# R - Poisson Regression

The general mathematical equation for Poisson regression is −

log(y) = a + b1x1 + b2x2 + bnxn.....Following is the description of the parameters used −

**y**is the response variable.**a**and**b**are the numeric coefficients.**x**is the predictor variable.

**glm()**function.

## Syntax

The basic syntax for**glm()**function in Poisson regression is −

glm(formula,data,family)Following is the description of the parameters used in above functions −

**formula**is the symbol presenting the relationship between the variables.**data**is the data set giving the values of these variables.**family**is R object to specify the details of the model. It's value is 'Poisson' for Logistic Regression.

## Example

We have the in-built data set "warpbreaks" which describes the effect of wool type (A or B) and tension (low, medium or high) on the number of warp breaks per loom. Let's consider "breaks" as the response variable which is a count of number of breaks. The wool "type" and "tension" are taken as predictor variables.### Input Data

input <- warpbreaks print(head(input))When we execute the above code, it produces the following result −

breaks wool tension 1 26 A L 2 30 A L 3 54 A L 4 25 A L 5 70 A L 6 52 A L

## Create Regression Model

output <-glm(formula = breaks ~ wool+tension, data = warpbreaks, family = poisson) print(summary(output))When we execute the above code, it produces the following result −

Call: glm(formula = breaks ~ wool + tension, family = poisson, data = warpbreaks) Deviance Residuals: Min 1Q Median 3Q Max -3.6871 -1.6503 -0.4269 1.1902 4.2616 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 3.69196 0.04541 81.302 < 2e-16 *** woolB -0.20599 0.05157 -3.994 6.49e-05 *** tensionM -0.32132 0.06027 -5.332 9.73e-08 *** tensionH -0.51849 0.06396 -8.107 5.21e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for poisson family taken to be 1) Null deviance: 297.37 on 53 degrees of freedom Residual deviance: 210.39 on 50 degrees of freedom AIC: 493.06 Number of Fisher Scoring iterations: 4In the summary we look for the p-value in the last column to be less than 0.05 to consider an impact of the predictor variable on the response variable. As seen the wooltype B having tension type M and H have impact on the count of breaks.

*Table of contents:*1. R - Overview

2. R - Environment Setup

3. R - Basic Syntax

4. R - Data Types

5. R - Variables

6. R - Operators

7. R - Decision Making

8. R - Loops

9. R - Functions

10. R - Strings

11. R - Vectors

12. R - Matrices

13. R - Arrays

14. R - Factors

15. R - Data Frames

16. R - Packages

17. R - Data Reshaping

18. R - CSV Files

19. R - Excel Files

20. R - Binary Files

21. R - XML Files

22. R - JSON Files

23. R - Web Data

24. R - Database

25. R - Pie Charts

26. R - Bar Charts

27. R - Boxplots

28. R - Histograms

29. R - Line Graphs

30. R - Scatterplots

31. R - Mean, Median and Mode

32. R - Linear Regression

33. R - Multiple Regression

34. R - Logistic Regression

35. R - Normal Distribution

36. R - Binomial Distribution

37. R - Poisson Regression

38. R - Analysis of Covariance

39. R - Time Series Analysis

40. R - Nonlinear Least Square

41. R - Decision Tree

42. R - Random Forest

43. R - Survival Analysis

44. R - Chi Square Tests

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