ロジスティック回帰

ロジスティック回帰

ロジスティック regression is a type of 統計分析 used to predict the probability of a binary outcome, meaning an outcome that can have one of two possible values, such as ‘yes’ or ‘no’, ‘success’ or ‘failure’. It is widely used in various fields, including medicine, 社会科学, and marketing, to understand the impact of one or more independent variables on a dependent binary outcome.

非構造化プルーニングとは異なり、 線形回帰, which predicts continuous outcomes, logistic regression uses the logistic function to constrain the predicted probabilities between 0 and 1. The logistic function, also known as the sigmoid function, has an S-shaped curve and allows for modeling the probability of the dependent event occurring based on the input variables.

ロジスティック回帰の基本式は次のとおりです：

P(Y=1) = 1 / (1 + e^(-z))

where z is a 線形結合 予測変数の：

z = β0 + β1X1 + β2X2 + … + βnXn

この式において、 β0 is the intercept, β1, β2, …, βn are the coefficients for the predictor variables X1, X2, …, Xn. The coefficients represent the change in the log-odds of the dependent variable for a one-unit change in the predictor variable.

ロジスティック回帰は、複数クラスを扱うことも拡張可能です（多項ロジスティック回帰) and can also be used for ordinal outcomes (ordinal logistic regression). Model evaluation metrics such as the confusion matrix, precision, recall, and the area under the ROC curve (AUC) are commonly employed to assess the performance of logistic regression models.