25 Facts About Logistic regression

Formally, in binary logistic regression there is a single binary dependent variable, coded by an indicator variable, where the two values are labeled "0" and "1", while the independent variables can each be a binary variable or a continuous variable (any real value).

The logistic regression model itself simply models probability of output in terms of input and does not perform statistical classification, though it can be used to make a classifier, for instance by choosing a cutoff value and classifying inputs with probability greater than the cutoff as one class, below the cutoff as the other; this is a common way to make a binary classifier.

Parameters of a logistic regression are most commonly estimated by maximum-likelihood estimation.

Logistic regression is used in various fields, including machine learning, most medical fields, and social sciences.

Multinomial logistic regression is the generalization of binary logistic regression to include any number of explanatory variables and any number of categories.

An explanation of logistic regression can begin with an explanation of the standard logistic function.

The goal of logistic regression is to use the dataset to create a predictive model of the outcome variable.

Basic idea of logistic regression is to use the mechanism already developed for linear regression by modeling the probability pi using a linear predictor function, i e a linear combination of the explanatory variables and a set of regression coefficients that are specific to the model at hand but the same for all trials.

Where are Logistic regression coefficients indicating the relative effect of a particular explanatory variable on the outcome.

Logistic regression model has an equivalent formulation as a latent-variable model.

Two separate sets of Logistic regression coefficients have been introduced, just as in the two-way latent variable model, and the two equations appear a form that writes the logarithm of the associated probability as a linear predictor, with an extra term at the end.

Widely used rule of thumb, the "one in ten rule", states that logistic regression models give stable values for the explanatory variables if based on a minimum of about 10 events per explanatory variable; where event denotes the cases belonging to the less frequent category in the dependent variable.

For example, in simple linear Logistic regression, a set of K data points are fitted to a proposed model function of the form.

Goodness of fit in linear regression models is generally measured using R Since this has no direct analog in logistic regression, various methods including the following can be used instead.

Deviance is analogous to the sum of squares calculations in linear regression and is a measure of the lack of fit to the data in a logistic regression model.

In linear Logistic regression the squared multiple correlation, is used to assess goodness of fit as it represents the proportion of variance in the criterion that is explained by the predictors.

In logistic regression, however, the regression coefficients represent the change in the logit for each unit change in the predictor.

The Wald statistic, analogous to the t-test in linear Logistic regression, is used to assess the significance of coefficients.

Unlike ordinary linear regression, however, logistic regression is used for predicting dependent variables that take membership in one of a limited number of categories rather than a continuous outcome.

Thus, although the observed dependent variable in binary logistic regression is a 0-or-1 variable, the logistic regression estimates the odds, as a continuous variable, that the dependent variable is a 'success'.

In machine learning applications where logistic regression is used for binary classification, the MLE minimises the Cross entropy loss function.

Logistic regression can be seen as a special case of the generalized linear model and thus analogous to linear regression.

Second, the predicted values are probabilities and are therefore restricted to through the logistic distribution function because logistic regression predicts the probability of particular outcomes rather than the outcomes themselves.

Logistic regression is an alternative to Fisher's 1936 method, linear discriminant analysis.

Logistic regression function was independently developed in chemistry as a model of autocatalysis.