# Poisson Regression

Requires Analytica Optimizer

## Poisson_regression(Y, B, I, K)

A Poisson regression model is used to predict the number of events that occur, «Y», from a vector independent data, «B», indexed by «K». The Poisson_Regression function computes the coefficients, c, from a set of data points, («B», «Y»), both indexed by «I», such that the expected number of events is predicted by

$\displaystyle{ E(Y) = exp( \sum_k c_k B_k ) }$

The random component in the prediction is assumed to be Poisson-distributed, so that given a new data point «B», the distribution for that point is

Poisson(sum(c*B, K)

If your dependent variable is continuous, with normally-distributed error, use Regression or RegressionDist. If your dependent variable is binomially distributed (i.e., 0,1-valued), use Logistic_Regression or Probit_Regression. If your dependent variable models a count, such as the number of events that occur, use Poisson_Regression.

Note: The distribution here accounts for data variation only, and does not include error in the coefficients c, as the RegressionDist function does, for example. See the description on Secondary Statistics at Regression for additional information on estimation of error in the coefficients.

## Library

Generalized Regression (Generalized Regression.ana)