Logistic Regression

Logistic regression models the probability that a response variable belongs to a particular category.

To fit the model, we use a method called maximum likelihood. The method finds values for B(0) and B(1) that yields a number close to one (default status) and a number to zero (alternative status). The least squares approach is a special case of maximum likelihood.

P(X) = e ^B(o) + B(1)X / 1 + e^B(o) + B(1)X

P(X) / (1-P(X)) = e ^B(o) + B(1)X

Y = log ( P(X) / (1-P(X ) ) = B(o) + B(1)X

In linear regression, B(1) gives the average change in Y associated with a one-unit increase in X.

In a logistic regression model, increasing X by one unit changes the log odds by B(1), or equivalently it multiplies the odds by e^B(1).

The relationship between P(X) and X is not a straight line. The amount that P(X) changes due to a one-unit change in X will depend on the current value of X.