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  • R-squared与Adjust R-squared

    千次阅读 2018-07-26 00:05:08
     R-squared 增大,Adjust R-squared 增大 B. R-squared 增大,Adjust R-squared 减小 C. R-squared 减小,Adjust R-squared 减小 D. R-squared 减小,Adjust R-squared 增大 答案:AB 解析:线性回归问题中...

    如果在线性回归模型中增加一个特征变量,下列可能发生的是(多选)?

    A. R-squared 增大,Adjust R-squared 增大

    B. R-squared 增大,Adjust R-squared 减小

    C. R-squared 减小,Adjust R-squared 减小

    D. R-squared 减小,Adjust R-squared 增大

    答案:AB

    解析:线性回归问题中,R-Squared 是用来衡量回归方程与真实样本输出之间的相似程度。其表达式如下所示:

    上式中,分子部分表示真实值与预测值的平方差之和,类似于均方差 MSE;分母部分表示真实值与均值的平方差之和,类似于方差 Var。一般来说,R-Squared 越大,表示模型拟合效果越好。R-Squared 反映的是大概有多准,因为,随着样本数量的增加,R-Squared 必然增加,无法真正定量说明准确程度,只能大概定量。

    单独看 R-Squared,并不能推断出增加的特征是否有意义。通常来说,增加一个特征特征,R-Squared 可能变大也可能保持不变,两者不一定呈正相关。

    如果使用校正决定系数(Adjusted R-Squared):

    其中,n 是样本数量,p 是特征数量。Adjusted R-Squared 抵消样本数量对 R-Squared 的影响,做到了真正的 0~1,越大越好。

    增加一个特征变量,如果这个特征有意义,Adjusted R-Square 就会增大,若这个特征是冗余特征,Adjusted R-Squared 就会减小。

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  • R-squared 和 Adjusted R-squared联系与区别

    万次阅读 2018-06-11 19:23:38
    原文见: ... 下面是自己理解的总结: ...大概意思就是说,R-squared(值范围0-1)描述的 输入变量对输出变量的解释程度。在单变量线性回归中R-squared 越大,说明拟合程度越好。 然而只要曾加了...

    原文见:

    https://discuss.analyticsvidhya.com/t/difference-between-r-square-and-adjusted-r-square/264/8

     

    下面是自己理解的总结:

    大概意思就是说,R-squared(值范围0-1)描述的 输入变量对输出变量的解释程度。在单变量线性回归中R-squared 越大,说明拟合程度越好。
    然而只要曾加了更多的变量,无论增加的变量是否和输出变量存在关系,则R-squared 要么保持不变,要么增加。
    So, 需要adjusted R-squared ,它会对那些增加的且不会改善模型效果的变量增加一个惩罚向。
    结论,如果单变量线性回归,则使用 R-squared评估,多变量,则使用adjusted R-squared。
    在单变量线性回归中,R-squared和adjusted R-squared是一致的。
    另外,如果增加更多无意义的变量,则R-squared 和adjusted R-squared之间的差距会越来越大,Adjusted R-squared会下降。但是如果加入的特征值是显著的,则adjusted R-squared也会上升

     

    知乎: https://zhuanlan.zhihu.com/albertwang

    微信公众号:AI-Research-Studio

    https://img-blog.csdnimg.cn/20190110102516916.png ​​

    下面是赞赏码

     

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  • R-Squared and adjusted R-Squared

    千次阅读 2019-06-16 04:45:10
    The easiest way to check the accuracy of a model is by looking at the R-squared ...The summary provides two R-squared values, namely Multiple R-squared, and Adjusted R-squared. The Multiple R-squa...

    The easiest way to check the accuracy of a model is by looking at the R-squared value.
    The summary provides two R-squared values, namely Multiple R-squared, and Adjusted R-squared.

