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# 统计代写|回归分析代写Regression Analysis代考|Review and Next Steps

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## 统计代写|回归分析代写Regression Analysis代考|Review and Next Steps

Over the previous three chapters, we’ve covered various types of relationships between the variables in your model.

We’ve looked at main effects for both continuous and categorical variables. For continuous variables, we also looked at both linear and curvilinear relationships. For main effects, the relationship between an independent and dependent variable does not depend on the value of another variable.

We also looked at interaction effects for both categorical and continuous variables. These relationships do depend on the value of other variables in the model. And, when you have significant interaction effects, it’s dangerous interpreting main effects without considering the interaction effect. You don’t want to put chocolate sauce on your hot dogs!

You also learned how independent variables can have a portion of their total effects as main effects and interaction effects.

Now you know how to model and interpret these types of relationships. That’s great. However, if the model doesn’t fit the data, you’re barking up the wrong tree! The next chapter shifts gears and covers statistical measures of how well your model fits the data.

Review and Next Steps
Over the previous three chapters, we’ve covered various types of relationships between the variables in your model.

We’ve looked at main effects for both continuous and categorical variables. For continuous variables, we also looked at both linear and curvilinear relationships. For main effects, the relationship between an independent and dependent variable does not depend on the value of another variable.

We also looked at interaction effects for both categorical and continuous variables. These relationships do depend on the value of other variables in the model. And, when you have significant interaction effects, it’s dangerous interpreting main effects without considering the interaction effect. You don’t want to put chocolate sauce on your hot dogs!

You also learned how independent variables can have a portion of their total effects as main effects and interaction effects.

Now you know how to model and interpret these types of relationships. That’s great. However, if the model doesn’t fit the data, you’re barking up the wrong tree! The next chapter shifts gears and covers statistical measures of how well your model fits the data.

## 统计代写|回归分析代写Regression Analysis代考|Assessing the Goodness-of-Fit

First, a quick review of material in chapter 2 . Residuals are the distance between the observed value and the fitted value.

Linear regression identifies the equation that produces the smallest difference between all of the observed values and their fitted values. To be precise, linear regression finds the smallest sum of squared residuals that is possible for the dataset.

Statisticians say that a regression model fits the data well when the differences between the observations and the predicted values are small and unbiased. Unbiased in this context means that the fitted values are not systematically too high or too low anywhere in the observation space.

However, before assessing numeric measures of goodness-of-fit, like R-squared, you should evaluate the residual plots. Residual plots can expose a biased model far more effectively than numeric output by displaying problematic patterns in the residuals. If your model is biased, you cannot trust the results. If your residual plots look good, go ahead and assess your R-squared and other statistics. Chapter 9 covers residual plots.

R-squared
After fitting a linear regression model, you need to determine how well the model fits the data. Does it do a good job of explaining changes in the dependent variable? There are a several key goodnessof-fit statistics for regression analysis. First, we’ll examine R-squared $\left(\mathrm{R}^2\right)$, highlight some of its limitations, and discover some surprises. For instance, small R-squared values are not always a problem, and high R-squared values are not necessarily good!

R-squared evaluates the scatter of the data points around the fitted regression line. It is also called the coefficient of determination, or the coefficient of multiple determination for multiple regression. For the same data set, higher R-squared values represent smaller differences between the observed data and the fitted values.
$\mathrm{R}$-squared is the percentage of the dependent variable variation that a linear model explains.
$$R^2=\frac{\text { Variance explained by the model }}{\text { Total variance }}$$
$\mathrm{R}$-squared is always between 0 and $100 \%$ :

• $0 \%$ represents a model that does not explain any of the variation in the response variable around its mean. The mean of the dependent variable predicts the dependent variable as well as the regression model.
• $100 \%$ represents a model that explains all of the variation in the response variable around its mean.

## 统计代写|回归分析代写Regression Analysis代考|Assessing the Goodness-of-Fit

R 平方

，突出它的一些局限性，并发现一些惊喜。例如，小的 R 平方值并不总是问题，高的 R 平方值也不一定好！

R 平方评估拟合回归线周围数据点的散布。它也被称为决定系数，或多元回归的多重决定系数。对于相同的数据集，较高的 R 平方值表示观测数据与拟合值之间的差异较小。
-squared 是线性模型解释的因变量变化的百分比。

$$R^2=\frac{\text { Variance explained by the model }}{\text { Total variance }}$$
$\mathrm{R}$-平方始终介于 0 和 $100 \%$ :

• $0 \%$ 表示不解释响应变量围绕其均值的任何变化的模型。因变量的均值预测因变量以及回归模型。
• $100 \%$ 表示解释响应变量围绕其均值的所有变化的模型。

## 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。