Logistic Regression


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 variable

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


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