How to Interpret Regression Summary Tables in statsmodels

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When building a regression model using Python’s statsmodels library, a key feature is the detailed summary table that is printed after fitting a model. This summary provides a comprehensive set of statistics that helps you assess the quality, significance, and reliability of your model.

In this article, we’ll walk through the major sections of a regression summary output in statsmodels and explain what each part means.

Fitting a Model with statsmodels

Before you can get a summary, you need to fit a model. Here’s a basic example:

import statsmodels.api as sm
import pandas as pd

# Example data
df = sm.datasets.get_rdataset('mtcars').data
X = sm.add_constant(df[['hp', 'wt']])          # Independent variables with constant
y = df['mpg']                                  # Dependent variable

# Fit the model
model = sm.OLS(y, X).fit()

# Show the summary
print(model.summary())

Output:

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    mpg   R-squared:                       0.827
Model:                            OLS   Adj. R-squared:                  0.815
Method:                 Least Squares   F-statistic:                     69.21
Date:                Fri, 18 Jul 2025   Prob (F-statistic):           9.11e-12
Time:                        13:51:31   Log-Likelihood:                -74.326
No. Observations:                  32   AIC:                             154.7
Df Residuals:                      29   BIC:                             159.0
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const         37.2273      1.599     23.285      0.000      33.957      40.497
hp            -0.0318      0.009     -3.519      0.001      -0.050      -0.013
wt            -3.8778      0.633     -6.129      0.000      -5.172      -2.584
==============================================================================
Omnibus:                        5.303   Durbin-Watson:                   1.362
Prob(Omnibus):                  0.071   Jarque-Bera (JB):                4.046
Skew:                           0.855   Prob(JB):                        0.132
Kurtosis:                       3.332   Cond. No.                         588.
==============================================================================

Interpreting the Summary Table

Let’s now explore each section of the summary() output.

1. Model Information (Top Block)

Dep. Variable: The dependent or target variable being predicted, which in this example is mpg.
Model: The type of regression used, which is Ordinary Least Squares (OLS).
R-squared: The proportion of variance in the dependent variable explained by the model.
Adj. R-squared: R-squared adjusted for the number of predictors; more reliable when comparing models.
F-statistic / Prob (F-statistic): A test of overall model significance, meaning at least one predictor has a meaningful effect on the outcome.
AIC (Akaike Information Criterion): AIC helps compare multiple models by balancing fit and complexity.
BIC (Bayesian Information Criterion): BIC also compares models but penalizes complexity more heavily than AIC.

2. Coefficient Table (Middle Block)

coef: The estimated regression coefficient. A positive value means a positive relationship with the dependent variable.
std err: The standard error of the coefficient, which measures the uncertainty in its estimate.
t: Tests whether a coefficient is significantly different from zero.
P>|t|: The p-value for the t-test. A low p-value (commonly < 0.05) suggests the predictor is statistically significant.
[0.025, 0.975]: The 95% confidence interval for the coefficient. If this range does not include zero, the effect is likely statistically significant.

3. Model Diagnostics (Bottom Block)

Omnibus / Prob(Omnibus): A test for the normality of residuals. A high p-value (greater than 0.05) suggests normality, which is desirable.
Durbin-Watson: Tests for autocorrelation in the residuals. Values close to 2 suggest that there is no autocorrelation.
Jarque-Bera: Another test for the normality of residuals, similar to Omnibus. A high p-value also supports the assumption of normality here.
Skew / Kurtosis: Measures the shape of the residual distribution. Skew measures asymmetry, while kurtosis indicates whether residuals are heavy- or light-tailed.
Cond. No.: Refers to potential multicollinearity problems. Values above 30 may signal that the model has unstable or highly correlated predictors.

Key Takeaways for Interpretation

Look for low p-values (< 0.05) in the coefficient table to identify significant predictors.
A high R-squared indicates a good fit, but watch for overfitting with many predictors.
Check diagnostic metrics to validate regression assumptions (normality, independence, and multicollinearity).
Use confidence intervals to assess the precision of your estimates.

Conclusion

The regression summary indicates that the model fits the data reasonably well, as evidenced by the R-squared and adjusted R-squared values. Significant predictors are identified by p-values less than 0.05. The sign and magnitude of each coefficient indicate the direction and strength of the relationship. The F-statistic and its p-value confirm whether the overall model is statistically significant. If the key assumptions of linear regression are met, the model is suitable for inference and prediction.