sklearn r2_score and python stats lineregress function give very different values of R^2. Why?

Question

I´m using the same data but different python libraries to calculate the coefficient of determination R^2. Using stats library and sklearn yield different results.

What is the reason behind this behavior?

# Using stats lineregress
slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)
print r_value**2

0.956590054918

# Using sklearn
from sklearn.metrics import r2_score
print r2_score(x, y)

0.603933484937

Answer 1

The r_value returned by linregress is the correlation coefficient r of x and y. In general, the squared correlation coefficient r² is not the same as the coefficient of determination R².

The coefficient of determination tells you how well a model fits the data. Thus, r2_score thinks that x are the true values and y are values predicted by a model.

If your x and y are true and predicted data, R² is what you want. However, if both are measured data you most likely want r² instead.

Details about the correlation coefficient and the coefficient of determination can be found at Wikipedia.