R language Poisson returns

Poisson regression includes regression models, where the response variable is in the form of a count rather than a fraction.

For example, the number of births or victories in a football game series. In addition, the value of the response variable follows the Poisson distribution.

The general mathematical equation for Poisson's regression is -

log(y) = a + b1x1 + b2x2 + bnxn.....

The following is a description of the parameters used -

• y the response variable.

• a and b are numeric coefficients.

• x is a predictor.

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

Grammar

The basic syntax of glm() regression is -

glm(formula,data,family)

The following is a description of the parameters used in the above features -

• formula a symbol that represents the relationship between variables.

• data a dataset that gives the values of these variables.

• family an R language object that specifies the details of the model. I ts value is the logical regression of Poisson.

Cases

We have a built-in dataset called warpbreaks which describes the effect of wool type A or B and stress (low, medium or high) on the number of yarn breaks per loom. L et's consider Break as a response variable, which is a count of the number of fractures. W ool "type" and "stress" are predictors.

Enter the data

input <- warpbreaks
print(head(input))

When we execute the code above, it produces the following results -

      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 a regression model

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

When we execute the code above, it produces the following results -

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 p look for p-values less than 0.05 in the last column to consider the effect of predictors on response variables. A s shown in the figure, wool M stress types H and B have an effect on the break count.