### 统计代写|实验设计作业代写experimental design代考| AGGREGATION OF DATA

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|AGGREGATION OF DATA

The dummy variable approach of the previous section provides one method of combining together different sets of data. In other situations $1 \mathrm{t}$ may be appropriate to merely sum or average data sets, but it is wise to tread warily for the pattern followed by an individual data set may be quite different from that of the aggregate of the data sets. Aggregation sometimes gives rather disturbing and nonsensical results. Consider Figure $3.9 .1$ in which there is a slight overall downwards trend in the $y$ values as the $x$ values inorease. If there are, as shown, three identifiable subgroups in the data, they may, in fact, suggest a positive trend within each group. In this example, it would be spurious to aggregate the groups. One overall model could be used provided that dummy variables were included to distinguish the $y$-intercepts of each group.
For the lactation records of Appendix $C 3$, it would be useful to fit an overall model to the aggregated data of the five cows. One approach may be to fit a model to each cow’s yield and then to average the estimated coefficients. Problems remain, however, for the model with these averaged coefficients may not fit well any of the individual data sets. Another approach is to average the sets of values of the dependent variable. With different patterns of ylelds, one must ask whether this aggregation is a reasonable thing to do. For example, the maximum yield for cow no, 1 occurred in the sixth week, but for cow no. 5 it occurred in the ninth week. Perhaps the data for each cow should be lagged so that the maxima correspond, and then the appropriate milk yields added (that is $16.30$ of cow no. 1 added to $31.27$ of cow no. 2 etc.). This would ensure that the maxima correspond, but it does not take into account the different shapes of the graphs or that one cow may give milk for a longer time than another. (For convenience, the lactation records here were all truncated to 38 weeks even though some actually gave milk for a longer period).

## 统计代写|实验设计作业代写experimental design代考|PECULIARITIES OF OBSERVATIONS

In Chapter 3 we considered the relationship between variables $\mathbf{y}$ and $X=\left(x_{1}, x_{2}, \ldots, x_{k}\right)$, that $1 s$, the relationship between the column vectors. In this chapter, we turn our attention to the rows or individual data points
$$\left(x_{11}, x_{2 i}, \ldots, x_{k i}, y_{1}\right)$$
We have already seen that the variances of the predicted values and of the residuals depend on the particular values of the predictor variables, $x$. Peculiar values of the $x^{\prime} s$ could be termed sensitive, or high leverage, points as will be explained in Section 2. On the other hand, the observed value of $y$ may be unusual for a given set of $x$ values and y may then be termed an outlier as explained in Section $3 .$
Also, in Sections 6 through 8 , the emphasis is again on the variables in the model and perhaps these topios, more logically, should fall into Chapter 3. They have been added for completeness as they are topics often referred to in other texts.

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

Both the prediotor and dependent variables will have their parts to play $1 n$ deciding whether an observation $1 s$ unusual. The predictor variables determine whether a point has hfgh leverage. The value of the dependent variable, $y$, for a given set of $x$ values will determine whether the point is an outlier.

Finst, we consider the residuals, or preferably the studentized residuals. As explained in section 1.3, it is good practice to plot the residuals against the predioted values of $y$ and the predictor variables which are already in the model or which are being considered for inelusion $1 n$ the model. A studentized residual of large absolute value may suggest that an error of measurement or of coding or some such has occurred in the response variable. If the sample size is reasonably large, the observation could be deleted from the analys1s. It is always worthwhile, though, to consider such outliers

very carefully for they may suggest conditions under whioh the model is not valid.

It should be noted that the size of the residuals depends on the model which is fitted. If more, or different, predictor variables are included in the model then it is likely that different points will show up as being potential outliers. It is not possible, then, to completely divorce the detection of outliers from the search for the best model.

Outliers may also be obscured by the presence of points of high leverage for these tend to constrain the prediction curve to pass close to their associated y values. These interrelated effects should warn us to tread cautiously as there is no guaranteed failsafe approach to the problem. Many solutions have been suggested and the interested reader may consult Hoaglin and Welsch (1978). We shall not consider the tests in detail which are contained in this article. To decide whether the i-th observation is an outlier, a fruitful approach is to see the effect that would result from the omission of the 1 -th row of the data. In particular, how would this omission affect the residual at the point and how would it affect the slope of the prediction line?

## 统计代写|实验设计作业代写experimental design代考|PECULIARITIES OF OBSERVATIONS

(X11,X2一世,…,Xķ一世,是的1)

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

prediotor 和因变量都将发挥作用1n决定是否观察1s异常。预测变量确定一个点是否具有 hfgh 杠杆。因变量的值，是的, 对于给定的一组X值将确定该点是否为异常值。

Finst，我们考虑残差，或者最好是学生化的残差。如第 1.3 节所述，将残差与是的以及已经在模型中或正在考虑排除的预测变量1n该模型。绝对值较大的学生化残差可能表明响应变量中出现了测量或编码错误等。如果样本量相当大，则可以从分析中删除观察值。不过，考虑这些异常值总是值得的

## 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。