What is R-squared and how to calculate it in sklearn?

by Amrita Mitra | Jan 13, 2023 | AI, Machine Learning and Deep Learning, Featured, Machine Learning Using Python, Python Scikit-learn, Statistics For Machine Learning

for which the calculated values of y exactly match the actual or expected values of y,

$RSS=\sum_{i=1}^{n}e_{i}^{2}=\sum_{i=1}^{n}(y_{i}-y_{ai})^{2}=0$

And hence,

$R^{2}=1-\frac{RSS}{TSS}=1-0=1$

A linear regression model, which always predicts y_i to be the overall mean

$TSS=\sum_{i=1}^{n}(y_{i}-\bar{y})^{2} \quad where \quad \bar{y}=\frac{\sum_{i=1}^{n}y_{i}}{n}$

and

$RSS=\sum_{i=1}^{n}e_{i}^{2}=\sum_{i=1}^{n}(y_{i}-y_{ai})^{2}=\sum_{i=1}^{n}(y_{i}-\bar{y})^{2}$

And hence,

$R^{2}=1-\frac{RSS}{TSS}=1-1=0$

How to calculate R-squared using the sklearn Python library?

We can use the following Python code to calculate R-squared.

from sklearn.metrics import r2_score
 
Ya = [1.2, 2.3, 2.9, 4.8, 5.2, 5.8, 7.1, 8.0, 9.2, 10.0]
Y = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
 
r2 = r2_score(Ya, Y)
print("R2 score: ", r2)

Here, Ya is the actual output and Y is the predicted output of the model. The output of the above program is:

R2 score:  0.9884348986465019

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