当我使用 python statsmodels 在 OLS 中添加外生变量时，为什么 R-Squared 会减少 [英] Why would R-Squared decrease when I add an exogenous variable in OLS using python statsmodels

问题描述

如果我正确理解了 OLS 模型，那应该永远不会是这种情况?

If I understand the OLS model correctly, this should never be the case?

trades['const']=1
Y = trades['ret']+trades['comms']
#X = trades[['potential', 'pVal', 'startVal', 'const']]
X = trades[['potential', 'pVal', 'startVal']]

from statsmodels.regression.linear_model import OLS
ols=OLS(Y, X)
res=ols.fit()
res.summary()

如果我打开 const，我得到 0.22 的 rsquared，关闭它，我得到 0.43.这怎么可能?

If I turn the const on, I get a rsquared of 0.22 and with it off, I get 0.43. How is that even possible?

推荐答案

在此处查看答案 Statsmodels:计算拟合值和 R 平方

Rsquared 遵循不同的定义，具体取决于模型中是否存在常量.

Rsquared follows a different definition depending on whether there is a constant in the model or not.

带有常数的线性模型中的 Rsquared 是标准定义，它使用与仅均值模型的比较作为参考.总平方和被贬低.

Rsquared in a linear model with a constant is the standard definition that uses a comparison with a mean only model as reference. Total sum of squares is demeaned.

没有常数的线性模型中的 Rsquared 与完全没有回归量的模型进行比较，或者常数的影响为零.在这种情况下，R 平方计算使用不贬值的总平方和.

Rsquared in a linear model without a constant compares with a model that has no regressors at all, or the effect of the constant is zero. In this case the R squared calculation uses a total sum of squares that does not demean.

因为如果我们添加或删除一个常数，定义就会发生变化，所以 R 平方可以采用任何一种方式.如果我们添加额外的解释变量，实际解释的平方和总是会增加，如果新变量没有贡献，则保持不变，

Since the definition changes if we add or drop a constant, the R squared can go either way. The actual explained sum of squares will always increase if we add additional explanatory variables, or stay unchanged if the new variable doesn't contribute anything,

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