# Logistic Regression

Introduction

**Logistic regression**(or logit regression), unlike the ordinary

**least squares regression**, is a type of regression analysis used to predict the outcome of a categorical variable using one or more predictors. The categorical variable can have two categories (

**binomial logistic regression**) or more (

**multinomial logistic regression**). The name logistic stems from the logistic probability density function used in statistic:

If the values of t is assumed to be a linear function of an explanatory variable x, that is,

then the density function above can be written as:

We then define the inverse logit function as

The method of Maximum Likelihood (ML) estimation is used to find estimates of the regression coefficients

*a*and*b*, but since the residuals are not normally distributed (and therefore there is no closed-form formula for the expression that maximizes the ML function), iterative methods such as the Gauss-Newton algorithm are used. The parameter*L*is often estimated as the largest value of the variableNote that by linearization,

*a*and*b*can also be found using simple linear regression analysis suggested by the function*g(x).*

Applications

R | SAS | Minitab |