    The Multiple R-squared is calculated as follows:

    Multiple R-squared = 1 – SSE/SST where:
    SSE is the sum of square of residuals. Residual is the difference between the predicted value and the actual value.
    SST is the total sum of squares. It is calculated by summing the squares of difference between the actual value and the mean value.
    在这里插入图片描述
    在这里插入图片描述

    For example,
    lets say that we have 5, 6, 7, and 8, and a model predicts the outcomes as 4.5, 6.3, 7.2, and 7.9. Then,
    SSE can be calculated as: SSE = (5 – 4.5) ^ 2 + (6 – 6.3) ^ 2 + (7 – 7.2) ^ 2 + (8 – 7.9) ^ 2;
    and
    SST can be calculated as: mean = (5 + 6 + 7 + 8) / 4 = 6.5; SST = (5 – 6.5) ^ 2 + (6 – 6.5) ^ 2 + (7 – 6.5) ^ 2 + (8 – 6.5) ^ 2

    The Adjusted R-squared value is similar to the Multiple R-squared value,
    but it accounts for the number of variables. This means that the Multiple R-squared will always increase
    when a new variable is added to the prediction model, but if the variable is a non-significant one, the Adjusted R-squared value will decrease.
    For more info, refer here.

    An R-squared value of 1 means that it is a perfect prediction model,

    R-squared or R2 explains the degree to which your input variables explain the variation of your output / predicted variable. So, if R-square is 0.8, it means 80% of the variation in the output variable is explained by the input variables. So, in simple terms, higher the R squared, the more variation is explained by your input variables and hence better is your model.

    However, the problem with R-squared is that it will either stay the same or increase with addition of more variables, even if they do not have any relationship with the output variables. This is where “Adjusted R square” comes to help. Adjusted R-square penalizes you for adding variables which do not improve your existing model.
    在这里插入图片描述
    Meaning of Adjusted R2
    Both R2 and the adjusted R2 give you an idea of how many data points fall within the line of the regression equation. However, there is one main difference between R2 and the adjusted R2: R2 assumes that every single variable explains the variation in the dependent variable. The adjusted R2 tells you the percentage of variation explained by only the independent variables that actually affect the dependent variable.

    How Adjusted R2 Penalizes You
    The adjusted R2 will penalize you for adding independent variables (K in the equation) that do not fit the model. Why? In regression analysis, it can be tempting to add more variables to the data as you think of them. Some of those variables will be significant, but you can’t be sure that significance is just by chance. The adjusted R2 will compensate for this by that penalizing you for those extra variables.

    While values are usually positive, they can be negative as well. This could happen if your R2 is zero; After the adjustment, the value can dip below zero. This usually indicates that your model is a poor fit for your data. Other problems with your model can also cause sub-zero values, such as not putting a constant term in your model.

    Problems with R2 that are corrected with an adjusted R2

    1. R2 increases with every predictor added to a model. As R2 always increases and never decreases, it can appear to be a better fit with the more terms you add to the model. This can be completely misleading.
    2. Similarly, if your model has too many terms and too many high-order polynomials you can run into the problem of over-fitting the data. When you over-fit data, a misleadingly high R2 value can lead to misleading projections.

    Hence, if you are building Linear regression on multiple variable, it is always suggested that you use Adjusted R-squared to judge goodness of model. In case you only have one input variable, R-square and Adjusted R squared would be exactly same.

    Typically, the more non-significant variables you add into the model, the gap in R-squared and Adjusted R-squared increases.

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  • R-squared 和 Adjusted R-squared 的区别

    千次阅读 2019-03-11 12:01:23
    如果在现有model中,再加入一个“无关自变量”,则R-squared的值仍然会增加,但是,实质上,model的拟合度并未增加; 为了弥补R-suqared的缺陷,提出了Adjusted R-squared,它在R-squared的基础上,加入了一个...

    如果在现有model中,再加入一个“无关自变量”,则R-squared的值仍然会增加,但是,实质上,model的拟合度并未增加;
    为了弥补R-suqared的缺陷,提出了Adjusted R-squared,它在R-squared的基础上,加入了一个“惩罚项”,当向现有model加入一个“无关自变量”时,Adjusted R-squared会给这个“无关自变量”一个惩罚,从而使得Adjusted R-squared的值不一定增加,防止了“虚假提升信息的产生”。
    参考博文:【统计学习3】线性回归:R方(R-squared)及调整R方(Adjusted R-Square)

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  • R-Squared

    千次阅读 2018-07-25 00:42:49
    在一个线性回归问题中,我们使用 R 平方(R-Squared)来判断拟合度。此时,如果增加一个特征,模型不变,则下面说法正确的是? A. 如果 R-Squared 增加,则这个特征有意义 B. 如果R-Squared 减小,则这个特征没有...
  • R-squared

