I came across it whiles reading a report from the Society of Actuaries, "Predictive Modeling Symposium October 8- 9, 2009" at the following link "www.soa.org/files/pd/2009-chicago-pred-mod-1a.pdf"
Insurance Company Expenses
1. This exercise considers insurance company data from the NAIC database and described in Frees Exercises 1.6 and 3.5. Our dependent variable is EXPENSES, the nonclaim expenses for a company. Nonclaim expenses are based on three components: unallocated loss adjustment, underwriting, and investment expenses. The unallocated loss adjustment expense is the expense not directly attributable to a claim but indirectly associated with settling claims; this includes items such as salaries of claims adjusters, legal fees, court costs, expert witnesses, and investigation costs. Underwriting expenses consist of policy acquistion costs, such as commissions, as well as the portion of administrative, general, and other expenses attributable to underwriting operations. Investment expense are those expenses related to investment activities of the insurer. Table 1. below includes the variables and the expenses.
We would like to develop a model for EXPENSES based on the other variables provided.
Begin by limiting ourselves to the 384 companies with some losses in the ﬁle ”NAICEx-
(a) Plot the non-binary variables in the data and note the skewness pattern.
1(b) Transform these skewed variables with the transformation ln(x−min(x)+.001). Use
LNEXPENSES = log(EXPENSES − min(x) + .001) as your response variable.
(c) Look at the VIF’s for the non-binary variables. Are any of them particularly high?
(d) Using a variable selection technique like regsubsets(), ﬁnd a best ﬁtting model or
small subset of good models.
(e) Explore interactions in the model. Do quadratic versions of the loss or gross premium variables add value? How about separate slopes by group?
(f) Check your best ﬁt model for constant variance, normality, inﬂuential points, and
structure using the usual functions.
(g) Interpret the eﬀect of GPWPersonal in your model. A $1M increase in GPWPersonal
has what eﬀect/relationship with expenses.
(h) Produce a 95% Prediction interval for a company with LOSSLONG = 0.025, LOSSSHORT =0.040, GPWPERSONAL = 0.50, GPWCOMM = 0.120, ASSETS = 0.400, CASH =0.350 and GROUP = 1.