### Introduction

The fundamental assumption of logistic regression is that probabilities under a continuous process of change are expected to follow a logistic or ‘S-curve’ pattern. This is a reasonable assumption in certain limited circumstances.

Regression is a set of computational methods that attempts to find the closest match between an observed set of data and a function, such as a straight line, a polynomial, a power curve or, in this case, an S-curve. We can say that the logistic curve is the underlying model we expect data to be matched against (regressed to).

In another post, I comment on the feasibility of employing Wilson score intervals in an efficient logistic regression algorithm. What are these ‘limited circumstances’?

- We assume probabilities are free to vary from 0 to 1.
- The envelope of variation must be constant, i.e. it must always be possible for an observed probability to reach 1.

Taken together this also means that probabilities are Binomial, not multinomial. Continue reading