# 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

- [math]\displaystyle{ E(Y) = exp( \sum_k c_k B_k ) }[/math]

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)

- Use
**File → Add Library...**to add this library

## History

In Analytica 4.5, the Poisson_Regression function has been superseded by the PoissonRegression function that does not require the Optimizer edition.

## See Also

- Poisson
- Binomial
- Regression: When «Y» is continuous with normally-distributed error
- RegressionDist: When «Y» is continuous with normally-distributed error
- Logistic_Regression: When «Y» is binomial (0, 1-valued)
- Probit_Regression: When «Y» is binomial (0, 1-valued)
- Generalized Regression
- Generalized Regression.ana

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