A regression table is a structured model output that summarizes estimated coefficients, uncertainty, significance, fit, and related statistics. It supports numerical evaluation more effectively than a scatter plot, especially when a model has multiple predictors. section 4.2.3
In Python, statsmodels produces a regression table after a fitted model is printed. For ordinary least squares, the output includes coefficient estimates, standard errors, t statistics, p-values, R-squared, adjusted R-squared, the F-statistic, observation counts, and information criteria. section 4.2.2
Read the table by connecting each measure to a modeling decision:
- Interpret coef values as the estimated intercept and predictor effects; together they define predictions such as stage2 = −3.0778 + 1.3083 × stage1. section 4.2.3
- Use standard errors, t statistics, and p-values to evaluate uncertainty and statistical significance for individual coefficients. section 4.2.3
- Use R-squared to quantify explained variance; the fitted example reports approximately 0.575, while SST, SSR, and SSE separate total, explained, and unexplained variation. section 4.2.3
- Use the F-statistic and its p-value to assess whether a linear model explains a statistically significant amount of response variance. section 4.2.3
- For logistic regression, inspect coefficient estimates, p-values, goodness-of-fit statistics, and the likelihood-ratio p-value before considering predictor removal or model reduction. section 5.2.2
Printing a fitted table
Fit an ordinary least-squares model with statsmodels, then print its summary: lm = sm.OLS(y, x).fit(); print(lm.summary()). The resulting table reports the model structure and statistics needed to evaluate the relationship between stage1 and stage2. section 4.2.2
>>> lm = sm.OLS(y, x).fit()
>>> print(lm.summary())
OLS Regression Results
===========================================================================
Dep. Variable: stage2 R-squared: 0.575
Model: OLS Adj. R-squared: 0.551
Method: Least Squares F-statistic: 24.35
Date: Mon, 11 Mar 2024 Prob (F-statistic): 0.000107
Time: 14:06:15 Log-Likelihood: -97.991
No. Observations: 20 AIC: 200.0
Df Residuals: 18 BIC: 202.0
Df Model: 1
Covariance Type: nonrobust
===========================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------
const -3.0778 52.150 -0.059 0.954 -112.640 106.485
stage1 1.3083 0.265 4.934 0.000 0.751 1.865
===========================================================================
Omnibus: 2.616 Durbin-Watson: 2.326
Prob(Omnibus): 0.270 Jarque-Bera (JB): 2.150
Skew: 0.749 Prob(JB): 0.341
Kurtosis: 2.420 Cond. No. 1.34e+03
===========================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the
errors is correctly specified.
[2] The condition number is large, 1.34e+03. This might
indicate that there are strong multicollinearity or other
numerical problems.
Inspect a complete statsmodels OLS regression table, including coefficient and fit-statistic columns. section 4.2.2
