请选择 进入手机版 | 继续访问电脑版
楼主: oliyiyi
1143 6

How To Interpret R-squared and Goodness-of-Fit in Regression Analysis [推广有奖]

版主

泰斗

0%

还不是VIP/贵宾

-

TA的文库  其他...

计量文库

威望
7
论坛币
272091 个
通用积分
31269.1729
学术水平
1435 点
热心指数
1554 点
信用等级
1345 点
经验
383778 点
帖子
9599
精华
66
在线时间
5466 小时
注册时间
2007-5-21
最后登录
2024-3-21

初级学术勋章 初级热心勋章 初级信用勋章 中级信用勋章 中级学术勋章 中级热心勋章 高级热心勋章 高级学术勋章 高级信用勋章 特级热心勋章 特级学术勋章 特级信用勋章

oliyiyi 发表于 2017-2-15 18:20:10 |显示全部楼层 |坛友微信交流群

+2 论坛币
k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群
赵安豆老师微信:zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

感谢您参与论坛问题回答

经管之家送您两个论坛币!

+2 论坛币

本帖隐藏的内容

After you have fit a linear model using regression analysis, ANOVA, or design of experiments (DOE), you need to determine how well the model fits the data. To help you out, Minitab statistical software presents a variety of goodness-of-fit statistics. In this post, you will explore the R-squared (R2 ) statistic, some of its limitations, and uncover some surprises along the way. For instance, low R-squared values are not always bad and high R-squared values are not always good!

What Is Goodness-of-Fit for a Linear Model?Definition: Residual = Observed value - Fitted value

Linear regression calculates an equation that minimizes the distance between the fitted line and all of the data points. Technically, ordinary least squares (OLS) regression minimizes the sum of the squared residuals.

In general, a model fits the data well if the differences between the observed values and the model's predicted values are small and unbiased.

Before you look at the statistical measures for goodness-of-fit, you should check the residual plots. Residual plots can reveal unwanted residual patterns that indicate biased results more effectively than numbers. When your residual plots pass muster, you can trust your numerical results and check the goodness-of-fit statistics.

What Is R-squared?

R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.

The definition of R-squared is fairly straight-forward; it is the percentage of the response variable variation that is explained by a linear model. Or:

R-squared = Explained variation / Total variation

R-squared is always between 0 and 100%:

  • 0% indicates that the model explains none of the variability of the response data around its mean.
  • 100% indicates that the model explains all the variability of the response data around its mean.

In general, the higher the R-squared, the better the model fits your data. However, there are important conditions for this guideline that I’ll talk about both in this post and my next post.

Graphical Representation of R-squared

Plotting fitted values by observed values graphically illustrates different R-squared values for regression models.

The regression model on the left accounts for 38.0% of the variance while the one on the right accounts for 87.4%. The more variance that is accounted for by the regression model the closer the data points will fall to the fitted regression line. Theoretically, if a model could explain 100% of the variance, the fitted values would always equal the observed values and, therefore, all the data points would fall on the fitted regression line.

To learn more about regression analysis, click here.



二维码

扫码加我 拉你入群

请注明:姓名-公司-职位

以便审核进群资格,未注明则拒绝

关键词:regression regressio Interpret Goodness Analysis determine software explore always design

缺少币币的网友请访问有奖回帖集合
https://bbs.pinggu.org/thread-3990750-1-1.html
auirzxp 学生认证  发表于 2017-2-15 18:22:36 |显示全部楼层 |坛友微信交流群

使用道具

nieqiang110 学生认证  发表于 2017-2-15 18:55:31 |显示全部楼层 |坛友微信交流群
How To Interpret R-squared and Goodness-of-Fit in Regression Analysis

使用道具

h2h2 发表于 2017-2-15 19:11:13 |显示全部楼层 |坛友微信交流群
谢谢分享

使用道具

yangke74 在职认证  发表于 2017-2-16 09:47:59 |显示全部楼层 |坛友微信交流群
好资料,支持一下

使用道具

ekscheng 发表于 2017-2-16 15:47:45 |显示全部楼层 |坛友微信交流群

使用道具

遇到相似问题前来求助

使用道具

您需要登录后才可以回帖 登录 | 我要注册

本版微信群
加好友,备注jltj
拉您入交流群

京ICP备16021002-2号 京B2-20170662号 京公网安备 11010802022788号 论坛法律顾问:王进律师 知识产权保护声明   免责及隐私声明

GMT+8, 2024-3-28 23:30