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Poisson Regression in R Programming

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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:

    Last Updated : 10 May, 2020
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