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# 统计代写|线性回归代写Linear Regression代考|Predicting the Weather

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## 统计代写|线性回归代写Linear Regression代考|Predicting the Weather

Can early season snowfall from September 1 until December 31 predict snowfall in the remainder of the year, from January 1 to June 30 ? Figure 1.6, using data from the data file ftcollinssnow.txt, gives a plot of Late season snowfall from January 1 to June 30 versus Early season snowfall for the period September 1 to December 31 of the previous year, both measured in inches at Ft. Collins, Colorado $^2$. If Late is related to Early, the relationship is considerably weaker than in the previous examples, and the graph suggests that early winter snowfall and late winter snowfall may be completely unrelated, or uncorrelated. Interest in this regression problem will therefore be in testing the hypothesis that the two variables are uncorrelated versus the alternative that they are not uncorrelated, essentially comparing the fit of the two lines shown in Figure 1.6. Fitting models will be helpful here.

Turkey Growth
This example is from an experiment on the growth of turkeys (Noll, Weibel, Cook, and Witmer, 1984). Pens of turkeys were grown with an identical diet, except that each pen was supplemented with a Dose of the amino acid methionine as a percentage of the total diet of the birds. The methionine was provided using either a standard source or one of two experimental sources. The response is average weight gain in grams of all the turkeys in the pen.

Figure 1.7 provides a summary graph based on the data in the file turkey . txt. Except at Dose $=0$, each point in the graph is the average response of five pens of turkeys; at $D o s e=0$, there were ten pens of turkeys. Because averages are plotted, the graph does not display the variation between pens treated alike. At each value of Dose $>0$, there are three points shown, with different symbols corresponding to the three sources of methionine, so the variation between points at a given Dose is really the variation between sources. At Dose $=0$, the point has been arbitrarily labelled with the symbol for the first group, since Dose $=0$ is the same treatment for all sources.

For now, ignore the three sources and examine Figure 1.7 in the way we have been examining the other summary graphs in this chapter. Weight gain seems to increase with increasing Dose, but the increase does not appear to be linear, meaning that a straight line does not seem to be a reasonable representation of the average dependence of the response on the predictor. This leads to study of mean functions.

## 统计代写|线性回归代写Linear Regression代考|MEAN FUNCTIONS

Imagine a generic summary plot of $Y$ versus $X$. Our interest centers on how the distribution of $Y$ changes as $X$ is varied. One important aspect of this distribution is the mean function, which we define by
$$\mathrm{E}(Y \mid X=x)=\text { a function that depends on the value of } x$$
We read the left side of this equation as “the expected value of the response when the predictor is fixed at the value $X=x$,” if the notation ” $\mathrm{E}(\mathrm{)}$ ” for expectations and “Var( )” for variances is unfamiliar, please read Appendix A.2. The right side of (1.1) depends on the problem. For example, in the heights data in Example 1.1, we might believe that
$$\mathrm{E}(\text { Dheight } \mid \text { Mheight }=x)=\beta_0+\beta_1 x$$
that is, the mean function is a straight line. This particular mean function has two parameters, an intercept $\beta_0$ and a slope $\beta_1$. If we knew the values of the $\beta \mathrm{s}$, then the mean function would be completely specified, but usually the $\beta$ s need to be estimated from data.

Figure 1.8 shows two possibilities for $\beta \mathrm{s}$ in the straight-line mean function (1.2) for the heights data. For the dashed line, $\beta_0=0$ and $\beta_1=1$. This mean function would suggest that daughters have the same height as their mothers on average. The second line is estimated using ordinary least squares, or oLs, the estimation method that will be described in the next chapter. The oLs line has slope less than one, meaning that tall mothers tend to have daughters who are taller than average because the slope is positive but shorter than themselves because the slope is less than one. Similarly, short mothers tend to have short daughters but taller than themselves. This is perhaps a surprising result and is the origin of the term regression, since extreme values in one generation tend to revert or regress toward the population mean in the next generation.

## 统计代写|线性回归代写Linear Regression代考|Predicting the Weather

9月1日至12月31日的早期降雪能否预测1月1日至6月30日的降雪?图1.6使用数据文件ftcollinsnow .txt中的数据，给出了1月1日至6月30日晚季降雪量与前一年9月1日至12月31日早季降雪量的对比图，两者均以英寸为单位，位于科罗拉多州的Ft Collins $^2$。如果Late与Early相关，则这种关系比前面的例子弱得多，并且该图表明，初冬降雪和晚冬降雪可能完全不相关或不相关。因此，对这个回归问题的兴趣将在于检验两个变量不相关的假设与它们不相关的替代假设，本质上是比较图1.6所示两条线的拟合。在这里，拟合模型会有所帮助。

## 统计代写|线性回归代写Linear Regression代考|MEAN FUNCTIONS

$$\mathrm{E}(Y \mid X=x)=\text { a function that depends on the value of } x$$

$$\mathrm{E}(\text { Dheight } \mid \text { Mheight }=x)=\beta_0+\beta_1 x$$

## 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。