### 统计代写|实验设计作业代写experimental design代考|Adjustment for Degrees of Freedom

statistics-lab™ 为您的留学生涯保驾护航 在代写实验设计experimental designatistical Modelling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。我们的专家在代写实验设计experimental design代写方面经验极为丰富，各种代写实验设计experimental design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|实验设计作业代写experimental design代考|Adjustment for Degrees of Freedom

The coefficient $R^{2}$ measures the proportion of the variation in $y$ which is explained by the predictor variables. Actually, it overestimates this proportion and the adjustment suggested here aims to correct this.

If the $y$ values were entirely random in the space of $n d 1 m e n-$ sions (the deviations from their mean would then be in an $n-1$ dimensioned sub-space) the $k$ predictor variables would still explain some variation in $y$, on average $k /(n-1) . R^{2}$ is corrected for this random effect by subtracting $k /(n-1)$. This is then scaled to give a value of 1 (perfect explanation of $y$ ) when $R^{2}=1$. Finally
$\operatorname{adj} R^{2}=\left[R^{2}-k /(n-1)\right][n-1] /[n-k-1]$
This adjusted value could even be negative if $\mathrm{R}^{2}$ is small, which highlights the only problem with it. What would a negative value mean? On the other hand the unadjusted value has a clear interpretation as the proportion of the variance of $y$ explained by the predictor variable.

## 统计代写|实验设计作业代写experimental design代考|The Univariate Case

Consider again the simple model
$$y=\alpha 1+\beta x+E$$
with $x$ in deviation form and $\varepsilon=N\left(0, \sigma^{2} I\right)$. Notice that 1 is orthogonal to $x$ so that the least squares estimates of $\alpha$ and $\beta$ are the same as would be obtained by regressing $y$ separately on 1 and $x$.

$$a=\Sigma y_{1} / n, b=\Sigma x_{1} y_{1} / \Sigma x_{1}^{2}$$
For a given value of $x=x_{0}$, the predicted value of $y$ is
$$\hat{y}{0}=a+b x{0}$$
A number of points should be kept in mind relating to this expression.
(i) The $x_{0}$ need not be one of the $x$ in the sample, but there are obvious dangers in predicting outside of the range of the sample. For one thing, the relationships between $x$ and $y$ may be linear for the $x$ values of the sample but the relationship may change outside of these values, as in Figure $2.7 .1$. One example of this could be the cancer causing effects of low doses of radiation. The incidence of cancer in this situation would be so low that it would be difficult to measure, requiring a very large sample size. To facilitate the research one could work at higher dosage rates $(x)$ and hope that one could extrapolate down to lower dosage rates, but this procedure is fraught with danger.
(ii) The predicted value of $y$ depends on all the $y$ values in the sample. We shall comment further on this in Chapter 4 where we shall discuss sensitive or high leverage values of $x$, by which we mean those $x^{\prime} s$ which have a very large effect on the predicted values of $\mathrm{y}$.
(iii) $\hat{y}$ estimates the mean value of $y$ when $x=x_{0}$.
(iv) $y$ is a linear combination of the $y$ values in the sample.

## 统计代写|实验设计作业代写experimental design代考|RESIDUALS

If the fltted model is the correct one (or close to the correct one), we would expect the residuals to refzect the properties of the deviations. In this chapter, we are mainly concerned with checking the residuals to be assured that the model with its assumptions is reasonable for the data, Is the distribution of the residuals consonant with the assumed distribution of the deviations? Does it appear that the variance about the line is constant? Does it appear that the deviations are independent?

If we recall that the prediction equation is $\mathbf{y}=\hat{y}+e$ then, in a sense, the residual and the predicted y value are opposite faces of the same coin for when one is large, the other is small. We shall not have much to say at this point on the sizes of individual residuals. Large values may indicate that the points are outliers but we shall say more on this in Chapter $4 .$

## 统计代写|实验设计作业代写experimental design代考|The Univariate Case

(一)X0不必是其中之一X在样本中，但在样本范围之外进行预测存在明显的危险。一方面，之间的关系X和是的可能是线性的X样本的值，但关系可能会在这些值之外发生变化，如图2.7.1. 这方面的一个例子可能是低剂量辐射的致癌作用。在这种情况下，癌症的发病率将非常低，以至于难以测量，需要非常大的样本量。为了促进研究，可以在更高的剂量率下工作(X)并希望人们可以推断出更低的剂量率，但这个过程充满了危险。
(ii) 的预测值是的取决于所有是的样本中的值。我们将在第 4 章进一步评论这一点，我们将讨论敏感或高杠杆值X, 我们的意思是那些X′s对预测值有很大影响是的.
㈢是的^估计平均值是的什么时候X=X0.
(四)是的是一个线性组合是的样本中的值。

## 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。