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  "body": "\n## Summary\n\nLogistic regression models the probability of a binary outcome as the logistic function of a linear combination of regressors.\nEquivalently, the log-odds of the outcome is linear in the regressors.\nSo each coefficient is the change in log-odds for a unit change of its regressor.\nIt is the [[generalized linear model|K6C48KMRKC]] for [[Bernoulli|0386Y0Z7Y7]] responses with the canonical logit link, and it is fitted by [[maximum likelihood|0FREPFKNS7]].\nIt is one of the most used models in medicine, the social sciences and machine learning, where it is a basic linear classifier.\n\n## Explanations\n\n### L1 human\n\nMany questions have a yes/no answer: does a patient recover, does a customer buy.\nA straight line can predict values below $0$ or above $1$, which make no sense as probabilities.\nLogistic regression bends the line into an S-shaped curve that always stays between $0$ and $1$.\nIf the model says $\\log(p / (1 - p)) = -2 + 0.5 x$, then at $x = 4$ the odds are $e^0 = 1$, so the probability is $1/2$.\nEach extra unit of $x$ multiplies the odds by $e^{0.5} \\approx 1.65$.\n",
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