    千次阅读 2019-01-23 21:15:31
    第一R-squareda and Adjusted R-squared R-squared: 定义:衡量模型拟合度的一个量,是一个比例式,比例区间为[0,1],越接近1,表示模型拟合度越高 公式:R-squared= SSR/SST  = 1-SSE/SST 其中:SST是原始数据...
  • R-square6.Adjusted R-square 概述 首先通过一张表格对几种误差的名称有一个了解 简称(中文) 英文全称 SSE(残差平方和、和方差) The sum of squares due to error MSE(均方差、方差) Mean squared ...
  • R-squared与Adjusted R-Square

    千次阅读 2019-06-14 16:57:57
    第一:R方(R-squared) 定义:衡量模型拟合度的一个量,是一个比例形式,被解释方差/总方差。 公式:R-squared = SSR/TSS =1 -RSS/TSS 其中:TSS是执行回归分析前,响应变量固有的方差。 RSS残差平方和就是,...
  • R-squared 是一个线性回归指标, 它计算当前趋势的"可信度
  • 第一:R方(R-squared)定义:衡量模型拟合度的一个量,是一个比例形式,被解释方差/总方差。公式:R-squared = SSR/TSS =1 - RSS/TSS其中:TSS是执行回归分析前,响应变量固有的方差。 RSS残差平方和就是,回归...
  • 回归评价指标MSE、RMSE、MAE、R-Squared

    万次阅读 多人点赞 2018-01-19 15:17:34
    分类问题的评价指标是准确率,那么回归算法的评价指标就是MSE,RMSE,MAE、R-Squared。下面一一介绍 均方误差(MSE) MSE (Mean Squared Error)叫做均方误差。看公式 这里的y是测试集上的。 用 真实值-...
  • 回归模型的评估+MAE、MSE、RMSE、MAPE、SMAPE、R-squared 目录 回归模型的评估+MAE、MSE、RMSE、MAPE、SMAPE、R-squared 误差 决定系数(R-squared) 误差 当预测值与真实值完全吻合时等于0,即完美模型;误差...
  • 如何评价回归算法的优劣 MSE、RMSE、MAE、R-Squared前言均方误差 MSE(Mean Squared Error)代码实现均方根误差(RMSE)代码实现平均绝对误差 (MAE)R Squared代码实现通过scikit-learn来计算metricsNoticeMAE vs ...
  • 回归评价指标SSE、MSE、RMSE、MAE、R-Squared 前言 分类问题的评价指标上一篇文章已讲述,那么回归算法的评价指标就是SSE、MSE,RMSE,MAE、R-Squared。下面一一介绍: 一、SSE(和方差) 该统计参数计算的是拟合...
  • 分类问题的评价指标是准确率,那么回归算法的评价指标就是MSE,RMSE,MAE、R-Squared。  MSE和MAE适用于误差相对明显的时候,大的误差也有比较高的权重,RMSE则是针对误差不是很明显的时候;MAE是一个线性的...
  • R-squared是什么意思

    千次阅读 2014-02-11 10:45:00
    在回归分析中,R-squared值应该为多大? 就像经常被问到,在回归分析中,R平方应该为多大才表示回归模型是好的?我经常能够听到这类问题,在没回答这个问题之前,我会解释如 何来解释R平方值,我也会阐述为何这个...
  • R-squared居然是负数

    千次阅读 2019-10-24 09:43:28
    R^2的计算是用(总离差平方和-残差平方和)/回归平方和得到。 2、 因为你方程中的解释变量中含有内生变量的滞后值.所以导致拟合优度为负值. 拟合优度度量的是被解释变量与所有解释...
  • 分类问题的评价指标是准确率,那么回归算法的评价指标就是MSE,RMSE,MAE、R-Squared。下面一一介绍: 1、均方误差(MSE) MSE (Mean Squared Error)叫做均方误差,是反映估计量与被估计量之间差异程度的一种...
  • import pandas as pd import numpy as np from sklearn import datasets, linear_model from sklearn.linear_model import LinearRegression import statsmodels.api as sm from scipy import stats ...
  • BIC/AIC/Adjusted R-Squared

    2020-03-25 20:30:09
    基于SSE(sum of squared errors), 但是包含了一个惩罚项。 AIC(k)=ln(SSET)+(k+1)2T AIC(k) = ln(\frac{SSE}{T}) + \frac{(k+1)2}{T} AIC(k)=ln(TSSE​)+T(k+1)2​ k 代表变量的个数,T是样本的大小。 当样本的大小...

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