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Interview prep / ML/Data

Logistic probabilities and a linear score

Question

A logistic model predicts whether a return is positive. Which part of the model is linear, and why does a score of zero give probability one half?

Short answer

The log odds are a linear score: intercept plus a weighted sum of features. Applying the logistic function maps this score to a probability. At zero, the odds are one, so the event and its complement receive equal probability. Linear log odds do not imply probabilities are linear in features, nor do classification probabilities directly determine the expected size of a return.

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