How to Calculate R-Squared in Python (With Example)

R-squared, often written R², is the proportion of the variance in the response variable that can be explained by the predictor variables in a linear regression model.

The value for R-squared can range from 0 to 1 where:

• 0 indicates that the response variable cannot be explained by the predictor variable at all.
• 1 indicates that the response variable can be perfectly explained without error by the predictor variables.

The following example shows how to calculate R² for a regression model in Python.

Example: Calculate R-Squared in Python

Suppose we have the following pandas DataFrame:

import pandas as pd

#create DataFrame
df = pd.DataFrame({'hours': [1, 2, 2, 4, 2, 1, 5, 4, 2, 4, 4, 3, 6],
                   'prep_exams': [1, 3, 3, 5, 2, 2, 1, 1, 0, 3, 4, 3, 2],
                   'score': [76, 78, 85, 88, 72, 69, 94, 94, 88, 92, 90, 75, 96]})

#view DataFrame
print(df)

    hours  prep_exams  score
0       1           1     76
1       2           3     78
2       2           3     85
3       4           5     88
4       2           2     72
5       1           2     69
6       5           1     94
7       4           1     94
8       2           0     88
9       4           3     92
10      4           4     90
11      3           3     75
12      6           2     96

We can use the LinearRegression() function from sklearn to fit a regression model and the score() function to calculate the R-squared value for the model:

from sklearn.linear_model import LinearRegression

#initiate linear regression model
model = LinearRegression()

#define predictor and response variables
X, y = df[["hours", "prep_exams"]], df.score

#fit regression model
model.fit(X, y)

#calculate R-squared of regression model
r_squared = model.score(X, y)

#view R-squared value
print(r_squared)

0.7175541714105901

The R-squared of the model turns out to be 0.7176.

This means that 71.76% of the variation in the exam scores can be explained by the number of hours studied and the number of prep exams taken.

If we’d like, we could then compare this R-squared value to another regression model with a different set of predictor variables.

In general, models with higher R-squared values are preferred because it means the set of predictor variables in the model is capable of explaining the variation in the response variable well.

Related: What is a Good R-squared Value?

Additional Resources

The following tutorials explain how to perform other common operations in Python:

How to Perform Simple Linear Regression in Python
How to Perform Multiple Linear Regression in Python
How to Calculate AIC of Regression Models in Python