In the logit regression model, the predicted values for the
dependent or response variable will never be less than (or equal to) 0, or greater than (or equal to) 1, regardless of the values of the independent variables;it is, therefore, commonly used to analyze binary dependent or response variables (see also the
binomial distribution ).This is accomplished by applying the following regression equation (the term logit was first used by Berkson, 1944):
y=exp(b
0 +b
1*x
1 + ... + b
n*x
n)/{1+exp(b
0 +b
1*x
1 + ... + b
n*x
n)}
One can easily recognize that,regardless of the regression coefficients or the magnitude of the x values,this model will always produce predicted values (predicted y's) in the range of 0 to 1.The name logit stems from the fact that one can easily linearize this model via the logit transformation. Suppose we think of the binary dependent variable y in terms of an underlying continuous probability p,ranging from 0 to 1.We can then transform that probability p as:
p' = log
e{p/(1-p)}
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