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The basic idea of logistic regression is to use the mechanism already developed for linear regression by modeling the probability p i 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.
The capital asset pricing model uses linear regression as well as the concept of beta for analyzing and quantifying the systematic risk of an investment. This comes directly from the beta coefficient of the linear regression model that relates the return on the investment to the return on all risky assets.
Log-linear analysis is a technique used in statistics to examine the relationship between more than two categorical variables. The technique is used for both hypothesis testing and model building. In both these uses, models are tested to find the most parsimonious (i.e., least complex) model that best accounts for the variance in the observed ...
The formulation of binary logistic regression as a log-linear model can be directly extended to multi-way regression. That is, we model the logarithm of the probability of seeing a given output using the linear predictor as well as an additional normalization factor , the logarithm of the partition function :
The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as [1]
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression.The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis).
In statistics, the ordered logit model or proportional odds logistic regression is an ordinal regression model—that is, a regression model for ordinal dependent variables—first considered by Peter McCullagh. [1]