### 统计代写|AP统计辅导AP统计答疑|Exploring and Graphing Bivariate Data

AP统计学与大学的统计学课程在核心内容上是一致的，只是涉及的深度稍浅，AP统计学主要包含以下四部分内容。 第一部分 如何获取数据，获取数据的方式有哪些呢？ 获取数据的方式主要包括普查、抽样调查、观测研究和实验设计等。

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• 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|AP统计辅导AP统计答疑|Scatterplots

• Scatterplots are ideal for exploring the relationship between two quantitative variables. When constructing a scatterplot we often deal with explanatory and response variables. The explanatory variable may be thought of as the independent variable, and the response variable may be thought of as the dependent variable.
• It’s important to note that when working with two quantitative variables, we do not always consider one to be the explanatory variable and the other to be the response variable. Sometimes, we just want to explore the relationship between two variables, and it doesn’t make sense to declare one variable the explanatory and the other the response.
• We interpret scatterplots in much the same way we interpret univariate data; we look for the overall pattern of the data. We address the form, direction, and strength of the relationship. Remember to look for outliers as well. Are there any points in the scatterplot that deviate from the overall pattern?
• When addressing the form of the relationship, look to see if the data is linear (Figure 2.1) or curved (Figure 2.2).

## 统计代写|AP统计辅导AP统计答疑|Correlation

• When dealing with linear relationships, we often use the r-value, or the correlation coefficient. The correlation coefficient can be found by using the formula:
$$r=\frac{1}{n-1} \sum\left(\frac{x_{i}-\bar{x}}{s_{x}}\right)\left(\frac{y_{i}-\bar{y}}{s_{y}}\right)$$
• In practice, we avoid using the formula at all cost. However, it helps to suffer through a couple of calculations using the formula in order to understand how the formula works and gain a deeper appreciation of technology.
• It’s important to remember the following facts about correlation (make sure you know all of them!):

Correlation (the r-value) only describes a linear relationship. Do not use $r$ to describe a curved relationship.

Correlation makes no distinction between explanatory and response variables. If we switch the $x$ and $y$ variables, we still get the same correlation.
Correlation has no unit of measurement. The formula for correlation uses the means and standard deviations for $x$ and $y$ and thus uses standardized values.

If $r$ is positive, then the association is positive; if $r$ is negative, then the association is negative.
$-1 \leq r \leq 1: r=1$ implies that there is a perfectly linear positive
relationship. $r=-1$ implies that there is a perfectly linear negative relationship. $r=0$ implies that there is no correlation.

The r-value, like the mean and standard deviation, is not a resistant measure. This means that even one extreme data point can have a dramatic effect on the r-value. Remember that outliers can either strengthen or weaken the r-value. So use caution!
The r-value does not change when you change units of measurement. For example, changing the $x$ and/or $y$ variables from centimeters to millimeters or even from centimeters to inches does not change the r-value.

Correlation does not imply causation. Just because two variables are strongly associated or even correlated (linear) does not mean that changes in one variable are causing changes in another.

## 统计代写|AP统计辅导AP统计答疑|Least Squares Regression

• When modeling linear data, we use the Least Squares Regression Line (LSRL). The LSRL is fitted to the data by minimizing the sum of the squared residuals. The graphing calculator again comes to our rescue by calculating the LSRL and its equation. The LSRL equation takes the form of $\hat{y}=a+b x$ where $b$ is the slope and $a$ is the $y$-intercept. The AP* formula sheet uses the form $\hat{y}=b_{0}+b_{1} x$. Either form may be used as long as you define your variables. Just remember that the number in front of $x$ is the slope, and the “other” number is the $y$-intercept.
• Once the LSRL is fitted to the data, we can then use the LSRL equation to make predictions. We can simply substitute a value of $x$ into the equation of the LSRL and obtain the predicted value, $\hat{y}$.
• The LSRL minimizes the sum of the squared residuals. What does this mean? A residual is the difference between the observed value, $y$, and the predicted value, $\hat{y}$. In other words, residual-observed – predicted. Remember that all predicted values are located on the LSRL. A residual can be positive, negative, or zero. A residual is zero only when the point is located on the LSRL. Since the sum of the residuals is always zero,

we square the vertical distances of the residuals. The LSRL is fitted to the data so that the sum of the square of these vertical distances is as small as possible.

