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Interview prep / ML/Data

Interactions in a linear model

Question

Can a linear regression represent a signal whose effect changes with volatility? Give a model specification and explain the coefficient.

Short answer

Include the signal, volatility and their product as separate features. The model remains linear in its coefficients, while the marginal effect of the signal becomes its own coefficient plus the interaction coefficient times volatility. Centre variables for a useful reference point and estimate all transformations within training windows. Check that the training data support the combinations on which you make predictions.

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