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.
R2= 1- SSres / SStotWhere,
SSres is the sum of squares of the residual errors.
SStot 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.
R2 indicates 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.
Case 1 Model gives accurate results
Case 2 Model gives same results always
Case 3 Model gives ambiguous results
We can import r2_score from sklearn.metrics in Python to compute R2 score.
Code 1: Import r2_score from sklearn.metrics
Code 2: Calculate R2 score for all the above cases.
r2 score for perfect model is 1.0
r2 score for a model which predicts mean value always is 0.0
r2 score for a worse model is -2.0
- 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