Numbers of Car Insurance claims

The data given in data frame Insurance consist of the numbers of policyholders of an insurance company who were exposed to risk, and the numbers of car insurance claims made by those policyholders in the third quarter of 1973.

Insurance

Format

This data frame contains the following columns:

District

factor: district of residence of policyholder (1 to 4): 4 is major cities.

Group

an ordered factor: group of car with levels <1 litre, 1--1.5 litre, 1.5--2 litre, >2 litre.

Age

an ordered factor: the age of the insured in 4 groups labelled <25, 25--29, 30--35, >35.

Holders

numbers of policyholders.

Claims

numbers of claims

Source

L. A. Baxter, S. M. Coutts and G. A. F. Ross (1980) Applications of linear models in motor insurance. Proceedings of the 21st International Congress of Actuaries, Zurich pp. 11--29.

M. Aitkin, D. Anderson, B. Francis and J. Hinde (1989) Statistical Modelling in GLIM. Oxford University Press.

References

Venables, W. N. and Ripley, B. D. (1999) Modern Applied Statistics with S-PLUS. Third Edition. Springer.

Examples

## main-effects fit as Poisson GLM with offset
glm(Claims ~ District + Group + Age + offset(log(Holders)),
    data = Insurance, family = poisson)
#> 
#> Call:  glm(formula = Claims ~ District + Group + Age + offset(log(Holders)), 
#>     family = poisson, data = Insurance)
#> 
#> Coefficients:
#> (Intercept)    District2    District3    District4      Group.L      Group.Q  
#>   -1.810508     0.025868     0.038524     0.234205     0.429708     0.004632  
#>     Group.C        Age.L        Age.Q        Age.C  
#>   -0.029294    -0.394432    -0.000355    -0.016737  
#> 
#> Degrees of Freedom: 63 Total (i.e. Null);  54 Residual
#> Null Deviance:	    236.3 
#> Residual Deviance: 51.42 	AIC: 388.7

# same via loglm
loglm(Claims ~ District + Group + Age + offset(log(Holders)),
      data = Insurance)
#> Call:
#> loglm(formula = Claims ~ District + Group + Age + offset(log(Holders)), 
#>     data = Insurance)
#> 
#> Statistics:
#>                       X^2 df  P(> X^2)
#> Likelihood Ratio 51.42003 54 0.5745071
#> Pearson          48.62933 54 0.6809086