Automobile Injury Insurance Claims. Refer to the description in Exercise 1.5 .We consider \(n=1,340\) bodily injury liability claims from a single state using a 2002 survey conducted by the Insurance Research Council (IRC). The IRC is a division of the American Institute for Chartered Property Casualty Underwriters and the Insurance Institute of America. The survey asked participating companies to report claims closed with payment during a designated two-week period. In this exercise, we are interested in understanding the characteristics of the claimants who choose to be presented by an attorney when settling their claim. Variable descriptions are given Table 11.11.

a. Summary Statistics.
i. Calculate histograms and summary statistics of continuous explanatory variables CLMAGE and LOSS. On the basis of these results, create a logarithm version of LOSS, say, lnLOSS.
ii. Examine the means of CLMAGE, LOSS and lnLOSS by level of ATTORNEY. Do these statistics suggest that the continuous variables differ by ATTORNEY?
iii. Create tables of counts (or percentages) of ATTORNEY by level of CLMSEX, MARITAL, SEATBELT, and CLMINSUR. Do these statistics suggest that the categorial variables differ by ATTORNEY?

iv. Identify the number of missing values for each explanatory variable.
b. Logistic Regression Models.
i. Run a logistic regression model using only the explanatory variable CLMSEX. Is it an important factor in determining the use of an attorney? Provide an interpretation in terms of the odds of using an attorney.
ii. Run a logistic regression model using the explanatory variables CLMAGE, CLMSEX, MARITAL, SEATBELT, and CLMINSUR. Which variables appear to be statistically significant?
iii. For the model in part (ii), who uses attorneys more, men or women? Provide an interpretation in terms of the odds of using an attorney for the variable CLMSEX.
iv. Run a logistic regression model using the explanatory variables CLMAGE, CLMSEX, MARITAL, SEATBELT, CLMINSUR, LOSS, and lnLOSS. Decide which of the two loss measures is more important and rerun the model using only one of the variables. In this model, is the measure of losses a statistically significant variable?
v. Run your model from part (iv) but omit the variable CLMAGE. Describe differences between this model fit and that in part (iv), focusing on statistically significant variables and number of observations used in the model fit.
vi. Consider a single male claimant who is age 32. Assume that the claimant was wearing a seat belt, that the driver was insured and the total economic loss is \(\$ 5,000\). For the model in part (iv), what is the estimate of the probability of using an attorney?

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Variable ATTORNEY CLMAGE CLMSEX MARITAL Description Whether the claimant is represented by an attorney (=1 if yes and =2 if no) Claimant's age Claimant's sex (=1 if male and -2 if female) Claimant's marital status (=1 if married, =2 if single, -3 if widowed, and -4 if divorced/separated) SEATBELT Whether the claimant was wearing a seatbelt/child restraint (=1 if yes, -2 if no, and -3 if not applicable) CLMINSUR Whether the driver of the claimant's vehicle was uninsured (=1 if yes, =2 if no, and -3 if not applicable) The claimant's total economic loss (in thousands) LOSS