# R Poisson Regression - r - learn r - r programming

• Poisson Regression involves regression models in which the response variable is in the form of counts and not fractional numbers.
• For example, the count of number of births or number of wins in a football match series. Also the values of the response variables follow a Poisson distribution.
• r programming poisson regression

• The general mathematical equation for Poisson regression is -
• 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.
• The function used to create the Poisson regression model is the glm()function.

## Syntax

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

• 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

• 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: 4
```
• In 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.