如何获得线性回归的调整后R平方 [英] How to get Adjusted R Square for Linear Regression

问题描述

使用sklearn.metrics可以计算R平方。如何使用线性回归模型计算调整后的调整R平方？

解决方案

Scikit-Learn的线性回归不返回调整后的R平方。但是，根据R平方，您可以根据公式计算调整后的R平方：

其中p是预测变量的数量（也称为特征或解释变量），n是数据点的数量。因此，如果您的数据位于一个名为train的数据框中，并且具有r平方， r2 ，则公式为：

< pre class = lang-py prettyprint-override> adj_r2 =（1-（1-r2）*（（train.shape [0]-1）/
（train.shape [ 0]-train.shape [1]-1））））


train .shape [0] 是观测值的数量， train.shape [1] 是要素的数量。

StatsModels 库具有线性回归方法，该方法确实返回调整后的R平方（在许多其他指标中）。 此处是文档。

上面的公式来自此Stack Exchange答案，它说这是已知的如 Wherry Formula-1 。有许多不同的公式用于计算调整后的R平方，但这是R中使用的方法。有关调整后的R平方方法之间差异的更多信息，请参见链接到的答案或论文估计
R ^ 2回归中的收缩

Using sklearn.metrics I can compute R square.How I can compute Adjusted Adjusted R square using Linear Regression model?

解决方案

Scikit-Learn's Linear Regression does not return the adjusted R squared. However, from the R -squared you can calculate the adjusted R squared from the formula:

Where p is the number of predictors (also known as features or explanatory variables) and n is the number of data points. So if your data is in a dataframe called train and you have r-squared, r2, the formula would be:

adj_r2 = (1 - (1 - r2) * ((train.shape[0] - 1) / 
          (train.shape[0] - train.shape[1] - 1)))

train.shape[0] is the number of observations, and train.shape[1] is the number of features.

The StatsModels library has a linear regression method that does return the adjusted R squared (among many other metrics). Here is the documentation.

The formula above is from this Stack Exchange Answer which says this is known as Wherry Formula - 1. There are a number of different formulas used to calculate adjusted R squared, but this is the method used in R. For more on the differences between adjusted R squared methods, see the answer linked to or the paper Estimating R^2 Shrinkage in Regression

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