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There are several ways in which the regression outputs may differ in Statsmodel, depending on the method used and the specific data set being analyzed. Some possible differences include:

1. Model Specification: The regression models in Statsmodel can be specified in different ways, such as using the formula interface or specifying the model equation manually. The choice of model specification can affect the output, such as the coefficients, intercept, and standard errors.

2. Method: Statsmodel offers different regression methods, such as ordinary least squares (OLS), logistic regression, and robust regression. Each method may produce different regression outputs, such as R-squared, F-statistic, and coefficients.

3. Model Diagnostics: Statsmodel provides a wide range of model diagnostic tools, such as residual plots, Durbin-Watson statistic, and Cook's distance. These diagnostics can help identify potential issues with the model, such as heteroscedasticity, multicollinearity, and outliers. The outputs from the diagnostics can differ depending on the specific model and data set.

4. Options: Statsmodel regression functions often have several optional arguments that can affect output. Examples of these include choices for handling missing values, options for the solver used for optimization (e.g. BFGS vs. Newton), and weighting schemes for weighted regression.

Overall, the regression outputs in Statsmodel can vary depending on the choices made in modeling, method selection, and diagnostics. It's important to carefully review the results and consider the context of the data set to interpret their meaning.