# 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.
• a and b: 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:
Approach: To understand how we can create:
• We use the data set “warpbreaks”.
• Considering “breaks” as the response variable.
• The wool “type” and “tension” are taken as predictor variables.
Code:
 `input` `<``-` `warpbreaks ``print``(head(``input``)) `

Output:

#### Create Regression Model

Approach: Creating the poisson regression model:
• Take the parameters which are required to make model.
• let’s use summary() function to find the summary of the model for data analysis.
Example:
 `output <``-``glm(formula ``=` `breaks ~ wool ``+` `tension, ``             ``data ``=` `warpbreaks, family ``=` `poisson) ``print``(summary(output))      `

Output:

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

Approach: Creating the regression model with the help of the glm() function as:
• With the help of this function, easy to make model.
• Now we draw a graph for the relation between “formula”, “data” and “family”.
Example:
 `output_result <``-``glm(formula ``=` `breaks ~ wool ``+` `tension, ``                    ``data ``=` `warpbreaks, family ``=` `poisson)   ``output_result  `

Output:

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