that contains a constant but no nontrivial predictors, then try to understand the model with a constant and one nontrivial predictor, then the model with a constant and two nontrivial predictors, and then the general model with many predictors. In this text, most of the models are such that $Y$ is independent of $\boldsymbol{x}$ given $\boldsymbol{x}^T \boldsymbol{\beta}$, written
$$Y \Perp \boldsymbol{x} \mid \boldsymbol{x}^T \boldsymbol{\beta} .$$
Then $w_i=\boldsymbol{x}_i^T \hat{\boldsymbol{\beta}}$ is a scalar, and trying to understand the model in terms of $\boldsymbol{x}_i^T \hat{\boldsymbol{\beta}}$ is about as easy as trying to understand the model in terms of one nontrivial predictor. In particular, the response plot of $\boldsymbol{x}_i^T \hat{\boldsymbol{\beta}}$ versus $Y_i$ is essential.

For MLR, the two main benefits of studying the MLR model with one nontrivial predictor $X$ are that the data can be plotted in a scatterplot of $X_i$ versus $Y_i$ and that the OLS estimators can be computed by hand with the aid of a calculator if $n$ is small.

线性回归代写

统计代写|线性回归代写线性回归代考| Wald t Test

$x_1 \equiv 1$。如果$x_k$在$x_1, \ldots, x_{k-1}, x_{k+1}, \ldots, x_p$上的OLS回归具有较高的决定系数$R_k^2$，则预测因子$x_k$与其他预测因子高度相关。如果是这种情况，那么在模型中通常不需要$x_k$，因为模型中有其他预测器。如果$k \geq 2$至少有一个$R_k^2$是高的，那么预测器之间存在多重共线性

i)陈述假设Ho: $\beta_k=0 \quad$ Ha: $\beta_k \neq 0$。

有限元方法代写

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MATLAB代写

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