Recently I have been trying to solve one of my problems with OLS and WLS respectively, and was trying to determine whether a weighted regression would be more suitable by comparing the R^2 value.
I used statsmodels to produce the R^2 for both of the models and I also have another function which uses its own formula to calculate the R^2 of the model:
y_pred = model.predict(X)
SS_Residual = sum((y - y_pred) ** 2)
SS_Total = sum((y - np.mean(y)) ** 2)
r_squared = 1 - (float(SS_Residual)) / SS_Total
This works perfectly when the model is an OLS, but the result differs by a huge margin (what statsmodels produce and what my hardcoded module produce_ when the model is a WLS.
I would like to know if there's a different way for statsmodels to calculate the R-squared for WLS model or there's something wrong with my approach. Thank you!
This is the OLS result which has ~0.3 R^2, same as what my function have calculated.
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.306
Model: OLS Adj. R-squared: 0.298
Method: Least Squares F-statistic: 40.93
Date: Mon, 26 Feb 2018 Prob (F-statistic): 6.30e-09
Time: 14:27:34 Log-Likelihood: 315.72
No. Observations: 95 AIC: -627.4
Df Residuals: 93 BIC: -622.3
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const -0.0007 0.001 -0.725 0.470 -0.002 0.001
p5 0.5629 0.088 6.397 0.000 0.388 0.738
==============================================================================
Omnibus: 5.067 Durbin-Watson: 2.182
Prob(Omnibus): 0.079 Jarque-Bera (JB): 4.416
Skew: 0.500 Prob(JB): 0.110
Kurtosis: 3.341 Cond. No. 97.3
==============================================================================
However, when I use a WLS with weights, the R-squared produced is drastically increased to ~0.7, while the coefficient in fact doesnt change a lot, and my function have calculated a 0.3 R^2 for this WLS model instead.
WLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.772
Model: WLS Adj. R-squared: 0.769
Method: Least Squares F-statistic: 314.5
Date: Mon, 26 Feb 2018 Prob (F-statistic): 1.37e-31
Time: 14:27:34 Log-Likelihood: -14.763
No. Observations: 95 AIC: 33.53
Df Residuals: 93 BIC: 38.63
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const -0.0006 0.001 -1.170 0.245 -0.002 0.000
p5 0.6230 0.035 17.733 0.000 0.553 0.693
==============================================================================
Omnibus: 27.432 Durbin-Watson: 1.889
Prob(Omnibus): 0.000 Jarque-Bera (JB): 161.320
Skew: 0.609 Prob(JB): 9.33e-36
Kurtosis: 9.267 Cond. No. 63.8
==============================================================================
