Logistische Regression
Logistisch regression is a type of statistische Analyse 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, Sozialwissenschaften, and marketing, to understand the impact of one or more independent variables on a dependent binary outcome.
Im Gegensatz zu linearer Regression, 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.
Die Grundformel für die logistische Regression lautet:
P(Y=1) = 1 / (1 + e^(-z))
where z is a lineare Kombination der Prädiktorvariablen vorherzusagen:
z = β0 + β1X1 + β2X2 + … + βnXn
In dieser Gleichung, 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.
Die logistische Regression kann erweitert werden, um mehrere Klassen zu handhaben (multinomiale logistische Regression) 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.