Python – Coefficient of Determination-R2 score

Coefficient of determination also called as R² score is used to evaluate the performance of a linear regression model. It is the amount of the variation in the output dependent attribute which is predictable from the input independent variable(s). It is used to check how well-observed results are reproduced by the model, depending on the ratio of total deviation of results described by the model.

Mathematical Formula:

R²= 1- SS_res/ SS_totWhere,
SS_res is the sum of squares of the residual errors.
SS_tot is the total sum of the errors.

Interpretation of R² score:
Assume R² = 0.68
It can be referred that 68% of the changeability of the dependent output attribute can be explained by the model while the remaining 32 % of the variability is still unaccounted for.
R²indicates the proportion of data points which lie within the line created by the regression equation. A higher value of R² is desirable as it indicates better results.

Examples
Case 1 Model gives accurate results

R² = 1- 0/200 = 1

Case 2 Model gives same results always

R² = 1- 200/200 = 0

Case 3 Model gives ambiguous results

R² = 1- 600/200 = -2

We can import r2_score from sklearn.metrics in Python to compute R² score.

Python Implementation:
Code 1: Import r2_score from sklearn.metrics

from sklearn.metrics import r2_score

Code 2: Calculate R² score for all the above cases.

### Assume y is the actual value and f is the predicted values
y =[10, 20, 30]
f =[10, 20, 30]
r2 = r2_score(y, f)
print('r2 score for perfect model is', r2)

Output:

r2 score for perfect model is 1.0

### Assume y is the actual value and f is the predicted values
y =[10, 20, 30]
f =[20, 20, 20]
r2 = r2_score(y, f)
print('r2 score for a model which predicts mean value always is', r2)
 

Output:

r2 score for a model which predicts mean value always is 0.0

Code 3:

### Assume y is the actual value and f is the predicted values
y = [10, 20, 30]
f = [30, 10, 20]
r2 = r2_score(y, f)
print('r2 score for a worse model is', r2)

Output:

r2 score for a worse model is -2.0

Conclusion:

The best possible score is 1 which is obtained when the predicted values are the same as the actual values.
R² score of baseline model is 0.
During the worse cases, R² score can even be negative.

Last Updated on March 17, 2022 by admin

Python – Coefficient of Determination-R2 score