Question

*** Please solve in R ***

You now pull another sample of 20 policyholders. See “Prob 11-2 claims data.csv” for the data. For this data set, assume a negative binomial distribution is your first choice as a data generating process that could have produced the counts of claims. Perform a negative binomial regression to analyze the data; report your findings.

Claims	Years
1	1.042191
7	2.497906
2	3.676603
4	3.798047
1	4.870992
9	7.689958
1	8.02383
6	8.305029
2	9.052364
9	10.44021
5	11.44318
5	12.12458
2	13.32714
4	14.65696
11	14.78745
5	16.20412
0	16.27578
13	16.48458
21	16.94984
22	18.3575

Answer 1

Answer --> To Perform the negative binomial regression in R, Below is the stepwise process and also the finding

#### data import /Input data ######

> Claims <- c(1,7,2,4,1,9,1,6,2,9,5,5,2,4,11,5,0,13,21,22)

> Years <- c(1.042191,2.497906,3.676603,3.798047,4.870992,7.689958,8.02383,8.305029,9.052364,10.44021,11.44318,12.12458,13.32714,14.65696,14.78745,16.20412,16.27578,16.48458,16.94984,18.3575)

> Policy_Data <- data.frame(Claims,Years) # Make the data table

> dim(Policy_Data) # check dimention of data( 20 obs with 2 variables)

[1] 20 2

##### Import library ‘MASS’ required to Perform the negative binomial regression ########

> library (MASS)

##### Syntax of To Perform the negative binomial regression ############

> negBinomModel <- glm.nb(Claims ~ Years, data = Policy_Data) # negative Binomial model

> negBinomModel

Call: glm.nb(formula = Claims ~ Years, data = Policy_Data, init.theta = 2.359874145,

    link = log)

Coefficients:

(Intercept)       Years

    0.74543      0.09494

Degrees of Freedom: 19 Total (i.e. Null); 18 Residual

Null Deviance:     30.44

Residual Deviance: 21.81      AIC: 115.8

After performing the negative binomial regression below is the our finding / R output.

> summary (negBinomModel) # Model summary

Call:

glm.nb(formula = Claims ~ Years, data = Policy_Data, init.theta = 2.359874145,

    link = log)

Deviance Residuals:

    Min       1Q   Median       3Q      Max

-2.7874 -0.8940 -0.3172   0.4420   1.3660

Coefficients:

            Estimate Std. Error z value Pr(>|z|)  

(Intercept) 0.74543    0.42534   1.753 0.07968 .

Years        0.09494    0.03441   2.759 0.00579 **

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(2.3599) family taken to be 1)

    Null deviance: 30.443 on 19 degrees of freedom

Residual deviance: 21.806 on 18 degrees of freedom

AIC: 115.85

Number of Fisher Scoring iterations: 1

              Theta: 2.36

          Std. Err.: 1.10

2 x log-likelihood: -109.849