当我使用python statsmodels在OLS中添加外生变量时，为什么R-Squared会减少

Question

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()

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?

Answer 1

see the answer here Statsmodels: Calculate fitted values and R squared

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

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.

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.

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,