Logistic regression assumes one or more real independent variables and a binary response variable with values 0 or 1, usually representing logical value like false/true, good/bad, etc. Alternatively, the response may have a form of frequency ratio in the interval <0, 1> in case of repeated measurements. This ratio should be the number of positive results divided by number of trials n1/n at a given value of the independent variable. Logistic regression is then used to model probability of some event in dependence on the independent variables x. It is supposed that the response is a random variable with alternative distribution with parameter pi which denotes the probability of a positive outcome of a trial. Thus, the number of positive outcomes out of a fixed number n of trials have a binomial distribution Binom(n, pi). This parameter depends on x monotonously and logistic regression model will be an estimate of this dependence. Applications of logistic models are wide and include diverse fields of science and technology. Typically logistic models are used to estimate risks or failures under given conditions, bank credit scoring of a client, probability of suvirval of an organism in given environment, in toxicology, pharmaceutical, medicine, ecology, reliability analysis, maket research, etc.

Logistic regression - Pdf manual