Linear logistic regression
Logistic regression is a form of regression for a
dichotomous prediction variable. Predictors can be numerical or categorical. Logistic regression
constructs a linear model of the following form:
Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk
where Y is the logit tranformation of the probability p. The
logit transformation of the probability of a value is defined as:
Y = log(p/(1-p))
where p is the probability of an outcome. The linear function
can also be written as a prediction of the probability of a value, e.g.
P(class = pos) = 1 / (1 + ea + b1*X1 + b2*X2
+ bk*Xk)
The constant a and the weights b1 .. bn are chosen by a regression
method so that the predictions for the class are optimal for the sample. A number of tools are
available for computing the weights.
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