Scikit-learn is returning coefficient of determination (R^2) values less than -1

Question

I\'m doing a simple linear model. I have

fire = load_data()
regr = linear_model.LinearRegression()
scores = cross_validation.cross_val_score(regr, fire.data, fir         


        

Answer 1

R² = 1 - RSS / TSS, where RSS is the residual sum of squares ∑(y - f(x))² and TSS is the total sum of squares ∑(y - mean(y))². Now for R² ≥ -1, it is required that RSS/TSS ≤ 2, but it's easy to construct a model and dataset for which this is not true:

>>> x = np.arange(50, dtype=float)
>>> y = x
>>> def f(x): return -100
...
>>> rss = np.sum((y - f(x)) ** 2)
>>> tss = np.sum((y - y.mean()) ** 2)
>>> 1 - rss / tss
-74.430972388955581