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Chunk #9 — Background — Logistic regression (LR)

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Random forest versus logistic regression: a large-scale benchmark experiment.
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Let Y denote the binary response variable of interest and X1,…,Xp the random variables considered as explaining variables, termed features in this paper. The logistic regression model links the conditional probability P(Y=1|X1,...,Xp) to X1,…,Xp through 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ P(Y=1|X_{1},...,X_{p})=\frac{\exp\left(\beta_{0}+\beta_{1}X_{1}+\dots+\beta_{p}X_{p}\right)}{1+\exp\left(\beta_{0}+\beta_{1}X_{1}+\dots+\beta_{p}X_{p}\right)}, $$ \end{document}P(Y=1|X1,...,Xp)=expβ0+β1X1+⋯+βpXp1+expβ0+β1X1+⋯+βpXp,