Regresilogistik

Regresilogistik refers to the statistical method commonly known as logistic regression. It is used to model the probability of a categorical outcome, typically a binary event, as a function of one or more predictor variables. The method is widely applied in fields such as medicine, social sciences, marketing, and finance to assess how explanatory factors influence the likelihood of a particular outcome.

In the binary case, if Y is the outcome and X represents a vector of predictors, the model expresses the log-odds of Y being 1 as a linear function: log(p/(1−p)) = β0 + β1x1 + ... + βk xk, where p is P(Y=1|X). The coefficients βj quantify the effect of predictors on the log-odds; exponentiating them gives odds ratios, indicating how the odds of the event change with a one-unit increase in the predictor.

Estimation is typically performed by maximum likelihood estimation. Predicted probabilities are obtained by applying the inverse logit function to the linear predictor. A common classification rule uses a threshold (often 0.5) to assign observations to classes. The model can also be extended to multinomial logistic regression for more than two classes and to ordinal logistic regression when the outcome has a natural order. Regularized versions with L1 or L2 penalties help when predictors are numerous or correlated.

Assumptions include independence of observations and a linear relationship between the log-odds and predictors for continuous variables, with attention to potential multicollinearity and sample size. Model fit and discrimination are assessed using statistics such as deviance, AIC/BIC, and ROC-AUC. Software commonly supports regresilogistik in environments like R and Python (glm, logistic regression in scikit-learn, or statsmodels).