Posted on Categories:Regression Analysis, 回归分析, 统计代写, 统计代考

# 统计代写|回归分析代写Regression Analysis代考|Graph Curvature with Main Effects Plots

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 统计代写|回归分析代写Regression Analysis代考|Graph Curvature with Main Effects Plots

In the example above, we can graph the curved relationship on a fitted line plot because there is only one independent variable. However, what can you do if your model contains two or more independent variables? Let me introduce you to main effects plots!

You can use main effect plots with linear terms, but I find they’re even more valuable when you need to understand curvilinear relationships. Its value lies in the fact that it can graph isolated main effects on a twodimensional plot even when your model has more than one independent variable.

Let’s see this in action. If you want to try this yourself, use the following CSV dataset: Hardness. Suppose we have a regression model that includes two independent variables and obtain the following regression equation:
Regression Equation in Uncoded Units
Hardness $=-38.8+0.759$ Temp -1.60 Pressure +0.1657 Pressure*Pressure
In this model, we’re using temperature and pressure to predict the hardness of a product. Temperature is a linear term. From the previous chapter, you know that for every one-degree increase in temperature, stiffness increases by 0.759 units of hardness.

Pressure also relates to hardness, but it includes a polynomial term in the portion I circled. How do you interpret this relationship? Because we have two independent variables, we can’t graph it using a fitted line plot. The equation has a squared term, like the machine setting example. So, we can guess that density has either a U or inverted Ushaped relationship with temperature. The positive coefficient indicates it is in fact U-shaped.

You could enter different pressure values into the equation over and over to get an idea of how it affects hardness. Or, simply create a main effects plot! To calculate the pressure curve below, the plot’s algorithm enters the mean temperature into the equation for the Temp term, and then it cycles through the range of pressure values to calculate the corresponding hardness values. It follows the same process to draw the temperature line.

## 统计代写|回归分析代写Regression Analysis代考|Why You Need to Fit Curves in a Regression Model

The fitted line plot below illustrates the problem of using a linear relationship to fit a curved relationship. The R-squared is high, but the model is clearly inadequate. The fitted line does not represent the data because the model is systematically incorrect. You must specify a model that fits the curve! We’ll come back to these data and try various ways to fit the curve.

When you have one independent variable, using a fitted line plot both to see curvature in the data and determining whether your model fits the curvature is easy. With multiple regression, main effects plots display how your model fits the curvature. However, these plots don’t indicate how well your model fits the curvature. For multiple regression, residual plots are a crucial indicator of whether your model adequately fits curved relationships.

If you see a pattern in the residual plots, your model doesn’t provide an adequate fit for the data. A common reason is that your model incorrectly models the curvature. Plotting the residuals by each of your independent variables can help you identify curved relationships that you need to model. We’ll come back to this method in chapter 9 .
In others cases, you might need to depend on subject-area knowledge to fit the curve. Previous experience or research can tell you that the effect of one variable on another varies based on the value of the independent variable. Perhaps there’s a limit, threshold, or point of diminishing returns where the relationship changes?

TIP: When you start working with your dataset, the best way to determine whether the relationships between variables are curved is to graph them in a scatterplot. Additionally, the curve that the plot displays often helps you determine how to model it.

The majority of this book focuses on ordinary least squares regression, which is a type of linear model. However, linear models can fit curves. I know, statistics isn’t known for terminology that makes sense!
Nonlinear regression is a type of analysis that can fit more types of curves. Consequently, I will show you methods for fitting curves using both linear and nonlinear regression. Nonlinear regression functions very differently than linear regression. For this book, I’m just showing you enough about nonlinear regression so you know when to use it. You’re just dipping your toe in it.

Despite the limitations on the types of curves that linear models can fit, I’m always surprised at how often they adequately fit the curvature!

## 统计代写|回归分析代写Regression Analysis代考|Graph Curvature with Main Effects Plots

Regression Equation in Uncoded Units
Hardness $=-38.8+0.759$ Temp -1.60 Pressure +0.1657 Pressure*Pressure

## 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。