# Poisson Regression in R Programming

A Poisson Regression model is used to model count data and model response variables (Y-values) that are counts. It shows which X-values work on the Y-value and more categorically, it counts data: discrete data with non-negative integer values that count something.

In other words, it shows which explanatory variables have a notable effect on the response variable. Poisson Regression involves regression models in which the response variable is in the form of counts and not fractional numbers.

Mathematical Equation:log(y) = a + b1x1 + b2x2 + bnxn.....

Parameters:

y:This parameter sets as a response variable.aandb:The parameter a and b are the numeric coefficients.x:This parameter is the predictor variable.

#### Creating Poisson Regression Model

The function used to create the Poisson regression model is the ** glm()** function.

Syntax:glm(formula, data, family)

Parameters:

formula:This parameter is the symbol presenting the relationship between the variables.data:The parameter is the data set giving the values of these variables.family:This parameter R object to specify the details of the model. It’s value is ‘Poisson’ for Logistic Regression.

**Example:**

- We use the data set “warpbreaks”.
- Considering “breaks” as the response variable.
- The wool “type” and “tension” are taken as predictor variables.
- Take the parameters which are required to make model.
- let’s use summary() function to find the summary of the model for data analysis.
- With the help of this function, easy to make model.
- Now we draw a graph for the relation between “formula”, “data” and “family”.

**Approach:**To understand how we can create:

**Code:**

`input` `<` `-` `warpbreaks` `print` `(head(` `input` `))` |

**Output:**

#### Create Regression Model

**Approach:** Creating the poisson regression model:

**Example:**

`output <` `-` `glm(formula ` `=` `breaks ~ wool ` `+` `tension,` ` ` `data ` `=` `warpbreaks, family ` `=` `poisson)` `print` `(summary(output)) ` |

**Output:**

#### Creating Poisson Regression Model using `glm()`

function

`glm()`

**Approach:** Creating the regression model with the help of the **glm() **function as:

**Example:**

`output_result <` `-` `glm(formula ` `=` `breaks ~ wool ` `+` `tension,` ` ` `data ` `=` `warpbreaks, family ` `=` `poisson) ` `output_result ` |

**Output:**