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Interview prep / ML/Data

Transforming a positive target

Question

You regress log price on features. Why is exponentiating the predicted log value generally not the conditional mean of price?

Short answer

Expectation and exponentiation do not commute. The exponential of the conditional mean log price is a geometric-scale quantity and, under a symmetric log-error model, can correspond to a median. Under homoscedastic Gaussian log errors with variance s squared, the conditional mean includes the multiplier exp(s squared / 2). Other error distributions require a justified retransformation estimate, fitted without test leakage.

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