• The slope of the regression line (LSRL) is important. Consider the time required to run the last mile of a marathon in relation to the time required to run the first mile of a marathon. The equation $\hat{y}=1.25 x$, where $x$ is the time required to run the first mile in minutes and $\hat{y}$ is the predicted time it takes to run the last mile in minutes, could be used to model or predict the runner’s time for his last mile. The interpretation of the slope in context would be that for every one minute increase in time needed to run the first mile, the predicted time to run the last mile would increase by $1.25$ minutes, on average. It should be noted that the slope is a rate of change and that that since the slope is positive, the time will increase by $1.25$ minutes. A negative slope would give a negative rate of change.

## 统计代写|AP统计辅导AP统计答疑|Scatterplots

• 散点图非常适合探索两个定量变量之间的关系。在构建散点图时，我们经常处理解释变量和响应变量。解释变量可以被认为是自变量，而响应变量可以被认为是因变量。
• 需要注意的是，在处理两个定量变量时，我们并不总是将一个视为解释变量，而将另一个视为响应变量。有时，我们只是想探索两个变量之间的关系，而将一个变量声明为解释变量，另一个变量声明为响应变量是没有意义的。
• 我们解释散点图的方式与解释单变量数据的方式大致相同；我们寻找数据的整体模式。我们解决关系的形式、方向和强度。记住也要寻找异常值。散点图中是否有任何点偏离整体模式？
• 在处理关系的形式时，查看数据是线性的（图 2.1）还是曲线的（图 2.2）。

## 统计代写|AP统计辅导AP统计答疑|Correlation

• 在处理线性关系时，我们经常使用 r 值，或相关系数。相关系数可以通过使用公式找到：
r=1n−1∑(X一世−X¯sX)(是一世−是¯s是)
• 在实践中，我们不惜一切代价避免使用该公式。但是，它有助于使用公式进行几次计算，以了解公式的工作原理并更深入地了解技术。
关于相关性的事实
• 记住以下有关相关性的事实很重要（确保您了解所有这些事实！）：

−1≤r≤1:r=1意味着存在完全线性的正

r 值与均值和标准差一样，不是一种抗性测量。这意味着即使是一个极端数据点也会对 r 值产生巨大影响。请记住，异常值可以加强或削弱 r 值。所以要小心！

## 统计代写|AP统计辅导AP统计答疑|Least Squares Regression

• 在对线性数据建模时，我们使用最小二乘回归线 (LSRL)。LSRL 通过最小化残差平方和来拟合数据。图形计算器通过计算 LSRL 及其方程再次帮助我们。LSRL 方程的形式为是^=一种+bX在哪里b是斜率和一种是个是-截距。AP* 公式表使用表格是^=b0+b1X. 只要您定义了变量，就可以使用任何一种形式。只要记住前面的数字X是斜率，“其他”数字是是-截距。
• 一旦将 LSRL 拟合到数据中，我们就可以使用 LSRL 方程进行预测。我们可以简单地替换一个值X代入LSRL的方程，得到预测值，是^.
• LSRL 最小化残差平方和。这是什么意思？残差是观察值之间的差异，是, 和预测值,是^. 换句话说，残差观察 – 预测。请记住，所有预测值都位于 LSRL 上。残差可以是正数、负数或零。只有当点位于 LSRL 上时，残差才为零。由于残差之和始终为零，

• 回归线的斜率 (LSRL) 很重要。考虑跑完马拉松最后一英里所需的时间与跑完马拉松第一英里所需的时间。方程是^=1.25X， 在哪里X是跑第一英里所需的时间，以分钟为单位，并且是^是以分钟为单位运行最后一英里的预测时间，可用于建模或预测跑步者最后一英里的时间。在上下文中对斜率的解释是，跑第一英里所需的时间每增加一分钟，跑最后一英里的预测时间将增加1.25分钟，平均。应该注意的是斜率是一个变化率，由于斜率为正，时间将增加1.25分钟。负斜率将产生负变化率。

## 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。