Poisson regression includes regression models, where the response variable is in the form of counts rather than fractions.
For example, the number of births or wins in a football match series. Furthermore, the values of the response variables follow 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 is the response variable.
- aandb are numeric coefficients.
- x is a predictor.
The function used to create a Poisson regression model isglm()function.
grammar
On the return of Poissonglm()The basic syntax of a function is
glm(formula,data,family)
The following is a description of the parameters used in the above functions
- Formula is a symbol that represents the relationship between variables.
- data is the dataset that gives the values of these variables.
- family is an R language object to specify the details of the model. Its value is a logistic regression of "Poisson".
example
We have built-in datasets"warpbreaks”, which describes the type of wool (AorB) and tension (low, medium or high) effects on the number of warp yarn breaks in each loom. Let's consider "break" as the response variable, which is the count of the number of breaks. Wool “type” and “tension” are used as predictors.
Enter 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 a 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: 4
In the summary, we look for the in the last columnpValue less than0.05, to consider the effect of predictors on response variables. As shown in the figure, there is a tension typeMandHTypes of woolBIt has an effect on the fracture count.
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