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Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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Regression with sample split

The first regression is for the entire sample, the second regression for z = 0, and the third regression for z = 1. … Should I include z as regressor in the first regression if I would like to compare all 3 regressions or should I omit it to have the same regressors for all three regressions? Thank you! …
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