We can estimate a linear regression model using OLS with statsmodels as demonstrated previously. We select a forward return, for example for a 10-day holding period, remove outliers below the 2.5% and above the 97.5% percentiles, and fit the model accordingly:

target = 'Returns10D'
model_data = pd.concat([y[[target]], X], axis=1).dropna()
model_data = model_data[model_data[target].between(model_data[target].quantile(.025), 
                                                   model_data[target].quantile(.975))]

model = OLS(endog=model_data[target], exog=model_data.drop(target, axis=1))
trained_model = model.fit()
trained_model.summary()